Segmentation et Détection du Cancer de la Peau en Utilisant la Variation Totale et l'Analyse Multi-résolution

Keywords: Segmentation, Détection, Variation Totale, Analyse Multi-résolution, Imagerie médicale Skin Cancer Segmentation and Detection Using Total Variation and Mutiresolution Analysis Segmentation, Detection, Total Variation, Multiresolutional Analysis, medical imaging

Les décès du cancer de la peau sont majoritairement des mélanomes malins. Il est considéré comme l'un des plus dangereux cancer. A ses débuts, les mélanomes malins sont traités avec des simples biopsies et sont complètement curable. Pour cela, une détection précoce est la meilleure solution pour réduire ses conséquences désastreuses. Imagerie médicale telle que la dermoscopie et les caméras à images standard sont les outils disponibles les plus adaptées pour diagnostiquer précocement les mélanomes. Le diagnostic assisté par ordinateur (CAD) est développé dans le but d'accompagner les radiologistes dans la détection et le diagnostic. Cependant, il y a un besoin d'améliorer la précision de la segmentation et de détection des lésions. Dans ce travail, le modèle de Chan et Vese a été adapté pour segmenter davantage les variations à l'intérieur des lésions avec un résultat très encouragent. La deuxième tâche consiste à extraire des caractéristiques afin de discriminer les mélanomes. Deux méthodes ont été développée, une se basant sur l'irrégularité des bords des lésions et l'autre par la fusion des caractéristiques texturales et structurelles. Les résultats ont montrés de bonnes performances avec une précision de 86.54% et de 86.07%, respectivement.

with 97.62% of true detection rate. In the second main task, two feature extraction methods were developed for the analysis of standard camera and dermoscopy images. The method developed for the standard camera skin cancer images is based on border irregularities, introducing two new concepts, which are valleys and crevasses as first and second level of the border irregularity. The method has been implemented on DermIs and DermQues, two databases of standard camera images, and achieved an accuracy of 86.54% with a sensitivity of 80% and a specificity of 95.45%. The second method consisted of a fusion of structural and textural features. The structural features were extracted from wavelet and curvelet coefficients, while the textural features were obtained from the local binary pattern operator. The method has been implemented on the PH2 database for dermoscopy images with 1000-random sampling cross validation. The obtained results achieved an accuracy, a sensitivity and a specificity of 86:07%, 78.93% and 93.25%. Compared to the existing methods, the proposed methods in this work show very good performances.

DEDICATION

To my beloved Dad and Mum. III I would like to express my sincere gratitude to my supervisors, Associate Professor Ibrahima FAYE and Professor Fakhreddine ABABSA for their continuous support, their patience and constant motivation, but also for the hard questions which encouraged and guided me to widen my research from various perspectives. Without their high quality supervision this work would not have been accomplished. I would like to thank also my co-supervisor in UTP, Associate Professor Sarat CHANDRA DASS.

Besides my supervisors, I would like to give my high, respectful gratitude to Professor Rachid JENANE, Professor Nur Ashidi BIN MAT ISA, Doctor Vincent VI-GNERON and Doctor Mohamed BIN OTHMAN for accepting to be part of the committee members, and for their brilliant comments and suggestions. I especially thank Virginie BRIANTAIS, medical expert, and Dalil ICHALAL, image processing expert, for evaluating my recent work, and providing good advice and perspectives.

A special gratitude to CISIR and IBISC Laboratory for their hospitality, a wonderful workspaces and facilities provided. My special gratitude to Sabine Segala, Marité QUINTIN, Professor Gilles DUC and Bahrul Ilmi. I am also grateful to all my collegues at the CISIR Laboratory, for their wonderful company and support, especially IV to Dr. Munsif, Dr. Jamal, Dr. Abu Elhassan, Amjad, Altahir, Nirbhay and Dr. Vedpal for their support during this work. I also would like to thanks IBISC collegues for their wonderful company and support, especially to Aylen, Dr. Alia, Dr. Abdelkader, Mahmoud, Dr. Junior and Ludovic.

I would like to thank my friend Peter and his wife Keri for their help and support, my friends Emefa, Sheela, Djoudi, Mounir, Krimo and all my friends of ACKB association for their support and encouragement.

I would like to express my eternal appreciation towards my brother Hassan and my sister-in-law Nadège, my nieces Pauline and Lisa, my nephew Akli and his wife for their support and continuous help during this three years of instability between two countries.

I would like to thank all my brothers and sisters living in Kabylia (Algeria), Slimane, Hayet, Zahir, Ferdjallah, Nabil, Toufik, Karima and all my nephews and nieces.

Finally, and most important, I want to thank my parents, Hadi and Nouara, who have been there unconditionally and urged me to be better. This accomplishment would not have been possible without them.

V Table 1.1: ABCD rule with the interval values of p i and the weight factor w i of each component [1]. . . . . . . . . . . . . . . . . . . . . Table 1.2: The major and minor criteria of 7-point checklist and the different weights for each criterion [1]. . . . . . . . . . . . . . . . . . 5.10: Comparison of the results of proposed approach with the results of recent methods in the literature using the same database . . . Table 5.11: Comparison of the results of proposed approach with the results of recent methods in the literature using the same database . . . Melanoma is the most dangerous abnormal skin tissue. Its treatment requires chemotherapy and radiotherapy and it becomes more difficult to treat when it is in advanced stages such as metastasis step [START_REF] World | How common is skin cancer?[END_REF], where one person die each 54 minutes [2]. The statistics show that approximately 132, 000 melanoma cases and 2 to 3 millions of non-melanoma cases [START_REF] World | How common is skin cancer?[END_REF][START_REF]Collection état des lieux et des connaissances, ouvrage collectif édité par l'inca[END_REF] are reported annually in the world. In total, it accumulates to 1.6% of cancer cases worldwide [START_REF] Luis | Detection of pigment network in dermoscopy images using supervised machine learning and structural analysis[END_REF]. Despite the rarity of this diseases, the vast majority of persons affected by malignant skin cancer deaths within two years [2]. As ozone levels are depleted, the World Health Organization (WHO) [START_REF] World | How common is skin cancer?[END_REF] estimates that 10% of decrease in ozone level will result in an additional of 300, 000 non melanoma and 4500 melanoma cases. According to WHO and Lee et al. [START_REF] Haur | Melanoma: differences between asian and caucasian patients[END_REF], Caucasian populations generally have a much higher risk of getting skin cancer disease than dark-skinned populations. Naturally, brown and black people can usually safely tolerate relatively high levels of sun exposure without getting sunburns or greatly increasing their skin cancer risk. In contrast, people with pale or freckled skin, fair or red hair and blue eyes belong to the highest risk group. Followed by people with dark hair and eyes who do not normally get sunburns are at medium risk of skin cancer developing [START_REF] World | How common is skin cancer?[END_REF]. According to the World Health Organization, the following items present a set of risk factors of skin cancer: fair skin; blue, green or hazel eyes; light-coloured hair; tendency to burn rather than suntan; history of severe sunburns; many moles and/or freckles; a family history of skin cancer.

In the United States and worldwide, skin cancer incidence is reported as one of the most 1 increasing tumor. The risk of developing invasive melanoma was estimated to 1 in 39 of Caucasian men and 1 in 58 for Caucasian women in American society in 2010 [START_REF] Rigel | The evolution of melanoma diagnosis: 25 years beyond the abcds[END_REF].

Causes of Skin Cancer

Cancer starts when cells in the body begin to grow out of control. Cells in nearly any part of the body can become cancer, and can then spread to other areas of the body [START_REF]American cancer society available online[END_REF].

Similarly, skin cancer is the uncontrolled growth of abnormal skin cells. It occurs when unrepaired DNA damage to skin cells, most often caused by ultraviolet radiation from sunshine or tanning beds, triggers mutations, or genetic defects, that lead the skin cells to multiply rapidly and form malignant tumors [2].

Types of Skin Cancer

The multitude of benign and malignant melanoma complicates the recognition of skin lesion cases. In the clinical practice, three main types of abnormal skin cells are noticed i.e. Basic cell carcinoma, Squamous cell carcinoma and Melanoma [START_REF]American cancer society available online[END_REF][START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF]. The Skin Cancer Foundation (SCF) [2], further into these, characterizes three more kinds of abnormal cells, i.e., Actinic keratosis, Merkel cell carcinoma and Atypical moles, which are less common. Figure 1.1 illustrates the six types of skin lesions. It notices also that the atypical moles are the second most dangerous cells after melanoma cases. According to Skin Cancer Foundation [2], the difference between these abnormality tissues are:

• Actinic Keratosis, also known as a solar keratosis, is a crusty and scaly growth.

It is considered as pre-cancer because if left alone, it could develop into a skin cancer.

• Merkel cell carcinoma is a rare and aggressive skin cancer that is at high risk of recurring and spreading (metastasizing) throughout the body. But, it is 40 times rarer than melanoma.

• Basic cell carcinoma is the most occurring form of skin cancer. It often looks like open sores, red patches, pink growths, shiny bumps or scares. This skin cancer very rarely spreads.

• Squamous cell carcinoma is the second most common form of skin cancer. It often looks like scaly red patches, open sores, elevated growths with a central depression, or warts.

• Atypical moles are unusual-looking benign moles, also known as dysplastic nevi.

They may resemble melanoma, and people who have them are at increased risk of developing melanoma in a mole or elsewhere on the body. They have 10 times or more the risk of developing melanoma.

• Melanoma is the most dangerous form of skin cancer, these cancerous growths develop when unrepaired DNA damage to skin cells, mostly caused by ultraviolet radiation from sunshine or tanning beds, triggers mutations (genetic defects) that lead the skin cells to multiply rapidly and form malignant tumors. The majority of melanomas are black or brown, but they can also be skin-colored, pink, red, purple, blue or white. If melanoma is recognized and treated early, it is almost always curable, but if it is not, the cancer can advance and spread to other parts of the body, where it becomes hard to treat and can be fatal.

It is noticed that the first cause of these skin cancer types are the damage of skin tissue from exposure to ultraviolet radiations [2,[START_REF] World | How common is skin cancer?[END_REF][START_REF]Collection état des lieux et des connaissances, ouvrage collectif édité par l'inca[END_REF][START_REF]American cancer society available online[END_REF].

Medical Diagnosis

To recognize melanoma cases, dermatologists compare and analyze a multiple signs of each tumor. Mostly, they use two scoring systems based on visual characteristics to recognize the melanoma tissue, which are ABCDE rule [2,[START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF][START_REF] Robert J Friedman | Early detection of malignant melanoma: The role of physician examination and self-examination of the skin[END_REF][START_REF] Stolz | Abcd rule of dermatoscopy-a new practical method for early recognition of malignant-melanoma[END_REF][START_REF] Gadeliya | Strategies for early melanoma detection: Approaches to the patient with nevi[END_REF] and Glascow 7-point checklist / 7-point checklist [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF][START_REF] Maglogiannis | Overview of advanced computer vision systems for skin lesions characterization[END_REF][START_REF] Argenziano | Epiluminescence microscopy for the diagnosis of doubtful melanocytic skin lesions: comparison of the abcd rule of dermatoscopy and a new 7-point checklist based on pattern analysis[END_REF][START_REF] Mackie | Seven-point checklist for melanoma[END_REF].

These two scoring systems are well known by medical experts and they constitute the basic methods of comparison for image processing experts. Most of the developed and explored methods are based on these systems, such as Bareiro et al. [START_REF] Raquel | Computerized medical diagnosis of melanocytic lesions based on the abcd approach[END_REF] and She et al. [START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF] for ABCD rule, and Argenziano et al. [START_REF] Argenziano | Seven-point checklist of dermoscopy revisited[END_REF] for 7-point checklist. The features used in these systems are also explored separately in the goal of melanoma recognition, for example, pigment network [START_REF] Luis | Detection of pigment network in dermoscopy images using supervised machine learning and structural analysis[END_REF][START_REF] Luis | Recognition of pigment network pattern in dermoscopy images based on fuzzy classification of pixels[END_REF] and vascular structure [START_REF] Argenziano | Vascular structures in skin tumors: a dermoscopy study[END_REF]. These systems are summarized in the current chapter and detailed in the literature review chapter.

ABCD Rule

The skin cancer foundation explained the ABCD rule, called also ABCDE rule when the evolving feature is available. The meaning used for each case is explained and illustrated below:

• Asymmetry (A): The pigment is considered asymmetric if by drawing one vertical or horizontal line, the two parts of the mole will not be similar.

Figure 1.2: Asymmetry of melanoma compared with benign lesion [2].

• Border (B): More the pigment border is not smooth, more it can be considered as malignant case.

Figure 1.3: Border irregularity between malignant and benign lesions [2].

• Color (C): Most benign pigments have one color (often brown color). Melanoma has a variety of colors (black, red, blue and/or wight).

Figure 1.4: Color variation between melanoma and benign lesion [2].

• Diameter (D): Benign pigments have usually smaller diameter than malignant ones. Melanoma is often greater than 6 mm, but it can be smaller. • Evolving (E): Over time, benign pigment looks the same. However, malignant melanoma evolves or changes in size, shape, color and/or elevation.

Figure 1.6: Evolving of melanoma over time [2]. 1 -6 0.5 0.5 -3

Dermoscopic structures

One value for each structure: pigment network, structureless area, dots, globules, branched streaks.

1 -5 0.5 0.5 -2.5

Figures from 1. the difference between malignant and benign lesion. The real computation of ABCD system is done only for the first four components using the following formula:

S abcd = 4 i=1 w i p i (1.1)
where w i and p i are the weight and the value attributed to each point. They are summarized in table 1.1 as explained by Capdehourat et al. [1], according to Stolz et al. [START_REF] Stolz | Abcd rule of dermatoscopy-a new practical method for early recognition of malignant-melanoma[END_REF].

Knowing that the evolution of the lesion over time is the most missed data, then the feature given by the item E is used only for visual comparison by dermatologists when it is available.

The evaluation of ABCD rule is performed following equation (1.1) using the scores given in the table 1.1 to classify the pigment into three cases, benign, clinically doubtful and malignant [1]:

             S abcd < 4.

7-point Checklist

The 7-point checklist [START_REF] Argenziano | Epiluminescence microscopy for the diagnosis of doubtful melanocytic skin lesions: comparison of the abcd rule of dermatoscopy and a new 7-point checklist based on pattern analysis[END_REF] and Glascow 7-point checklist system [START_REF] Mackie | Seven-point checklist for melanoma[END_REF], summarized by Capdehourat et al. [1] (see Figure 1.7) and Korotkov et al. [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF], is another scoring system based on seven criteria divided into two sets. For Glascow 7-point checklist, the major criteria are changes in shape, size and color, and the minor criteria are diameter, inflammation, crusting and sensory changes. The 7-point checklist criteria works in the same way, with some differences and more details, as presented below:

• Atypical pigment network: Black, brown, or gray thickened and irregular lines segments in the lesion.

• Blue-whitish veil: Irregular, confluent, gray-blue to whitish-blue diffuse pigmentation that can be associated with pigment network alteration, dots/globules, or streaks.

• Atypical vascular pattern: Linear-irregular and/or dotted red vessels not seen in regression area.

• Irregular streaks: Pseudo pods or radial streaming irregularities arranged at the periphery of lesion.

• Irregular pigmentation: Black, brown or gray featureless areas with irregular shape and/or distribution.

• Irregular dots/Globules: Black brown, or gray rounded to oval, and variously sized irregularity structures distributed in the lesion.

• Regression structures: White scar-like areas and/or blue pepper-like areas (grayblue areas and/or multiple blue-gray dots). For 7-point checklist, the scores given to each point, the same for Glascow 7-point checklist, are 2 for major criteria and 1 for minor ones as summarized in table 1.2. The evaluation of the score follows the following formula:

s 7pc = 3 i=1 M i + 4 j=1 m j (1.2)
where M i and m j define the i th major and j th minor criteria respectively.

The classification following this system is also based on thresholding functions into two different classes [1]:

     S 7pc < 3 the pigment is benign S 7pc ≥ 3 the pigment is malignant Table 1.
2 details the major and minor criteria of 7-point checklist system.

Computer Aided Diagnosis Systems

Computer Aided Diagnosis (CAD) systems have been developed in several contributions of medical imaging [START_REF] Doi | Computer-aided diagnosis in medical imaging: historical review, current status and future potential[END_REF][START_REF] Leila H Eadie | A systematic review of computer-assisted diagnosis in diagnostic cancer imaging[END_REF][START_REF] Hayit Greenspan | Medical content-based retrieval for clinical decision support[END_REF]. The objective of CAD systems is to provide a computer output as a second opinion in order to assist radiologists on interpretation to improve the accuracy of diagnosis and reduce the image reading time [START_REF] Doi | Current status and future potential of computer-aided diagnosis in medical imaging[END_REF]. A CAD system is generally identifying two types of systems depending upon its main function i.e. Computer Aided Detection (CADe) system and Computer Aided Diagnosis (CADx) system. It is also explored for the early both detection and diagnosis [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF].

A
CAD system is applied on different tumor images such as mammograms, dermoscopy, MRI, radiography, etc. A CAD system was already known in the 1960s and became more interesting topic in the 1980s, where many investigations and researches were explored in some laboratories and hospitals [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF]. Since 2000s, the number of papers in CAD system are mostly increased in the achievement of the detection and the diagnosis of melanoma [START_REF] Doi | Computer-aided diagnosis in medical imaging: historical review, current status and future potential[END_REF][START_REF] Doi | Current status and future potential of computer-aided diagnosis in medical imaging[END_REF].

The CAD system applied in medical imaging contains five main steps from the image acquisition to the classification and diagnosis:

1. Image acquisition: In image processing, this step is considered as source or data for the next steps. In addition to that, there are many important and consistent informations from the acquisition to help the image processing experts to have a baseline and an intuitive work direction to explore.

Image enhancement:

The objective of this step is to reduce noises and all artifacts in the images. These artifacts in most cases depend on the kind of image acquisition technique employed, and represent, for example, numbering in mammogram images, hair and blood vessels in dermocopic images.

Segmentation:

The segmentation of the Region Of Interest (ROI) is an important step in CAD system. The multitude of skin cancer images makes the segmentation task more difficult. It becomes one of the hardest and most challenging task in CAD system.

4. Feature extraction: Once the ROI is isolated, the objective of this step is to provide the best descriptor to extract features which discriminate the database into two or more classes.

Classification and detection:

The final step is classification and diagnosis where the proposed system is observed and analyzed. Depending on the feature extracted and the number of classes desired, the choice of the classifier is primordial to get better results on the detection. According to the classifier used, the classification rate is evaluated following some performance metrics, such as accuracy, sensitivity, specificity and receiver operating characteristic (ROC).

CAD system is developed in melanoma recognition as well. Following the five steps of the system, there are many methods adopted or developed specifically for melanoma detection. The next chapter summarizes the literature review on skin cancer detection according to these steps, it makes also in evidence the logic of these steps on CAD system and the different contributions in each step.

Problem Statement

Melanoma treatment needs chemotherapy and radiotherapy, as breast cancer, blood cancer, brain tumor, lung cancer, and other cancer types when they reach metastasis state [2,[START_REF]Treating skin cancer[END_REF]. To avoid these painful procedures and receive successful treatment, early detection is one of the most reliable solutions.

The CAD systems explored for improving the accurate decision is still in development. Nowadays, as reported by Korotkov et al. [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF], many CAD systems are available for pigment skin lesions detection such as Dell'Eva-Burroni Melanoma Image processing Software which is the most cited in the literature and gives lower performances in real applications. However, it is difficult to draw overall conclusions regarding the performance of these systems. The different image acquisition (dermoscopic, clinical and standard camera images) in structured studies complicates furthermore the classification task in one global methodology. Thus, the current CAD systems are still far from perfection and need more developments to improve the detection and the diagnosis of melanoma. Despite, the improvements of CAD systems over years, there are still some challenges involved, such as accurate and adaptive segmentation. Moreover, to classify the skin pigment lesions into malignant and benign cancer, two major problems are evoked.

• Firstly, the accurate segmentation is the first challenging task to improve in the first plan the detection of suspicious lesions, and in the second plan the classification of these lesions into malignant and benign.

• Secondly, the extraction of the most discriminative set of features describing the relevant characteristics separating the pigment lesions into benign and malignant skin cancer.

In addition to that, the key to improve the real output quality of CAD systems is to apply the proposed methods on free public datasets for the comparison of all developed algorithms. To reduce also the human error of diagnosis, each pigment skin lesion should be accompanied by the ground truth and diagnosis reported from several dermatologists [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF].

Research Objectives

The main objective of this thesis is to improve melanoma detection and recognition.

To accomplish this objective, the PhD work was oriented into the following specific directions:

• To investigate a method of segmentation adapted for skin lesions characteristics, that could segment even the small regions inside the skin pigment lesion.

• To develop a method of features extraction based on fusion of structural and textural features.

• To develop a method based on border irregularities of pigment lesions.

Research Hypothesis

To achieve our research objectives, the following research hypothesis are made:

• A total variation method exploring an extension of Chan and Vese model would be efficient for segmentation of regions of interest in skin lesion images.

• A fusion of structural and textural features exploring the Local Binary Pattern operator and multiresolution analysis methods (curvelet and wavelet transform) on dermoscopic image database would be efficient to discriminate further between malignant and benign lesion.

• An investigation of geometrical characteristics based on the border irregularities may provide a description of pigment skin lesions.

Scope of Research Work

The

Overview

Skin cancer recognition on CAD systems has been an active research area for more than 30 years back [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF]. For instance, many methods have been developed and explored for melanoma detection [START_REF] Nabin | An overview of melanoma detection in dermoscopy images using image processing and machine learning[END_REF]. Korotkov and Garcia [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF] presented an interesting overview of used and explored methods on clinical and dermoscopic images from 1984 to 2012.

Their review is organized following ABCDE [START_REF] Naheed R Abbasi | Early diagnosis of cutaneous melanoma: revisiting the abcd criteria[END_REF] Friedman [START_REF] Robert J Friedman | Early detection of malignant melanoma: The role of physician examination and self-examination of the skin[END_REF] in 1985 and developed by Stolz et al. [START_REF] Stolz | Abcd rule of dermatoscopy-a new practical method for early recognition of malignant-melanoma[END_REF] in 1994. This system is widely used in clinical practice [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF]. Following each feature, the system is divided into points values and weight factors as detailed in Table 1 comparing to other features with variation from 0 to more than 2.5.

The 7-point checklist was proposed by Argenziano et al. [START_REF] Argenziano | Epiluminescence microscopy for the diagnosis of doubtful melanocytic skin lesions: comparison of the abcd rule of dermatoscopy and a new 7-point checklist based on pattern analysis[END_REF], which is another variation of pattern analysis with fewer criteria for identification and analysis [1]. The idea of 7-point checklist system is to attribute the score of 2 for major and 1 for minor criteria as summarized in the table 1.2.

The classification is performed following a fixed threshold equal to 3 separating the pigment lesions on two classes. Thus, the pigment is classified as benign if the total value is lower than 3 (Total ≤ 3), on the other side it is classified as malignant if the total is greater than 3 (Total > 3) as explained in the previous chapter.

Preprocessing: Image Enhancement

The main objective of image enhancement is to improve the quality and readability of the images. In the literature, it is also known as the preprocessing image step. In skin cancer images, the goal of this step is specially to remove the artifacts, such as hair and human made artifacts. Image enhancement is also used to improve the contrast quality for the exploration and visibility of details. Therefore, to compensate the imperfection of image acquisition and eliminate different artifacts, many methods and algorithms are developed and explored on various skin lesion databases. The dermoscopic images artifacts can be obtained and observed as uneven illumination, dermoscopic gel, black frames, ink markings, rulers and air bubbles. In fact, the border detection can also be affected by intrinsic cutaneous features such as blood vessels, hairs, and skin lines [START_REF] Maglogiannis | Overview of advanced computer vision systems for skin lesions characterization[END_REF].

In the literature, according to Koroktov [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF], artifacts are divided into two sets, artifacts rejection and image enhancement. Artifacts rejection contains hair, air bubbles, specular reflections and ink marking. In the other part, image enhancement contains color correction and calibration, illumination correction, contrast enhancement and edge enhancement. In 2009, Celebi et al. [START_REF] Emre Celebi | Lesion border detection in dermoscopy images[END_REF] focused on the importance of the current step in border detection, mentioning the most important used methods such as Gaussian and Median filters.

In dermoscopic images, the most common artifact, and necessary to remove, is the hair. Many methods and algorithms are presented in the literature to remove the hair when it is not shaved before the acquisition step. Therefore, the typical algorithm of hair removal methods is based on two main steps:

1. The hair detection: it consists on detecting and removing the different hairs in the image using algorithms of detection. Most developed methods in this step use segmentation because the hair is an integral component compared to other noise types.

2. The image restoration: the restoration or inpainting step consists on filling the space occupied by the removed hair with proper intensity and color values. The image quality can be affected when the density of hair is big in the lesion border. Also, the texture of the pigment can be affected in some cases. Therefore, the shaving of the concerned area, when it is possible, is a good solution and compromise to reduce diagnosis errors.

Many methods are explored in the hair removal task. In the literature, DullRazor software [START_REF] Lee | Dullrazor R : A software approach to hair removal from images[END_REF], proposed in 1997, is the first widely adopted method for removal-of hair [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF]. DullRazor performs the identification of the dark hair location using morphological closing operation, the verification of hair pixel shape and the replacement using bilinear interpolation, and the smoothness of replaced pixels with median filter.

In 2008, Wighton et al. [START_REF] Wighton | Dermascopic hair disocclusion using inpainting[END_REF] proposed an alternative method for the inpainting step of DullRazor software. In addition to the interpolation used in DullRazor software, the authors explored other information, like the direction of the border using Laplacian to regulate and measure the smoothness.

In 2011, Kiani et al. [START_REF] Kiani | E-shaver: An improved dullrazor R for digitally removing dark and light-colored hairs in dermoscopic images[END_REF] proposed an improvement of DullRazor method using different approaches. The authors used Prewitt filter for edge detection and Radon transform for predominant direction of the hair, they also used different masks to isolate the hair from other noises. Following the same idea, Toossi et al. [START_REF] Taghi | An effective hair removal algorithm for dermoscopy images[END_REF] proposed a morphological operator using adaptive canny edge detector for hair detection and multiresolution coherence transform inpainting technique to repair and replace smoothly the emplacements of removed hair. On a database of 50 images, the method achieves 88.3%

of diagnostic accuracy and 9.9% of error segmentation. Nguyen et al. [START_REF] Nhi H Nguyen | Segmentation of light and dark hair in dermoscopic images: a hybrid approach using a universal kernel[END_REF] used universal matched filtering kernel and local entropy thresholding to get raw binary hair mask.

Therefore, a combination of morphological thinning with Gaussian curve fitting is used for refining and verification of hair masks. Xie et al. [START_REF] Xie | Pde-based unsupervised repair of hair-occluded information in dermoscopy images of melanoma[END_REF] focused their research on repairing removed hair using PDE-based image inpainting. The method proposed by the authors contains three main parts, morphological closing is used for enhancement in the first step, followed by hair segmentation using statistical thresholding and extracted by the elongate of connected regions, and at the end they used PDE-based image inpainting for restoration. The authors applied their proposed method on 80 images (40 images without hair and 40 with hair). The obtained result showed 5% of errors for the case without hair and 18% for the images containing hair. Following the same idea Fierose et al. [START_REF] Fiorese | Virtualshave: automated hair removal from digital dermatoscopic images[END_REF] proposed PDE-based image inpainting for restoration combined with top-hat operator (morphological enhancement) for segmentation and Otzu threshold for hair detection. Applying the current method on 20 images, the results showed an error of 15.6%. Huang et al. [START_REF] Huang | A robust hair segmentation and removal approach for clinical images of skin lesions[END_REF] explored multi-scale curvilinear matched filtering for hair detection and linear discriminant analysis for image restoration. Abbas et al. [START_REF] Abbas | Hair removal methods: a comparative study for dermoscopy images[END_REF] proposed a matched filtering with first derivative-of-Gaussian method for hair detection.

This approach showed accurate results, but the multitude of parameters complicates its implementation. Applied on 100 dermoscopic images, the method showed a diagnostic accuracy of 93.3%. The authors applied the same method in the next published paper [START_REF] Abbas | Unsupervised skin lesions border detection via two-dimensional image analysis[END_REF][START_REF] Abbas | A feature-preserving hair removal algorithm for dermoscopy images[END_REF] when hair removal was needed. Barata et al. [START_REF] Barata | A system for the detection of pigment network in dermoscopy images using directional filters[END_REF] used a bank of directional Gómez et al. [START_REF] Delgado | Independent histogram pursuit for segmentation of skin lesions[END_REF] proposed an unsupervised algorithm based on Independent Histogram Pursuit. This algorithm estimates a set of linear combinations of images bands to enhance the different structures of the image. The results obtained showed an increment of border quality detection. Following the similar objective of contrast enhancement, Celebi et al. [START_REF] Emre Celebi | Contrast enhancement in dermoscopy images by maximizing a histogram bimodality measure[END_REF], proposed for a given RGB image input, they maximize the histogram bi-modality measure to increase the contrast between the lesion and the background.

Madooei et al. [START_REF] Madooei | Automated pre-processing method for dermoscopic images and its application to pigmented skin lesion segmentation[END_REF] explored artifacts removal and image enhancement on 120 images based on the effect of light-intensity on the edges. The experience was implemented on border detection after enhancement with a sensitivity of 92% and a specificity of 88%.

Recently, in 2015, Koehoorn et al [START_REF] Koehoorn | Automated digital hair removal by threshold decomposition and morphological analysis[END_REF] proposed a new approach based on thresholding set decomposition and morphological analysis using gap-detection by multi-scale skeletons. Mizaarlian et al. [START_REF] Hengameh Mirzaalian | Hair enhancement in dermoscopic images using dual-channel quaternion tubularness filters and mrf-based multilabel optimization[END_REF] proposed an alternative approach to detect hair in dermoscopic images using the measurement of turbulence quaternion [START_REF] Frangi | Multiscale vessel enhancement filtering[END_REF] and dual matched filters for hair suppression. For the restoration, the authors used the interpolation used in DullRazor software developed in [START_REF] Lee | Dullrazor R : A software approach to hair removal from images[END_REF]. On a database of 40 dermoscopic image and 94 synthetic images, the results obtained for hair segmentation are 86% and 85% of accuracy for dermoscopic and synthetic images respectively. The results of enhancement gave 90% and 96% of sensitivity for dermoscopic and synthetic images respectively.

To remove other artifacts such as capillary and blood vessels, many methods are also developed and explored. Huang et al. [START_REF] Huang | Capillary detection for clinical images of basal cell carcinoma[END_REF] and Fisher tests. On a database of 531, the dots vessels showed a positive prediction on melanocytic lesions of 90%.

Abbas et al. [START_REF] Abbas | Unsupervised skin lesions border detection via two-dimensional image analysis[END_REF] also treated specular reflexion reduction using Fourier transform and median filter for air bubbles or dermoscopic-gel reduction. Barata et al. [START_REF] Barata | A system for the detection of pigment network in dermoscopy images using directional filters[END_REF] used in their work a sub-band thresholding for the intensity to reduce the reflexion to enhance the quality of images in pigment network detection. In hair segmentation and removing, there have been many contributions and less for published papers analyzing on tubular structures and vessels. In the state-of-theart research, the results obtained of most papers are based more on visual analysis and comparison. We notice that the majority of methods developed for skin image enhancement are based on thresholding. Despite the multitude approaches, it is very difficult to draw a clear conclusion due to the use of private databases and the application of these methods on small datasets.

Segmentation

The accurate detection of skin lesion border is the most important step and the crucial stage for classification and diagnosis. In image processing, many methods and algorithms were developed and applied in different databases. As mentioned in the previous chapter, the border detection is not so trivial and it has some shortcomings and problems [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF]. Two points are related, firstly, there are the ground truth problem done by dermatologists which is difficult to discriminate by algorithms and reproduce by the human observers, where the variation in contrast or blur [START_REF] Tim | Predictive power of irregular border shapes for malignant melanomas[END_REF] are not visible or well explored by naked eyes. Secondly, the issue between the manual and the automated segmentation is the morphological structure of the lesion as explained by Celebi et al. [START_REF] Emre Celebi | Lesion border detection in dermoscopy images[END_REF], specially the low contrast between the lesion and the normal skin and the fuzzy lesion borders in some cases.

The multitude of lesion development and its appearance in dermoscopic images complicates and influences the choice of the best method to detect lesion border [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF][START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF][START_REF] Emre Celebi | Lesion border detection in dermoscopy images[END_REF]. Therefore, the current subsection is organized following three major methods sets explored in image segmentation in generally, and skin lesion images particularly. In the first step, the methods developed using total variation segmentation are presented, then followed by multiresolution analysis and finally, those using thresholding approaches.

Other various methods, that do not belong to these sets are also studied and explored.

Recently, Celebi et al. [START_REF] Emre Celebi | A state-of-the-art survey on lesion border detection in dermoscopy images[END_REF] reviewed the border lesions detection and classified them into twelve categories, such as Histogram thresholding, clustering and active contours, etc.

Total Variation Segmentation

In the literature, as in general image processing, many methods are developed and/or implemented for skin lesion segmentation. Using total variation regularization, Abbas et al. [START_REF] Abbas | Unsupervised skin lesions border detection via two-dimensional image analysis[END_REF] for the segmentation part, used a modified region-based active contours (RACs) developed by Lankton et al. in [START_REF] Lankton | Localizing region-based active contours[END_REF]. The current method explored the same concept of Chan and Vese model [START_REF] Tony | Active contours without edges[END_REF], and its generalization [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF] proposed for the resolution of Mumford-Shah function [START_REF] Mumford | Optimal approximations by piecewise smooth functions and associated variational problems[END_REF] (see chapter 3). On a database of 320 images, the results present over than 90% true detection rate (TDR) and less than 10% of false positive rate (FPR). For the same objective, Safi et al. [START_REF] Safi | Computer-aided diagnosis of pigmented skin dermoscopic images[END_REF] the proposed extension is detailed in Chapter 4.

Multiresolution Analysis

Multiresolution analysis is also used for segmentation of pigment skin lesions. Therefore, Castillejos et al. [START_REF] Castillejos | Wavelet transform fuzzy algorithms for dermoscopic image segmentation[END_REF], in 2012, mixed wavelet transform [START_REF] Mallat | A theory for multiresolution signal decomposition: the wavelet representation[END_REF] with Fuzzy K-Means

Clustering algorithm, Fuzzy C-means algorithm and Cluster Preselection Fuzzy C-Means algorithm using all color channel for segmentation. On a database of 50 images, the diagnostic performance was quantified by the AUC measure, the best result was performed using Daubechies wavelet with an AUC value over than 0.96 for the three combinations. In another way, Ma et al. [START_REF] Ma | Multi-scale descriptors for contour irregularity of skin lesion using wavelet decomposition[END_REF][START_REF] Ma | Analysis of the contour structural irregularity of skin lesions using wavelet decomposition[END_REF] used wavelet decomposition banks [START_REF] Strang | Wavelets and filter banks[END_REF] to discriminate melanoma and non-melanoma cases, the artificial neural network (ANN) classifier is used for classification. The authors applied the approach on a database of 134 skin lesion images with 72 melanoma and 62 benign lesions. The obtained results achieved a sensitivity of 90% and a specificity of 83%.

A comparison between wavelet [START_REF] Mallat | A wavelet tour of signal processing[END_REF] and curvelet transforms [START_REF] Starck | The curvelet transform for image denoising[END_REF] for segmentation and identification of melanoma was implemented by Abu Mahmoud et al. [START_REF] Abu | Wavelet and curvelet analysis for automatic identification of melanoma based on neural network classification[END_REF]. Using the two layers back-propagation neural network classifier on 448 digital skin lesion images, the result showed a better performance for curvelet compared to wavelet transform. The accuracy obtained using curvelet transform is 86.57%, which is much higher than the result obtained by wavelet transform with 58.44% of accuracy. Erkol et al. [START_REF] Erkol | Automatic lesion boundary detection in dermoscopy images using gradient vector flow snakes[END_REF] proposed the gradient vector flow to find the border of skin lesions under 20 iterations.

On a database of 100 dermoscopic images (30 malignant melanoma and 70 benign lesions), 13.77% of error detection is obtained.

Thresholding Approaches

The idea of thresholding method is one of the simplest approaches of segmentation. The structure of these kind of methods is mostly to separate the image following some limits applied on gray-scale into binary image. Mostly, these methods are complemented by other approaches as morphological operators.

The thresholding approaches by morphological operators segmentation is one of the most known method and used in border detection in different imaging databases [START_REF] Mangan | Partitioning 3d surface meshes using watershed segmentation[END_REF][START_REF] Meyer | Morphological segmentation[END_REF][START_REF] Grau | Improved watershed transform for medical image segmentation using prior information[END_REF][START_REF] Pesaresi | A new approach for the morphological segmentation of high-resolution satellite imagery[END_REF][START_REF] Sirts | Minimally-supervised morphological segmentation using adaptor grammars[END_REF][START_REF] Emre | Lesion border detection in dermoscopy images using ensembles of thresholding methods[END_REF]. In skin cancer images, the morphological segmentation was used by Ganster et al. [START_REF] Ganster | Automated melanoma recognition[END_REF]. The authors explored a gray-scale morphology for segmentation. The method based on three algorithms of thresholding, global thresholding, dynamic thresholding and they also explore the blue color channel of RGB and CIE-Lab color space on 4000 lesion images, and after rejection of 159 images considered as rejected due to segmentation failures, they obtained around 96% of correctly segmented skin lesion images.

Earlier, Shmid [START_REF] Schmid | Lesion detection in dermatoscopic images using anisotropic diffusion and morphological flooding[END_REF] used anisotropic diffusion and morphological flooding on dermoscopic lesion detection. In [START_REF] Silveira | Comparison of segmentation methods for melanoma diagnosis in dermoscopy images[END_REF], the adaptive thresholding showed a potential result compared to other used methods in terms of TDR and FPR performances. It performed a better result of true detection rate and false detection rate in benign and malignant melanoma than gradient vector flow method, and it showed an equivalent result comparing to other methods. In 2013, Celebi et al. [START_REF] Emre | Lesion border detection in dermoscopy images using ensembles of thresholding methods[END_REF] proposed an automated fusion of thresholding method with a Markov random field, applied on 90 dermoscopic images (23 malignant melanoma and 67 benign lesions), and compared to the state of the art methods expressing the result using exlusive-OR errors of 9.16 ± 5.21%.

Otsu thresholding segmentation [START_REF] Jagat Narain Kapur | A new method for gray-level picture thresholding using the entropy of the histogram[END_REF] is developed and applied for automatic border detection in dermoscopic images [START_REF] Abu | Wavelet and curvelet analysis for automatic identification of melanoma based on neural network classification[END_REF][START_REF] Emre Celebi | Unsupervised border detection in dermoscopy images[END_REF][START_REF] Garnavi | Border detection in dermoscopy images using hybrid thresholding on optimized color channels[END_REF][START_REF] Abbas | Unified approach for lesion border detection based on mixture modeling and local entropy thresholding[END_REF][START_REF] Amran | Image processing for skin cancer features extraction[END_REF]. This method is always combined with other methods to perform the segmentation. In Abbas et al. [START_REF] Abbas | Unified approach for lesion border detection based on mixture modeling and local entropy thresholding[END_REF], the authors proposed a combined algorithm of Otsu thresholding algorithm and a morphological reconstruction-based algorithm. The authors presented a result of 92.10% of TDR and 6.41% of FPR on a database of 100 dermoscopic images.

Other Segmentation Methods

Genetic algorithms [START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF] were used by Xie et al. [START_REF] Xie | Automatic segmentation of dermoscopy images using self-generating neural networks seeded by genetic algorithm[END_REF], where a self-generating neural network and the genetic algorithm were combined for the segmentation of dermoscopic images. Watershed technique [START_REF] Grau | Improved watershed transform for medical image segmentation using prior information[END_REF][START_REF] Sonka | Image processing, analysis, and machine vision[END_REF] was also used for lesion segmentation by Wang et al. [START_REF] Wang | Watershed segmentation of dermoscopy images using a watershed technique[END_REF]. It was applied on 100 skin lesions and had a percentage error of 15.98%.

An anisotropic mean shift based on Fuzzy C-Mean (FCM) algorithm variant is used by

Zhou et al. [START_REF] Zhou | Anisotropic mean shift based fuzzy c-means segmentation of dermoscopy images[END_REF], where the authors utilized an anisotropic mean shift algorithm coupled with fuzzy c-means for the segmentation. Sobiecki et al. [START_REF] Sobiecki | Gap-sensitive segmentation and restoration of digital images[END_REF] used Gap-sensitive segmentation on digital images. The authors also applied their method on skin cancer images. Glaister et al. [START_REF] Glaister | Segmentation of skin lesions from digital images using joint statistical texture distinctiveness[END_REF] used TDLS algorithm for textural feature extraction joined with TD metric to calculate the dissimilarity of the texture. Applied to 126 standard camera images, the segmentation results achieved an accuracy of detection of 98.3%, a sensitivity of 91.2% and a specificity of 99%. An unsupervised segmentation algorithm using k means clustering under spatial constraints was also proposed by Zhou et al. [START_REF] Zhou | Spatially constrained segmentation of dermoscopy images[END_REF]. Qi et al. [START_REF] Qi | Global and local information based deep network for skin lesion segmentation[END_REF] applied a fully deep constitutional neural network to automatically segment melanoma. the authors learned their model on 2000 training images and tested on 600 images, then validated on 150 images. However, the authors illustrate visually their results and they did not present any performance due to the small dataset used for learning step.

Table 2.2 summarizes the different methods of segmentation explored for skin lesion images. For each paper, the method used, the result obtained and the size of the dataset (number of images) are mentioned. The majority of developed methods for segmentation step are based on usual methodologies developed in image processing segmentation. we can notice that Safi et al. [START_REF] Safi | Computer-aided diagnosis of pigmented skin dermoscopic images[END_REF] claimed an accuracy of 98.57% on a database 4472 images, however the authors did not highlight the parameters used in the model knowing that the model is an extension of Chan and Vese model which is dependent on parameters chosen. It can be seen also that Clawson et al. [START_REF] Kathy M Clawson | Analysis of pigmented skin lesion border irregularity using the harmonic wavelet transform[END_REF], on a database of only 30 images, the results obtained by their model shows a big difference sensitivity performance between the ground truth of two experts (50% and 95.2%). We noted also that the accuracy is affected by the difference between malignant and benign lesions. Therefore, there is a need to develop an adapted and specified method for skin lesions. From the literature, it can be seen that majority of contributions used a private databases which is very hard to re-implement the different methods. It can be seen also that the segmentation step development for skin cancer is not highlighted since few years. In the current work, an adequate and accurate segmentation for skin cancer using an extension of Chan and Vese model is developed.

Feature Extraction

Feature extraction of melanoma is the most important stage for the classification and diagnosis step (next stage). The main task of this step is to extract the discriminant features to aid the separation of malignant and benign skin lesions. To correctly diagnose and classify the lesion, the features extracted have to represent in the best way the characteristics of the tumor that can be used and understood by the computer. In hospitals as mentioned before, medical doctors use two famous scoring systems as features, ABCD criteria (or rule) [2,[START_REF] Robert J Friedman | Early detection of malignant melanoma: The role of physician examination and self-examination of the skin[END_REF] and 7-point checklist [START_REF] Naheed R Abbasi | Early diagnosis of cutaneous melanoma: revisiting the abcd criteria[END_REF]. The ABCD rule (Asymmetry, Border irregularities, Color variation and Diameter) is more used and explored than 7-point checklist.

In the literature, most of the papers develop their methods according to one or more points of ABCD rule, specially Asymmetry [START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF][START_REF] Amran | Image processing for skin cancer features extraction[END_REF][START_REF] Chakravorty | Dermatologistlike feature extraction from skin lesion for improved asymmetry classification in ph 2 database[END_REF][START_REF] Vincent | Determining the asymmetry of skin lesion with fuzzy borders[END_REF][START_REF] Sankaran | Quantifications of asymmetries on the spectral bands of malignant melanoma using six sigma threshold as preprocessor[END_REF][START_REF] Chang | Computer-aided diagnosis of skin lesions using conventional digital photography: a reliability and feasibility study[END_REF][START_REF] Amelard | Melanoma decision support using lighting-corrected intuitive feature models[END_REF], Border irregularities [START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF][START_REF] Safi | Computer-aided diagnosis of pigmented skin dermoscopic images[END_REF][START_REF] Ma | Multi-scale descriptors for contour irregularity of skin lesion using wavelet decomposition[END_REF][START_REF] Emre | Lesion border detection in dermoscopy images using ensembles of thresholding methods[END_REF][START_REF] Abbas | Unified approach for lesion border detection based on mixture modeling and local entropy thresholding[END_REF][START_REF] Amelard | Melanoma decision support using lighting-corrected intuitive feature models[END_REF][START_REF] Mh Jafari | Automatic detection of melanoma using broad extraction of features from digital images[END_REF][START_REF] Jaworek | Determination of border irregularity in dermoscopic color images of pigmented skin lesions[END_REF][START_REF] Tim K Lee | Irregularity index: a new border irregularity measure for cutaneous melanocytic lesions[END_REF][START_REF] Tb Holmstrom | A survey and evaluation of features for the diagnosis of malignant melanoma[END_REF][START_REF] Benjamin | A border irregularity measure using a modified conditional entropy method as a malignant melanoma predictor[END_REF][START_REF] Zhou | A new method describing border irregularity of pigmented lesions[END_REF] and Color variation [START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF][START_REF] Safi | Computer-aided diagnosis of pigmented skin dermoscopic images[END_REF][START_REF] Abbas | Unified approach for lesion border detection based on mixture modeling and local entropy thresholding[END_REF][START_REF] Chang | Computer-aided diagnosis of skin lesions using conventional digital photography: a reliability and feasibility study[END_REF][START_REF] Yue | Skin lesion classification using relative color features[END_REF][START_REF] Andrew J Round | Lesion classification using skin patterning[END_REF][START_REF] Chang | A systematic heuristic approach for feature selection for melanoma discrimination using clinical images[END_REF][START_REF] Stanley | A fuzzy-based histogram analysis technique for skin lesion discrimination in dermatology clinical images[END_REF][START_REF] Chen | Colour analysis of skin lesion regions for melanoma discrimination in clinical images[END_REF][START_REF] Claridge | From colour to tissue histology: physics-based interpretation of images of pigmented skin lesions[END_REF][START_REF] Abuzaghleh | Automated skin lesion analysis based on color and shape geometry feature set for melanoma early detection and prevention[END_REF][START_REF] Brian D'alessandro | Computer aided analysis of epi-illumination and transillumination images of skin lesions for diagnosis of skin cancers[END_REF][START_REF] Khakabi | Multilevel feature extraction for skin lesion segmentation in dermoscopic images[END_REF]. The non common utilization of the Diameter does not mean that it is useless comparing to the other ABCD rule points, but in most of the cases the diameter is missed data. Nevertheless, it was used by Shen et al. [START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF].

Many other methods of image processing are also used, specially textural and structural features. In Abbas et al. [START_REF] Abbas | Pattern classification of dermoscopy images: A perceptually uniform model[END_REF], in addition to color-related features, the authors combined them with textural ones extracted from Steerable Pyramids Transformation (SPT) algorithm, and performed a sensitivity of 89.28%, a specificity of 93.75% and an area under AUC of 0.986. Abu Mahmoud et al. [START_REF] Abu | Wavelet and curvelet analysis for automatic identification of melanoma based on neural network classification[END_REF] explored discrete wavelet and discrete curvelet transforms as features for melanoma recognition. For smart-phonebased real-time system, Abuzaghleh et al. [START_REF] Abuzaghleh | Automated skin lesion analysis based on color and shape geometry feature set for melanoma early detection and prevention[END_REF] proposed fast Fourier transform (FFT) mixed with discrete cosine transform applied on color and shape for feature extraction.

Earlier in 2009, Clawson et al. [START_REF] Kathy M Clawson | Analysis of pigmented skin lesion border irregularity using the harmonic wavelet transform[END_REF] used Harmonic Wavelet Transform [START_REF] Newland | Harmonic wavelet analysis[END_REF] for border smoothness features on 30 dermoscopic images. Using the ground truth of two experts and C5 algorithm with 10-fold cross-validation, the results show an accuracy of 93.3%

for both experts, and a sensitivity of 50% and 95.2% and a specificity of 100% and 88.9% for the ground truth of expert 1 and expert 2, respectively. Codella et al. [START_REF] Codella | Deep learning, sparse coding, and svm for melanoma recognition in dermoscopy images[END_REF] used Sequential Pattern Mining (SPAM) algorithm to learn dictionaries constructed on color (RGB) and gray level spaces of the dataset. The authors applied the approach on ISIC database of 4624 images with 334 melanoma, 144 atypical nevi and 2146 benign lesions. Using SVM classifier, the results obtained showed an accuracy of 93.1%, a sensitivity of 94.9% and a specificity of 92.8%. Local Binary Pattern (LBP) [START_REF] Ojala | Texture discrimination with multidimensional distributions of signed gray-level differences[END_REF][START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[END_REF] operator is also used for feature extraction on dermoscopic images by Gonzáles et al. [START_REF] González-Castro | Automatic classification of skin lesions using geometrical measurements of adaptive neighborhoods and local binary patterns[END_REF] and Adjed et al [START_REF] Adjed | Classification of skin cancer images using local binary pattern and svm classifier[END_REF].

Sadghi et al. [START_REF] Sadeghi | Detection and analysis of irregular streaks in dermoscopic images of skin lesions[END_REF], to classify absent, regular and irregular streaks, which are important for melanoma detection inspired from 7-point checklist system, used the orientation and spatial arrangement of streak lines. Takruri et al. [START_REF] Takruri | Automatic recognition of melanoma using support vector machines: A study based on wavelet, curvelet and color features[END_REF] proposed the extraction of features on wavelet or curvelet coefficients applied on gray scale lesions with color features obtained from original images. Using SVM classifier, the results performed an accuracy of 87.1%, a sensitivity of 86.4% and a specificity of 88.1% for the system based on wavelet features and an accuracy of 83.6%, a sensitivity of 76.9% and a specificity of 85.4% for the system based on curvelet features.

Cavalcanti et al. [START_REF] Pablo | Automated prescreening of pigmented skin lesions using standard cameras[END_REF] is a typical work following all the steps of ABCD rule on standard images database. Therefore, for asymmetry they used two axis passing through the center of the pigment, and magnitude of gradient using Sobel operator. They explored the values of pixel intensities in color variation channel for color features. However, on standard camera images, the morphological and vascular structures are not visible.

On a database of 220 images (138 melanoma and 82 benign lesions), they performed an accuracy of 93.63%, a sensitivity of 94.92% and a specificity of 91.46% using kNN classifier. Exploring the same method, Amelard et al. [START_REF] Amelard | Melanoma decision support using lighting-corrected intuitive feature models[END_REF] extracted features using multi-stage illumination algorithm and defined a set of high level intuitive features to quantify the asymmetry and border irregularities as [START_REF] Pablo | Automated prescreening of pigmented skin lesions using standard cameras[END_REF]. They applied their algorithm on a database of 206 standard digital camera images. Using SVM classifier, the results obtained performed an accuracy of 81.26%, a sensitivity of 84.04% and a specificity of 79.91%. Sabbaghi et al. [START_REF] Sabbaghi | A deep bag-of-features model for the classification of melanomas in dermoscopy images[END_REF] explored the Bag-Of-Feature using SIFT (Scale Invariant Feature Transform) descriptor mixed color identification [START_REF] Sabbaghi | Automated colour identification in melanocytic lesions[END_REF] to extract the features.

Classification

The classification and diagnosis is the last step of the CAD system on melanoma recognition. The classification stage uses the selected features in the previous section to separate the database into different groups. The result can be binary as malignant / benign or typical / atypical, ternary as common nevus / atypical nevus / melanoma, or more than three groups.

To accomplish the classification task, many classifier methods are explored and used depending on the descriptor used for feature selection. The performance of the whole proposed method depends extremely on the couple descriptor / classifier. The review of Korotkov et al [START_REF] Korotkov | Computerized analysis of pigmented skin lesions: a review[END_REF] enumerated several methods of classification used in the literature. According to the classifier used, many different performance metrics are used as accuracy, TDR, FPR or AUC. These performance metrics are explained and detailed in subsection 3.5.4.

Support Vector Machine (SVM) classifier [START_REF] Joachims | Text categorization with support vector machines: Learning with many relevant features[END_REF] and Artificial Neural Network methods (ANN) [START_REF] Yegnanarayana | Artificial neural networks[END_REF] Analysis [START_REF] Huang | A robust hair segmentation and removal approach for clinical images of skin lesions[END_REF][START_REF] Tim | Predictive power of irregular border shapes for malignant melanomas[END_REF][START_REF] Ilias | Characterization of digital medical images utilizing support vector machines[END_REF], Decision trees [1,[START_REF] Luis | Detection of pigment network in dermoscopy images using supervised machine learning and structural analysis[END_REF][START_REF] Pablo | Automated prescreening of pigmented skin lesions using standard cameras[END_REF], Regression Analysis [START_REF] Zhou | A new method describing border irregularity of pigmented lesions[END_REF][START_REF] Iyatomi | An improved internet-based melanoma screening system with dermatologist-like tumor area extraction algorithm[END_REF][START_REF] Dreiseitl | A comparison of machine learning methods for the diagnosis of pigmented skin lesions[END_REF] and AdaBoost [1,[START_REF] Luis | Detection of pigment network in dermoscopy images using supervised machine learning and structural analysis[END_REF][START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF]. The review of the comparative studies achieved by Masood et al. [START_REF] Masood | Computer aided diagnostic support system for skin cancer: a review of techniques and algorithms[END_REF] concluded that SVM classifier outperforms decisions trees, and many other statistical classifiers.

Abuzaghlegh et al. [START_REF] Abuzaghleh | Automated skin lesion analysis based on color and shape geometry feature set for melanoma early detection and prevention[END_REF], proposed to classify the PH 2 Database [149] into binary and ternary results. The ternary results used to classify between typical, atypical or melanoma and the binary is to classify only between normal and abnormal lesions. The authors used SVM classifier using 75% for training and 25% for tests. On the same database (PH 2 ), Barata et al. [START_REF] Barata | Improving dermoscopy image classification using color constancy[END_REF] used SVM classifier with the χ 2 kernel, the performance of the contribution is computed by the adjusted accuracy calculated with some interval of accuracy metric. In the same work, the authors are applied also their method on bigger database from the ERDA database [START_REF] Argenziano | Interactive atlas of dermoscopy (book and cd-rom)[END_REF]. AdaBoost with C4.5 decision trees was used by Capdehourat et al. [1] and performed their results by specificity and sensitivity metrics. Discriminant Analysis [START_REF] Huang | A robust hair segmentation and removal approach for clinical images of skin lesions[END_REF][START_REF] Tim | Predictive power of irregular border shapes for malignant melanomas[END_REF][START_REF] Ilias | Characterization of digital medical images utilizing support vector machines[END_REF] Regression Analysis [START_REF] Zhou | A new method describing border irregularity of pigmented lesions[END_REF][START_REF] Iyatomi | An improved internet-based melanoma screening system with dermatologist-like tumor area extraction algorithm[END_REF][START_REF] Dreiseitl | A comparison of machine learning methods for the diagnosis of pigmented skin lesions[END_REF] AdaBoost [1,[START_REF] Luis | Detection of pigment network in dermoscopy images using supervised machine learning and structural analysis[END_REF][START_REF] Abbas | Pattern classification of dermoscopy images: A perceptually uniform model[END_REF][START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF].

Summary

In the literature, skin cancer detection and classification is developed and explored by many researchers. There are two major topics where the contributions are focused.

These two topics are the lesion segmentation and the descriptors for feature extraction.

The multitude of artifacts in skin lesion images increases the contributions in image enhancement, specially for hair removing and blood vessels. Computer Aided Diagnosis systems for pigmented skin lesions have achieved good performances. However, the results obtained and methods proposed cannot provide the best diagnostic results as clinicians, they are only used as second opinions during screening procedure [START_REF] Korotkov | Automatic change detection in multiple pigmented skin lesions[END_REF].

The segmentation was studied in different views. Many approaches and methods were adapted and/or developed. Therefore, as it is detailed in section 2.3, the segmentation methods used the total variation methods following Mumford and Shah theory, specially Chan and Vese model and its extensions. The multiresolution analysis was also used for pigment lesion segmentation as wavelet and curvelet transforms. The thresholding methods were also mostly used for segmentation. Therefore, there is a need to perform and develop an accurate descriptor. Two research directions should be further investigated which are structural and textural features. The structure of lesion boundaries and the texture inside the lesions have an important information for discrimination and characterization of melanoma. Wavelet coefficients are ideal for single point discrimination but not for edges which characterize the lesion boundaries. Thus, curvelet coefficients can achieve better characterization. In addition to curvelet, a fusion of these coefficients with textural information of the lesion need to be investigated. On the other side, the investigation of the geometrical information from the borders with a new approach challenging irregular versus smooth border is also another direction for the discrimination of melanoma. given in section 3.6.

Total Variation

In classical analysis, the total variation for function f for one variable defined on the interval [a, b] ⊂ R, is given by the following formula:

T V (f ) = sup I I i=0 |f (x i+1 ) -f (x i )| (3.1)
where

I = {I 1 , I 2 , ..., I p } is a partition of [a, b] for i ∈ {1, ..., p}, x i ∈ I i .
The total variation of function f ∈ R n where n > 1 used in the current work is defined as follow:

Let Ω be an open subset of R n and f ∈ L 1 (Ω), then the total variation is:

T V n (f ) = sup Ω f (x) divφ(x)dx; φ ∈ C 1 c , φ L ∞ (Ω) ≤ 1 (3.2)
where C 1 c is the set of continuously differentiable functions of compact of Ω and φ L ∞ (Ω) is the essential infimum norm.

Mumford Shah Function

Mumford and Shah applied the total variation for image segmentation in 1989 [START_REF] Mumford | Optimal approximations by piecewise smooth functions and associated variational problems[END_REF].

Let R ∈ R 2 the domain divided in n disjoint subsets R i where a smooth function f i is defined and Γ will be the union of boundaries parts of the R i inside R . Let I be the given image and f a differentiable function on R, then the energy to minimize is :

E(f, Γ) = µ 2 R (f -I) 2 dxdy + R-Γ ∇f dxdy + ν|Γ| (3.3)
where |Γ| represents the total length of the curve Γ, µ and ν are the regulation parameters.

Chan and Vese Model

To minimize the given energy in equation (3.3), Chan and Vese [START_REF] Tony | Active contours without edges[END_REF] proposed to minimize first, the following energy function: Therefore, the energy functional is defined by F (c 1 , c 2 , C) given below:

F C (C) = λ 1 inside(C) |I(x, y) -c 1 | 2 dxdy + λ 2 outside(C) |I(x, y) -c 2 | 2 dxdy (3.
F (c 1 , c 2 , C) = µ Length(C) + ν Area(inside(C)) + F C (C) (3.5)
Using a zero level set of Lipschitz function φ : Ω → R, then :

             C = ∂ω = {(x, y) ∈ Ω; φ(x, y) = 0} inside(C) = ω = {(x, y) ∈ Ω; φ(x, y) > 0} outside(C) = Ω\ω = {(x, y) ∈ Ω; φ(x, y) < 0} (3.6)
Where ω ∈ Ω and C = ∂ω.

Using the heaviside function

H(z) =      1 if z ≥ 0 0 if z < 0 δ 0 = d dz H(z) (3.7)              C = Length(φ = 0) = δ 0 (x, y)|φ(x, y)|dxdy Inside(C) = Area(φ(x, y) > 0) = Ω H φ(x, y) dxdy Outside(C) = Area(φ(x, y) < 0) = Ω 1 -H φ(x, y) dxdy (3.8)
Then, equation (3.4) is also expressed by the heaviside function H:

F C (c) = λ 1 Ω |I(x, y)-c 1 | 2 H φ(x, y) dxdy+λ 2 Ω |I(x, y)-c 2 | 2 1-H(φ(x, y)) dxdy (3.9)
Therefore, the energy given in equation (3.5) becomes:

F (c 1 , c 2 , φ) = µ δ 0 (x, y)|φ(x, y)|dxdy + ν Ω H φ(x, y) dxdy +λ 1 Ω |I(x, y) -c 1 | 2 H φ(x, y) dxdy (3.10) +λ 2 Ω |I(x, y) -c 2 | 2 1 -H(φ(x, y)) dxdy
where,

c 1 = Ω I(x, y)H(φ(x, y)) Ω H(φ(x, y)) (3.11) c 2 = Ω I(x, y) 1 -H(φ(x, y)) Ω 1 -H(φ(x, y)) (3.12)
The energy to minimize for the segmentation of Chan and Vese model is given by equation (3.10).

Multiresolution Analysis

In this section, the multiresolution analysis is introduced. Mathematical theories of Fourier, wavelet, ridgelet and curvelet transforms are presented.

The Fourier transform has the ability to represent any integrable function in the frequency domain with a limitation of stationarity in time [START_REF] Grinsted | Application of the cross wavelet transform and wavelet coherence to geophysical time series[END_REF]. With wavelet transform, the time representation is resolved, however the line singularity of edges in wavelet transforms need many coefficients. An extension was presented which is ridgelet transform for detection of edges with less coefficients. The incapability to detect the angle of edges using ridgelet transform, curvelet transform was introduced to fit better the curves and edges. Curvelet and wavelet transforms are used in the proposed work, they are introduced in next sections and used in the next chapter.

Fourier Transform

Let f : R → C an integrable function, the Fourier transform of f is conventionally noted f decomposes into frequencies. Therefore, the function f is the continuous-time function defined in spatial domain, and f is its Fourier transform defined in frequency domain given by the following equation:

f (ξ) = ∞ -∞ f (x) e -2πxiξ dx (3.13)
The inverse Fourier transform of f , under suitable conditions is given by:

f (x) = ∞ -∞ f (ξ) e 2πixξ dξ (3.14)
This transform is an extension of Fourier series applied on periodic functions using the properties of sine and cosine. Therefore, suppose that T is large enough that the interval [-T /2, T /2] contains F non identically zero. Then, the nth Fourier coefficients c n is given by the following equation:

c n = 1 T T /2 -T /2 f (x) e -2πi(n/T )x dx (3.15)
Equation (3.14) can be written using Fourier coefficients. Then, lets ξ n = n/T and ∆ξ = 1/T :

f (x) = ∞ n=-∞ f (ξ n ) e 2πiξnx ∆x = ∞ n=-∞ c n e 2πi(n/T )x (3.16)
In signal and image processing, the discrete Fourier transform (DFT) is applied.

In the one-dimensional case (signals), the Fourier transform is given by the function f above. This signal is divided into N sequences denoted f 0 , f 1 , ..., f N -1 . Then the DFT of f is:

fk = N -1 n=0 f n e -2πikn/N , k ∈ Z (3.17)
The inverse DFT is as continuous case given by the following equation:

f n = 1 N N -1 k=0 fk e 2πikn/N (3.18)
For image which is 2 dimension matrix M × N , the DFT of the function f (x, y) is denoted by F(m,n) given by:

F (m, n) = M -1 x=0 N -1 y=0 f (x, y) e -2πi(xm/M +yn/n) (3.19)
where m = 0, 1, ..., M -1 and n = 0, 1, ..., N -1.

By the same, the inverse DFT in 2 dimensions is given by the function f below:

f (x, y) = 1 M N M -1 m=0 N -1 n=0 F (m, n) e 2πi(xm/M +yn/n) (3.20)
Different algorithms of fast Fourier transforms were implemented and combined with band filtering and convolutions. However, the Fourier transform indicates the spectral information without the instant when it happens [START_REF] Kleber | Comparison between fourier and wavelets transforms in biospeckle signals[END_REF]. In image implementation, Mallat [START_REF] Mallat | A wavelet tour of signal processing[END_REF] noticed that an apple in the corner of a given image required many Fourier coefficients to represent a localized event. Indeed, the Fourier transform f (ξ)

depends on the values f (t) for all times t ∈ R. Therefore, to analyze or represent any local property of f (t) from f (ξ) is difficult.

Wavelet Transform

Wavelet transform was introduced by Grosmann and Morlet [START_REF] Grossmann | Decomposition of hardy functions into square integrable wavelets of constant shape[END_REF] using translation and dilations on a 1square integrable function ψ ∈ L 2 (R). The wavelet transform is defined by the following formula:

ψ a,b (x) = 1 √ a ψ t -b a (3.21)
where a > 0 defines the scale and b the shift.

A multiresolution approximation of L 2 (R) is a sequence (V j ) j∈Z of closed subspaces of L 2 (R), such that:

{0} ⊂ • • • ⊂ V 1 ⊂ V 0 ⊂ V -1 ⊂ • • • ⊂ L 2 (R) (3.22)
Let φ(x) be a real square integrable function defined by:

φ j,k (x) = √ 2 j φ(2 j x -k), k ∈ Z (3.23)
Then, {φ j,k } j,k∈Z is the orthonormal basis of V j [START_REF] Mallat | A theory for multiresolution signal decomposition: the wavelet representation[END_REF].

All the functions expressible with this basis are referred to the closed span of the expansion set:

V j = Span{(φ j.k , k ∈ Z)} (3.24)
where if f (x) ∈ V j , then f (x) ∈ Span{(φ j.k , k ∈ Z)}, and f (x) = k α k φ j,k (x).

The subspace of L 2 (R), W j designs the orthogonal complements of the subspaces V j defined above, such that:

V j ⊕ W j = V j-1 (3.25)
In multiresolution analysis, the subspaces V j are generated by the function (φ j,k ) k∈Z and The subspace W j is generated by a scaling function (ψ j,k ) k∈Z as given below:

W j = Span{(ψ j.k , k ∈ Z)} (3.26)
then, the subspace V j represents the large scale and W j represents the small scale (details).

Let f (x) be a one-dimensional discrete function as sequence of numbers, the discrete wavelet transform coefficients are defined as:

C φ (j 0 , k) = 1 √ M M -1 x=0 f (x)φ j 0 ,k (x) (3.27) D ψ (j, k) = 1 √ M M -1 x=0 f (x)ψ j,k (x) (3.28)
where j > j 0 , M is power of 2 which ranges from 2 to j -1 and C φ (j 0 , k), D ψ (j, k)

are the approximation and details coefficients respectively. Using these coefficients, the signal function f (x) can be reconstructed as:

f (x) = 1 √ M k C φ (j 0 , k)φ j 0 ,k (x) + 1 √ M ∞ j=j 0 k D ψ (j, k)ψ j,k (x) (3.29)
The implementation of wavelet transform was presented by Mallat [START_REF] Mallat | A theory for multiresolution signal decomposition: the wavelet representation[END_REF] introducing a set of filters (h l ) l∈Z and (g l ) l∈Z where:

φ j,k = l h l φ j+1,2k+l (3.30)
ψ j,k = l h l ψ j+1,2k+l (3.31)
and

h l = (-1) n g 1-l (3.32)
Therefore, the approximation and details coefficients are computed.

In two dimensions case, there are one scaling function φ(x, y) and three directional wavelets as defined below:

                   φ(x, y) = φ(x)φ(y) ψ H (x, y) = ψ(x)φ(y) ψ V (x, y) = φ(x)ψ(y) ψ D (x, y) = ψ(x)ψ(y) (3.33)
where ψ H , ψ V and ψ D measure the horizontal, vertical and diagonal variation respectively as represented in figures 3.1 and 3.2.

Finally, the wavelet coefficients of a given image I (M × N ) are computed using the following formulas:

W φ (j, k) = 1 √ M N M -1 x=0 N -1 y=0 I(x, y)φ j,k (x, y) (3.34) W H ψ (j, k) = 1 √ M N M -1 x=0 N -1 y=0 I(x, y)ψ H j k (x, y) (3.35) W V ψ (j, k) = 1 √ M N M -1 x=0 N -1 y=0 I(x, y)ψ V j k (x, y) (3.36) W D ψ (j, k) = 1 √ M N M -1 x=0 N -1 y=0 I(x, y)ψ D j k (x, y) (3.37)
The potential of wavelet representation had a wide impact in theory and in practice.

It's used for non-linear approximation, compression and image denoising on different databases. But wavelet is less efficient in some cases for line singularities [START_REF] Minh | The finite ridgelet transform for image representation[END_REF].

Ridgelet Transform

The Ridgelet transform was introduced by Candés and Donoho [START_REF] Emmanuel | Ridgelets: A key to higherdimensional intermittency?[END_REF] and Finite ridgelet transform for image representation [START_REF] Minh | The finite ridgelet transform for image representation[END_REF] by Do and Vetterli. Ridgelet transform has the ability to detect line singularities.

The continuous ridgelet transform is defined for each a > 0, b ∈ R and θ ∈ [0, π/2] by the bivariate function ψ a,b,θ : R 2 → R 2 :

ψ a,b,θ (x) = a -1/2 ψ x 1 cos(θ) + x 2 sin(θ) /a (3.38)
This function is an extension of wavelet transform, where when (x 1 cos(θ) + x 2 sin(θ) is constant the two functions are equal. In addition to that the ridgelet transform has the ability to fit easily the lines compared to wavelet transform [START_REF] Emmanuel | Ridgelets: A key to higherdimensional intermittency?[END_REF].

Let f (x) be an integrable bivariate function, the ridgelet transform of f is R f given below:

R f (a, b, θ) = ψ a,b,θ (x)f (x)dx (3.39)
Do and Vetterli [START_REF] Minh | The finite ridgelet transform for image representation[END_REF] proposed the finite ridgelet transform for image representation, they used the inner product of finite radon transform and wavelet transform.

The Ridgelet transform is efficient for the detection of straight lines, unless it is inefficient for curves fitting.

Curvelet Transform

The Curvelet transform was designed to represent edge and curve singularities more efficiently than previous transforms presented in this chapter. It needs fewer coefficients to describe edges and curves through the directional parameter added.

Curvelet Transform was introduced in 2000 by Candes and Donoho [START_REF] Emmanuel | Curvelets: A surprisingly effective nonadaptive representation for objects with edges[END_REF], they presented the second generation of curvelet [START_REF] Candes | Fast discrete curvelet transforms[END_REF] known as the fast digital curvelet transform (FDCT) in 2006, which is less redundant and it has better performances than its predecessors. Curvelets have the capability to detect finest edges, those can present more details in curvelet coefficients [START_REF] Guha | Curvelet based feature extraction[END_REF].

Curvelet transforms are defined in two dimensions, with spatial variable x and frequency-domain variable w. The polar coordinates of the frequency-domain are r and θ. Two windows W (r) and V (t) called radial window and angular window respectively [START_REF] Candes | Fast discrete curvelet transforms[END_REF]. These windows will always obeying the following admissibility conditions:

∞ j=-∞ W 2 (2 j r) = 1, r ∈ (3/4, 3/2) (3.40) ∞ l=∞ V 2 (t -l) = 1, t ∈ (-1/2, 1/2) (3.41)
The frequency window U j , in Fourier domain given by equation (3.42), represents a polar wedge, which is supported by W (t) and V (t).

U j (r, θ) = 2 -3j/4 2 -j r V 2 j/2 2π (3.42)
At scale 2 -j , orientation θ l and position x k (j, l), the curvelet transform function of {x = (x 1 , x 2 )} is given by equation (3.43).

ϕ j,l,k (x) = ϕ j R θ l x -x (j,l) k (3.43)
Where R θ is the rotation in radians and ϕ j is the waveform and its Fourier transform φ(w) = U j (w) given in equation (3.42). It is considered as mother curvelet in the sens that all Curvelets are calculated by rotations and translations of ϕ j [START_REF] Candes | Fast discrete curvelet transforms[END_REF].

The curvelet coefficient, c given in equation (3.44), it is obtained by the inner product between the element f ∈ L 2 (R 2 ) and the curvelet transform ϕ j,k,l . Then, the discrete coefficients of FDCT are given below: pared to wavelet transform [3]. It can be seen easily that for the same curve curvelet transform is more accurate and needs fewer coefficients than wavelet transform.

c(j, k, l) = R 2 f (x)ϕ j,k,l (x)dx. ( 3
c D (j, l, k 1 , k 2 ) = 0≤m≤M, 0≤n≤N f [m, n]ϕ D j,l,k 1 ,k 2 [m, n] (3

Local Binary Pattern

The Local Binary Patterns (LBP) operator is used for texture description. It is one of the best performing texture descriptors and it has been widely used in multiple applications [START_REF] Timo Ahonen | Face description with 150 local binary patterns: Application to face recognition[END_REF][START_REF] Porebski | Haralick feature extraction from lbp images for color texture classification[END_REF]. This operator was developed by Ojala et al. [START_REF] Ojala | Texture discrimination with multidimensional distributions of signed gray-level differences[END_REF][START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[END_REF]. Many variants of LBP were developed, for example Heikkila et al. [START_REF] Heikkilä | Description of interest regions with center-symmetric local binary patterns[END_REF] proposed center-symmetric local binary pattern, then, Zhang et al. [START_REF] Zhang | Face detection based on multi-block lbp representation[END_REF] developed a new approach replacing the neighbor pixels by the mean of the neighbors' blocks, and Wolf et al. [START_REF] Wolf | Descriptor based methods in the wild[END_REF] proposed novel patches based LBP where they explored the similarities between neighboring patches of pixels. The majority of these developments are applied in face detection and recognition.

The LBP operator attributes for each pixel of the image a new value from 0 to 255 depending on its neighborhood as explained below:

Let the image I(x, y) and g c denote the gray level of an arbitrary pixel (x, y), i.e g c = I(x, y). And let g p denote the gray value of the local neighborhood, where P defines the number of pixels around the point (x, y) with radius R, then :

g p = I(x p , y p ), p = 0, ..., P -1

x p = x + R cos(2πp/P )

y p = y -R sin(2πp/P )
Assuming that the local texture of the image I(x, y) is characterized by the joint distribution t(.) of gray values of P + 1 (P > 0) pixels:

T = t(g c , g 0 , g 1 , .
.., g P -1 ).

(3.46)

Without loss of information, the center pixel value can be subtracted from the neighborhood pixel values and equation (3.46) can be written as the following formula:

T = t(g c , g 0 -g c , g 1 -g c , ..., g P -1 -g c ). (3.47)
Assuming that the center pixel is statistically independent to the differences, equation (3.47) is approximated by:

T ≈ t(g c )t(g 0 -g c , g 1 -g c , .
.., g P -1 -g c ).

(3.48)

The important information is given by the differences distribution part i.e t(g 0g c , g 1 -g c , ..., g P -1 -g c ). However, the estimation of this distribution from image data is difficult. Ojala et al. [START_REF] Ojala | Texture discrimination with multidimensional distributions of signed gray-level differences[END_REF] proposed to apply vector quantization given by the following formula:

t(s(g 0 -g c ), s(, g 1 -g c ), ..., s(g P -1 -g c ).

(3.49)

where s(z),

s(z) =      1, z ≥ 0 0, z < 0. (3.50)
Then, the generic local binary patterns operator is defined by: [START_REF] Pietikäinen | Computer vision using local binary patterns[END_REF]:

LBP P,R (x c , y c ) = P -1 p=0 s(g p -g c )2 p (3.51)
According to our previous work [START_REF] Adjed | Classification of skin cancer images using local binary pattern and svm classifier[END_REF], the choice of P = 8 and R = 1 is the best case for melanoma description.

Statistical Classification and Pattern Recognition

The classification is the method which cat attribute from a set of features observed or learned a new class to the studied object not belonging to the learned set. It can be achieved using supervised learning such as Support Vector Machine and Artificial Neural Network or unsupervised learning as K-means clustering and k-Nearest Neighbors.

In this section, the representation of basic ideas of support vector machine and artificial neural network are explained.

The pattern recognition is a branch of machine learning focused on description of patterns. It may use the supervised or unsupervised recognition [START_REF] Anil K Jain | Statistical pattern recognition: A review[END_REF]. The supervised learning utilizes a set of training data which is properly labeled with the correct output.

In the other hand, the unsupervised learning assumes training data has not been welllabeled and try to find the best pattern which can make a correct output value for the data.

Depending on the classifier used, many performance metrics can be explored to compare and analyze the obtained results such as accuracy, sensitivity, specificity. The mathematical equations of some of these metrics are given in the current chapter (see section 3.5.4).

Support Vector Machine

Support Vector Machine (SVM) was introduced by Vapnik and Lerner 1963, Vapnik and Chervonenskis 1964, an overview of the basic ideas of SVM and its advanced methods for large datasets are explained and detailed by Smola et all. [START_REF] Smola | A tutorial on support vector regression[END_REF]. The basic idea of SVM is introduced and developed in the current subsection.

Let {(x 1 , y 1 ), ..., (x m , y m )} ⊂ X × {±1} a set of empirical data, where X is some nonempty set that the patterns x i belongs. Let the function f : X → {±1}. In this current study only the hyperplane classifier is presented. Therefore, considering the class of hyperplanes

(w• x) + b = 0 (3.52)
where w ∈ R N , b ∈ R (in the current work, the choice of these parameters are done using Statistic and machine learning toolbox of Matlab 2015).

The decision of SVM corresponds to the results of the following formula:

f (x) = sign((w • x) + b) (3.53)
To construct an optimal hyperplane, it is needed to resolve the following optimization problem:

Minimize w 2 , (3.54) subject to:

     (x • x i + b) > 1, if y i = 1 (x • x i + b) ≤ -1, if y i = -1 (3.55)
The two contrast given in the formula (3.55) can be expressed by:

y i (w • x i + b) ≥ 1 (3.56)
The current formulation is used well in perfect separability of the data.

In the case of no-separability, the function to minimize is |w| 2 + C m i=1 ξ i where C is constant and ξ a real small positive (ξ i > 0). The constraint is to verify the following formula:

y i (w • x i + b) ≥ 1 -ξ i (3.57)
To classify the more complex cases, the linear SVM classifier cannot be accurate by constructing only a hyperplane between classes. Therefore, a non-linear SVM classifier was proposed using the following mapping function φ:

x → φ(x) (3.58)
Then, equation decision rule, such as given by (3.53) for linear case, is formulated by the following equation:

f (x) = w • φ(x) + b (3.59)
Depending on the choice of the mapping function φ, different variants of the non-linear SVM classifier could be built, such as the polynomial mapping and the kernel trick.

Artificial Neural Network

Artificial neural network (ANN) commonly referred to neural network has its inception for recognition as the human brain computes using different way in separate or parallel, linear and/or non-linear approaches [START_REF] Haykin | A comprehensive foundation[END_REF]. The first interest given in ANN emerged after the introduction of simplified neurons by McCulloch and Pitts in 1943 [START_REF] Abraham | Artificial neural networks. handbook of measuring system design[END_REF].

In the literature [START_REF] Kriesel | A brief Introduction to Neural Networks[END_REF], there are many different ANN models developed and implemented. In the current work, the basic idea on ANN model and the most used method variants are presented.

Let x i = (x i1 , x i2 , . . . , x in ) be the input vector considered as one neuron i and y i the output where n represents the number of layers, then the result of y i is given by the following formula [START_REF] Peter | Handbook of measuring system design[END_REF]:

y i = f (net(x i )) (3.60)
where f is the activation function and net is called Network input. It is very popular such as the sum function given below [START_REF] Kriesel | A brief Introduction to Neural Networks[END_REF]:

net(x i ) = n j=1 w ij x ij (3.61)
where w i = (w i1 , . . . w in ) is the wight vector.

For the output value y i , the simplest way to compute the activation function is following threshold level system given below:

y = f θ (x) =      1 if x > θ 0 otherwise (3.62)
where θ is the threshold. The formula given in equation (3.62) is the basic idea explored by McCulloch and Pitts in 1943. Many other variants and extensions were explored such as Hebb's method [START_REF] Peter | Handbook of measuring system design[END_REF] and Auto Regressive (AR) model [START_REF] Haykin | A comprehensive foundation[END_REF].

The introduction of hidden layers was introduced with the iteration concept between two instants following some conditions. Let g called the propagation function, then:

net j = g(o j , w j ) (3.63)
where o j defines the output of the neuron calculated using equation (3.60).

The propagation function g depends on the acceptance condition of the output o j and controls the evolution of the weight vector w j . There exist different models developed in the literature. The three models are detailed below:

• Hebbian learning: The basic idea of interconnection of two neurons simultaneously.

w j (t + 1) = w j (t) + x j o j (t) (3.64)
• Perceptron learning rule: It was introduced for single layer for linearly independent problems.

w j (t + 1) = w j (t) + δw j with δw j = η(o j (t) -y j (t))x j (3.65) where η is the learning rate.

• Back propagation learning: it defines the multiple layer and it can approximate the nonlinear functions to arbitrary accuracy.

∆w ij (t + 1) = η δE δw i,j + α∆(t) (3.66)
where E designs the average square error, η and α are the learning rate and the momentum respectively.

The last step is the activation function as given by f in equation (3.60) is also explored to make border between classes. Two common activation functions are used [START_REF] Kriesel | A brief Introduction to Neural Networks[END_REF], threshold function following some threshold θ given by f θ (x) in equation (3.62).

The second common function is the logistic which is differentiable and used in the continuous models, as given by the following equation:

f (x) = 1 1 + e -x (3.67)
Thus, f is a continuous function belonging to the interval [0, 1].

Validation of the Results

The validation of the results step is a statistical method to prove that there is an independence in the choice of training and test sets. The cross validation method [START_REF] Kohavi | A study of cross-validation and bootstrap for accuracy estimation and model selection[END_REF][START_REF] Burman | A comparative study of ordinary cross-validation, v-fold crossvalidation and the repeated learning-testing methods[END_REF] is the most used in skin cancer recognition. As reported by Massod et al. [START_REF] Masood | Computer aided diagnostic support system for skin cancer: a review of techniques and algorithms[END_REF], some articles do not report comparison and cross-validation for their results. They suggested that it is imperative to present in papers these details for the validity of the used methods.

Therefore, to validate the obtained results, the random cross-validation and n-fold cross validation methods [START_REF] Kohavi | A study of cross-validation and bootstrap for accuracy estimation and model selection[END_REF][START_REF] Burman | A comparative study of ordinary cross-validation, v-fold crossvalidation and the repeated learning-testing methods[END_REF] are applied in the literature. 10-fold cross validation method is the most used in skin cancer. It was used by Barata et al. [START_REF] Barata | A system for the detection of pigment network in dermoscopy images using directional filters[END_REF] for the region segmentation and lesion classification. Clawson et al. [START_REF] Kathy M Clawson | Analysis of pigmented skin lesion border irregularity using the harmonic wavelet transform[END_REF] and Abbas et al. [START_REF] Abbas | Pattern classification of dermoscopy images: A perceptually uniform model[END_REF] also applied 10-fold cross validation to validate their results. Two-cross validation is also used By Codella et al. [START_REF] Codella | Deep learning, sparse coding, and svm for melanoma recognition in dermoscopy images[END_REF]. Recently Barreiro et al. [START_REF] Raquel | Computerized medical diagnosis of melanocytic lesions based on the abcd approach[END_REF] used K-fold cross validation to present their result under ABCD rule for feature extraction and sensitivity, specificity and accuracy metrics to assess the result. The value of K began from 3 to 15.

D'Alesandro et al. [START_REF] Brian D'alessandro | Computer aided analysis of epi-illumination and transillumination images of skin lesions for diagnosis of skin cancers[END_REF], randomly repeated their proposed procedure 10 times to perform the average result, which is called random cross validation.

Performance Metrics

To measure how is close the prediction to the truth, the results of classifiers are evaluated following some performance metrics. Therefore, once the results attribution are computed, four sets are directly obtained:

• True Positives set contains all the malignant melanoma classified as malignant by the classifier used, and they are noted by TP.

• False positives set contains all the benign lesions incorrectly identified by the classifier used, and they noted FP.

• True Negatives set contains all the benign lesions classified as benign by the classifier used, and they are noted by TN.

• False negatives set contains all the malignant melanoma incorrectly identified by the classifier used, and they are noted FN.

The objective is to reduce the FP and FN to zeros. The false positives entrains more biopsies for medical doctors and analysts. In the other hand, the false negatives is more dangerous due to the non application of any medical treatment for these false negatives (unhealthy people) cases.

Several databases are used in different articles, therefore, for comparison, it is preferable to compute a percentage of detection or precision. For that, many performance equations are suggested and applied on skin cancer classification [START_REF] Masood | Computer aided diagnostic support system for skin cancer: a review of techniques and algorithms[END_REF]. The most used performance metrics in melanoma recognition are detailed below:

• Accuracy (Acc):

Acc = T P + T N T P + T N + F P + F N × 100% (3.68)
• Sensitivity (Sen):

Sen = T P T P + F N × 100% (3.69)
• Specificity (Spe):

Spe = T N T N + F P × 100% (3.70)
• Positive predictive value (PPR):

P P R = T P T P + F P × 100% (3.71)
• Negative predictive value (NPR):

N P R = T N T N + F N × 100% (3.72)
• Error probability (Ep):

Ep = F P + F N T P + T N + F P + F N × 100% (3.73)
• ROC curve : a plot of the true positives TP-rate versus false positives FP-rate.

These metrics are evaluated for classification and recognition step. But, they can be adapted for segmentation results, for example, attributing the variables FP, TP, FN and TN to pixels belonging into regions of interest or background.

Summary

This chapter introduced a mathematical background of the different methods used in next chapter. It provides as well a deep theoretical understanding of these methods.

The chapter is divided into four parts: In this chapter, the methods developed on skin cancer detection and recognition that can be used in CAD system are presented. Two domains are mainly developed, which are:

1. Segmentation of skin lesion using the adaption of Chan and Vese model for skin cancer images. This adaption can be seen as an extension of the model for other kind of images.

2. Classification of malignant and benign skin lesion using a new method based on border irregularities.

3. Classification of into malignant and benign lesions using a fusion of structural and textural features.

In this chapter, two domains are developed, the first domain is highlighted and discussed in section 4.2. This method is an adapted segmentation for skin cancer images.

It is focused to detect the border between the lesion and the background, and the main variation inside the lesion. The second domain is focused on features extraction presented in section 4.3, where two methods are developed. Firstly, border irregularities information is extracted for each lesion to build a descriptor separating the lesions into malignant and benign cases. Secondly, a fusion of structural and textural features using multiresolution analysis (wavelet and curvelet transforms) and local binary pattern is developed.

Segmentation

In this section, the proposed extension of Chan and Vese model is introduced as follow:

• Firstly, the work developed by Chan and Vese in 2001 [START_REF] Tony | Active contours without edges[END_REF] is summarized.

• Secondly, the generalization developed by Vese and Chan in 2002 [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF],

• Thirdly, the generalization proposed by Li et al. [START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF] in 2010.

• Finally, the proposed extension and adaption of Chand and Vese model

The basic idea of total variation segmentation and a brief theory of Chan and Vese model was introduced in the last chapter (section 3.2).

Chan and Vese Model

Chan and Vese model is introduced in [START_REF] Tony | Active contours without edges[END_REF] and its generalization in [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF]. The following definition is the one adapted for image segmentation. This method is used to minimize Mumford and Shah equation [START_REF] Mumford | Optimal approximations by piecewise smooth functions and associated variational problems[END_REF] Let Ω be open and bounded set and C an evolving curve in Ω. We consider C

H(z) =      1 if z ≥ 0 0 if z < 0
The length of C and the area of ω can be expressed respectively by [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF]:

|C| = Ω |∇H(φ)|, |ω| = Ω H(φ)dxdy (4.2)
Thus, Chan and Vese model is expressed by the following formula [START_REF] Tony | Active contours without edges[END_REF]:

F (c 1 , c 2 ) = Ω (u 0 -c 1 ) 2 H(φ)dxdy + Ω (u 0 -c 2 ) 2 (1 -H(φ))dxdy (4.3)
+ Ω |∇H(φ)|
Where c 1 and c 2 are the averages of u 0 inside the curve C (area of ω) and respectively outside (area of Ω \ ω). These constants (c 1 and c 2 ) are given by the formula (4.4) and (4.5) after approximation and regularization.

Considering H ε and δ ε any C 1 approximation and regularization of H and δ 0 function, as ε → 0 and with H ε = δ ε . The constants c 1 and c 2 are given by the following formula:

c 1 (φ) = Ω u 0 (x, y)H ε (φ(t, x, y))dxdy Ω H ε (φ(t, x, y))dxdy , (4.4) c 2 (φ) = Ω u 0 (x, y)H ε (1 -φ(t, x, y))dxdy Ω H ε (1 -φ(t, x, y))dxdy , (4.5)

Generalization of Chan and Vese model

The first generalization of this method was proposed by the same authors [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF]. Using a union of zero level set functions φ i , equation (4.3) becomes:

F n (c, Φ) = 1≤I≤2 m Ω (u 0 -c I ) 2 χ I dxdy + 1≤i≤m ν Ω |∇H(φ i )|. ( 4
F ({u i } m i=1 , {c k } N k=1 ) = m i=1 Ω |∇u i |dx + λ N k=1 Ω |u 0 -c k |M N k dx (4.7)
where for level set function φ i . Therefore, for each number of zero set level functions φ i , all possible configurations are studied. Furthermore, the challenge is to choose the best configuration for the segmentation of a given image without fixing the number of φ i beforehand. In this work, the detection of three regions (N = 3) are developed using 2 zero level set functions. An overview for four and five regions is also discussed.

k 0 = N -2 m-1 , k 1 = k -k 0 and b m,k-1 i = 0 ∨ 1 with S m k = m i=1 b m,k 1 i , then:              M 2 m k = (-1) s m k Π m i=1 (u i -b m,k-1 i ) if N = 2 m M N k = (-1) s m k Π m i=1 (u i -b m,k-1 i ) if 2 m-1 < N < 2 m and k = 1, • • • , k 0 M N k = (-1) s m-1 k 1 Π m i=1 (u i -b m-1,k-1 i ) if 2 m-1 < N < 2 m and k = 2k 0 + 1, • • • , N (4.8)
In the general case, the energy of minimization given in equation (4.3) becomes another minimization which takes all the possible combinations for each number of zero level sets:

F N = inf N,j inf c,Φ F N j (4.12)
where j designates the j th combination.

Detection of three regions

To detect three regions, exactly two zero level set functions φ 1 and φ 2 are needed. Thus, to study the case N = 3, figures F 32 . Then F 31 is:

F 31 (c, φ) = Ω (u 0 -c 01 ) 2 (1 -H(φ 1 ))H(φ 2 )dxdy + Ω (u 0 -c 10 ) 2 H(φ 1 )(1 -H(φ 2 ))dxdy + Ω (u 0 -c 00 ) 2 (1 -H(φ 1 ))(1 -H(φ 2 ))dxdy + ν Ω |∇H(φ 1 )| + ν Ω |∇H(φ 2 )| (4.13)
and

F 32 (c, φ) = Ω (u 0 -c 11 ) 2 H(φ 1 )H(φ 2 )dxdy + Ω (u 0 -c 10 ) 2 H(φ 1 )(1 -H(φ 2 ))dxdy + Ω (u 0 -c 00 ) 2 (1 -H(φ 1 ))(1 -H(φ 2 ))dxdy + ν Ω |∇H(φ 1 )| + ν Ω |∇H(φ 2 )| (4.14)
where c = (c 00 , c 01 , c 10 , c 11 ), with: [START_REF] Maglogiannis | Overview of advanced computer vision systems for skin lesions characterization[END_REF])

c 11 = Ω u 0 H(φ 1 )H(φ 2 )dxdy Ω H(φ 1 )H(φ 2 )dxdy (4.15) c 10 = Ω u 0 H(φ 1 )(1 -H(φ 2 ))dxdy Ω H(φ 1 )(1 -H(φ 2 ))dxdy (4.
c 01 = Ω u 0 (1 -H(φ 1 ))H(φ 2 )dxdy Ω (1 -H(φ 1
))H(φ 2 )dxdy (4.17)

c 00 = Ω u 0 (1 -H(φ 1 ))(1 -H(φ 2 ))dxdy Ω (1 -H(φ 1 ))(1 -H(φ 2 ))dxdy (4.18)
In this special case, equation (4.12) treats only two configurations expressed by equations (4.13) and (4.14) illustrated by figures 4.4 and 4.5. Thus the energy of the image given is expressed by the following formula:

F 3 = inf (inf c,Φ F 31 , inf c,Φ F 32 ) (4.19)
Using equation (4.13) and (4.14), the comparison will be only between the third component of each equation, then equation (4.19) becomes:

F 3 = Ω (u 0 -c 10 ) 2 H(φ 1 )(1 -H(φ 2 ))dxdy + Ω (u 0 -c 00 ) 2 (1 -H(φ 1 ))(1 -H(φ 2 ))dxdy + ν Ω |∇H(φ 1 )| + ν Ω |∇H(φ 2 )| + inf α 1 , α 2 (4.20)
where

α 1 = Ω (u 0 -c 11 ) 2 H(φ 1 )(H(φ 2 ))dxdy (4.21) α 2 = Ω (u 0 -c 01 ) 2 (1 -H(φ 1 ))H(φ 2 )dxdy (4.22)
The algorithm will not be more complex in computing, because the comparison is conducted only between the different parts (α 1 and α 2 ). For example, the background of the image will be computed once.

In the case where α 2 given in equation (4.22) is minimum then φ 2 ⊂ φ 1 as illustrated by figure 4.5. In this case, if φ 1 < 0, it means automatically φ 2 < 0 i.e (1 -H(φ 1 ))(1 -

H(φ 2 )) is equivalent to (1 -H(φ 1 )
), then equation 4.20 is simplified as follow:

F 3 = Ω (u 0 -c 10 ) 2 H(φ 1 )(1 -H(φ 2 ))dxdy + Ω (u 0 -c 01 ) 2 (1 -H(φ 1 ))H(φ 2 )dxdy + Ω (u 0 -c 00 ) 2 (1 -H(φ 1 ))dxdy + ν Ω |∇H(φ 1 )| + ν Ω |∇H(φ 2 )| (4.23)
This formulation joints M 3 of equation (4.9) developed by Li et al. [START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF], where it depends only on φ 1 .

Using a regularized version of H and the Dirac delta function δ 0 by H ε and δ ε respectively. Introducing an artificial time t > 0 in the Lipschitz function φ(t, x, y)

with φ(0, x, y) = φ 0 (x, y) as used by Chan and Vese [START_REF] Tony | Active contours without edges[END_REF][START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF]. Keeping c as fixed vector, and minimizing F 31 and F 32. The initial contour is giving by the following formulas:

• For F 31:

∂φ 1 ∂t = δ ε (φ 1 ) ν div ∇φ 1 |∇φ 1 | --(u 0 -c 01 ) 2 H(φ 2 ) + (u 0 -c 10 ) 2 -(u 0 -c 00 ) (1 -H(φ 2 )) (4.24) ∂φ 2 ∂t = δ ε (φ 2 ) ν div ∇φ 2 |∇φ 2 | --(u 0 -c 10 ) 2 H(φ 1 ) + (u 0 -c 01 ) 2 -(u 0 -c 00 ) (1 -H(φ 1 )) (4.25)
• For F 32:

∂φ 1 ∂t = δ ε (φ 1 ) ν div ∇φ 1 |∇φ 1 | -(u 0 -c 11 )H(φ 2 ) ((u 0 -c 10 ) 2 -(u 0 -c 00 ) 2 )(1 -H(φ 2 )) (4.26) ∂φ 2 ∂t = δ ε (φ 2 ) ν div ∇φ 2 |∇φ 2 | -(u 0 -c 11 ) 2 -(u 0 -c 10 ) H(φ 1 ) -(u 0 -c 00 ) 2 )(1 -H(φ 1 )) (4.27)
The soft smooth membership function u i ∈ [0, 1] introduced by Li et al. [START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF] for H 1 regularization is used. Then, in the current studied case, H(φ 1 ) and H(φ 2 ) are replaced by u 1 and u 2 respectively. These functions are introduced to verify the constraint of summation of all membership functions as required by Shen et al. [START_REF] Jianhong | A stochastic-variational model for soft mumford-shah segmentation[END_REF]. Therefore, our system will be presented by the following functions:

• F 31 will be defined by: (1 -u 1 )u 2 , u 1 (1 -u 2 ) and (1 -u 1 )(1 -u 2 ).

• F 32 will be defined by: u 1 u 2 , u 2 (1 -u 1 ) and (1 -u 1 )(1 -u 2 ).

For the energy F 31 given in equation (4.13) and illustrated in figure 4.4, to put the potential intersection in one of the sets and to respond to the constraint of summation, the following combination: Therefore, the constraint of summation is satisfied and the current combination will be presented by: u 1 u 1 , u 2 (1 -u 1 ) and 1 -u 2 . It corresponds to the combination developed by Li et al [START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF]. By symmetry this combination can be expressed by:

u 1 , u 2 (1 -u 1 ) and (1 -u 1 )(1 -u 2 ) is proposed. Therefore,
u 1 u 2 , u 1 (1 -u 2 ) and 1 -u 1 .
Then, all the possible configurations by the following system are encompassed as follow:

     u 1 , u 2 (1 -u 1 ), (1 -u 1 )(1 -u 2 ) u 1 u 2 , u 2 (1 -u 1 ), 1 -u 1 (4.28)
The system given in equation (4.28) is applied on skin images database. The obtained results and the implementation are illustrated in figures 4.12 and 4.13a in the next sub-section (4.2.3.5).

Extension to detect four regions

This extension developed can be adapted for the detection of more than 3 regions. Thus, to detect four regions, Li et al. [START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF] explored the one developed by Vese and Chan [START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF] using only two sets with intersection as illustrated in figure 4.2.

To detect four regions, a minimum of two sets and a maximum of three sets is needed. The possible configurations are illustrated below with the corresponding equation systems using soft membership function u i where numerically u i = H(φ i ). The proposed systems satisfy the constraint of summation of all membership function to be one given in equation (4.11). At all, 5 configurations are obtained, one configuration using two sets and four configurations using three sets as detailed below:

1. Using two sets φ 1 and φ 2 , there is only one possible configuration to get 4 different regions. It is the alone case developed for total variation segmentation.

                   u 1 u 2 u 1 (1 -u 2 ) u 2 (1 -u 1 ) (1 -u 1 )(1 -u 2 )
2. Using three sets, the first configuration is presented by total separability between

                   u 3 u 2 (1 -u 3 ) u 1 (1 -u 2 )(1 -u 3 ) (1 -u 1 )(1 -u 2 )(1 -u 3 )
3. The second configuration using three sets to detect four regions is characterized by the mixture between inclusion and separability as illustrated below. It illustrates separability between φ 2 and φ 3 and inclusion of φ 1 in φ 2 .

Figure 4.8: Four regions using two level set functions φ 1 , φ 2 and φ 3 using separation-inclusion

                   u 3 u 1 u 2 (1 -u 3 ) u 2 (1 -u 1 )(1 -u 3 ) (1 -u 2 )(1 -u 3 )
4. The third configuration using three sets to detect four regions is characterized by the mixture between inclusion of the two sets and their separability as illustrated below. It illustrates separability between φ 1 and φ 2 and inclusion of φ 1 and φ 2 in φ 3 .

Figure 4.9: Four regions using two level set functions φ 1 , φ 2 and φ 3 using inclusion-separation.

                   u 1 u 3 u 2 u 3 (1 -u 1 ) u 3 (1 -u 1 )(1 -u 2 ) (1 -u 3 )
5. The last configuration using three sets is presented only by the inclusion of sets as illustrated below. This configuration is equivalent to case developed to detect 3 regions illustrated in figure 4.5.

Figure 4.10: Four regions using two level set functions φ 1 , φ 2 and φ 3 using total inclusion.

                   u 1 u 2 u 3 u 2 (1 -u 1 ) u 3 (1 -u 1 )(1 -u 2 ) (1 -u 2 )(1 -u 3 )

Extension for five regions

To detect 5 regions, 12 configurations are possible. Thus, the minimum of sets (φ i )

required is three and the maximum is four. Therefore, 4 possible configurations in case of three sets (φ i ) and 8 possible configurations in the case of four sets (φ i ) are obtained.

comparison with Generalization of Chan and vese model

Implementation and illustration

The implementation of the proposed method is applied on skin cancer images. The illustration of some cases to present the method and its visual effect are shown. The image used in these figures (4.12 and 4.13) is taken from DermIs (http:

//www.dermis.net) under the name SSM34.

In the next chapter ( 5), the application of this method is analyzed and discussed.

More examples are given and compared to the previous approaches on standard camera skin cancer images. The result of the segmentation are also evaluated by three experts.

Feature Extraction

Overview

The random development of skin lesions, specially melanoma cases, complicate the classification and the recognition of malignant skin lesions. Therefore, there is a need to develop a discriminant set of features to well classify using CAD system.

In the current section, two distinct methods are developed to recognize benign and malignant lesions. For dermoscopic images, the fusion of structural and textural features is explored, as explained in subsection 4.3.2, and for standard camera images, the border irregularity features is presented in section 4.3.3.

Structural and textural features

The multitude of skin cancer lesions, benign and malignant, complicates the recognition of skin cancer. In addition to that, melanoma is developing randomly in different directions. However, finding the best descriptor to discriminate melanoma is one of the hardest task in medical image processing. In the current study, a set of discriminating features obtained from different descriptors to distinguish benign and malignant cases The fusion of two descriptors introduced in the last chapter (see section 3.3) are explored. Therefore, a set of structural features from multi-resolution analysis methods (wavelet and curvelet coefficients) are used. Further, local binary pattern (LBP) operator is used to extract the textural features. The method is also presented in section 3.4. The details and the implementation of the proposed approach are explained below.

1. First, the structural features are extracted using wavelet and curvelet coefficients.

Two level decompositions of Discrete Wavelet Transform (DWT) and Fast Digital Curvelet Transform (FDCT) via warping (see section 3.3) are applied on the melanoma region of interest (ROIs). For each coefficient matrix seven statistical features were computed namely: Energy, Entropy, M ean, Standard deviation, M aximum, M oment and Homogeneity.

Second, a set of textural features using different variants of local binary pattern

(LBP) i.e. rotationally invariant, uniform and non-uniform rotationally invariant distinct textures features are extracted.

3. Then, a feature fusion is performed using the concatenation of structural and textural features of each image.

4. Lastly, SVM classifier is used for classification and diagnosis. Then, 1000-random sampling cross validation is explored to validate the obtained results.

Structural features

The structural features are extracted as follow:

• For wavelet, we used Daubechies 4 waveform, then 8 coefficient matrices are computed, 4 from the first level and 4 from the second level (one approximation coefficient matrix and three details coefficient matrices) using equations (3.34) to (3.37). In total, we extracted 64 features from wavelet transforms.

• For two level of curvelet decomposition 9 curvelet coefficient matrices were obtained for each image i.e. 1 matrix from the first level and 8 matrices from the second level. These matrices are built using equation (3.45) detailed in the next section. Thus for each level, seven statistical features were computed. Thus a total of 63 features from curvelet two level decompostion were obtained.

Textural features

For textural features, Local Binary Pattern (LBP) operator is used to extract local textural variations. Thus, depending on the variant of LBP operator as detailed in section 3.4, three LBP variants are explored in the current work. Therefore, we have:

• 59 textural features from LBP u2 (Uniform pattern).

• 36 from LBP ri (invariant rotation).

• 9 from LBP riu2 (Invariant rotation uniform pattern).

Indeed, only radius R = 1 and eight neighborhood pixels (P = 8) are used in the experiments. Here it is worth mentioning that all the features were normalized to the range [0 -1] and their influence before and after fusion can be recorded in validation performances.

Implementation

The proposed approach is implemented on the public database PH 2 presented by Mendocca et al. [START_REF] Mendonça | Ph 2-a dermoscopic image database for research and benchmarking[END_REF]. A descriptive and statistical analysis of the database is also achieved and presented in next chapter. The result of this analysis is compared to the known ABCD rule used in the hospitals.

Many implementations are computed separately and/or by combination between structural and textural features selected. The obtained results of the three variants of LBP methods (invariant rotation LBP, uniform Pattern LBP and invariant rotation uniform pattern LBP), wavelet and curvelet coefficients, and the different combination are validated using random sampling cross validation under SVM classifier with linear kernel. Then, a comparison with the exiting results in the literature using the same database is also achieved. The results are presented and discussed in chapter 5.

Border Irregularity Features

The geometrical characteristics of borders are explored by the approach developed in this section. Therefore, the proposed work is divided mainly into two main stages. First, the standardization of image direction which is a kind of normalization of the database to have the same view for all images. Second, the border feature are extracted using two new concepts, valleys and crevasses, to explore the irregularities for diagnosis.

Border feature extraction

The border irregularities are one of the widely visible features to explore for discrimination. However, the benign lesion borders are not so smooth to fit them with a mathematical function. Malignant and benign lesions can be developed in different ways as indexed by Lee et al. [START_REF] Tim K Lee | Irregularity index: a new border irregularity measure for cutaneous melanocytic lesions[END_REF]. The construction of these features is started by the idea of evaluation of border irregularities exploring different features which are more local.

It is based on algorithm detecting each two consecutive null derivation of the border curve. However, it is very difficult to formulate the analytic function of each lesion border. Then, an new algorithm is implemented to express this need. Two new concepts, valleys and crevasses, are extracted as first and second level of border irregularity.

To detect these new concepts, a newer and simpler algorithm exploring the border irregularities in four directions is proposed. The horizontal direction explores all pixels from right to left and vice versa, and vertical direction explores the pixels from up to down and vice versa. approach. This algorithm is applied on the standard oriented images explained in the last sub-section (

The four directions shown in Figure 4.16 are divided into two groups, horizontal and vertical. Thus, for each line and column of pixels, the area between the box limit and the first contact of the arrow with the ROI's edge are isolated and removed. Thus, only the missed areas are kept. Therefore, if the border is more regular, all the outside part of the pigment will be detected and removed. In the other case, more the border is irregular, more it misses many parts of the outside part of the pigment.

Two kinds of missed parts are noted. Firstly, valley part is the missed one using only one direction (horizontal or vertical) separately. Secondly, the crevasse part is the missed one using both directions in the same time, the crevasse have almost the cul-desac geometrical form. Figure 4.17 illustrates the valley and the crevasse cases. They can be considered as the first and the second level of the border irregularities.

These border irregularities quantified by the valleys and crevasses are used as features exploring the size and number of the concepts detected. Thus, let v denotes valleys and c crevasses, two counting functions are defined, N to compute the number of areas detected and S to compute the size of each area detected. Therefore, 8 features are extracted and divided in 2 groups, globals and locals. The global ones are the features not depending on some thresholds and the local ones are those depending on these thresholds. The choice of these global and local features is done gradually to increase the performance of classification between the malignant and benign lesions.

The first group contains 4 global features concerning the total number of valleys and crevasses detected and their total size as detailed below.

• N (v) is the number of valleys and N (c) is the number of crevasses.

• S(v) is the size of all valleys and S(c) is the size of all crevasses.

The second group contains 3 other features computing the number and the size of detected valleys and crevasses greater or smaller than two thresholds τ v and τ c respectively.

These features are added in order to increase the performance of detection and decreasing the noises of border segmentation i.e a crevasse detected with a size of one or two pixels will be less important than a crevasse of fifty pixels of size, for example. Then, the following equations are formulating these three local features.

• N (1 S(v)≥τv ) and N (1 S(v)<τv ) quantify the number of valleys greater/smaller than the threshold τ v .

• N (1 S(c)≥τc ) quantify the number of crevasses greater than the threshold τ c where,

1 S(x)≥τ =      1 S(x) ≥ τ 0 otherwise , with      x ∈ {v, c} τ ∈ {τ v , τ c } (4.29)
Finally, the eighth features is the ratio of pigment pixels over the box area, this feature is introduced to moderate the differences of image dimensions in the database which are standard camera dataset with different size. It contains also information due the global border irregularity i.e after standardization step, the area of the background of the image is minimized, then the ratio is behaving like the relation of p-norms, where the border defines the 2-norm and the box the inf -norm as illustrated in figure 4.18.

This value is defined by Γ-value given by the following equation:

Γ = Area(r) Area(b) (4.30)
where r denotes the Region of Interest (ROI) and b the selected box containing the ROI. Therefore, combining all the characteristics defined above, for each image a set of 8 features are extracted, as summarized by the variable f eat given by equation (4.31):

f eat = N (v), N (c), N (s(v)), N (s(c)), N (1 s(v)≥τv ), N (1 s(v)<τv ), N (1 s(c)≥τc ), Γ (4.31)
where τ v , τ c ∈ N chosen empirically. In the implementation of the algorithm, τ c is fixed to 2 and τ v ∈ [0, 100].

The two steps of the current approach is implemented on skin database provided from standard camera. The results are presented and discussed in the next chapter.

Summary

This chapter provides the three methods developed in the current work.

• Firstly, the extension of Chan and Vese model is explored, which is a generalization of the model and an adaption for skin cancer images characteristics. It was adapted to segment the small details inside the lesions, such as colors and pigment areas and structures.

• Secondly, a fusion by concatenation of structural and textural features are explored and developed to discriminate benign and malignant pigment skin lesions.

The structural features are obtained exploring a wavelet and curvelet transforms, while the textural features are obtained exploring local binary pattern operator.

• Thirdly, a method based on border irregularities is developed, introducing two new concepts in skin images which are valleys and crevasses as first and second level of border irregularities. A normalization of skin cancer view is also proposed in the method as preprocessing step.

The proposed methods are applied on skin cancer databases. The results are presented in the next chapter.

CHAPTER 5

RESULTS AND DISCUSSION

Overview

The obtained results from the three proposed methods of the current work are presented and discussed in this chapter. Firstly, it started by the introduction of the different databases used which are dermoscopic images and standard camera images. Secondly, it is followed by the obtained results from the three methods developed which are, segmentation of the region of interest using the extension of Chan and Vese model, the fusion of textural and structural features and border irregularity features. Finally, the comparison of the obtained results with the existing methods is performed.

Datasets

Two different acquisition of database, dermoscopic and standard camera images, are used in the current work divided following their acquisition mode into dermoscopic and standard camera images. The two sets contains 406 images, 200 are dermoscopic and 206 are from standard camera. The two databases, dermoscopic and standard camera images, are presented in subsections 5.2.1 and 5.2.3, respectively.

Dermoscopic Images Database

PH 2 Database was introduced in 2013 by Mendoca et all. [START_REF] Mendonça | Ph 2-a dermoscopic image database for research and benchmarking[END_REF] and more detailed in 2015 by the same authors [START_REF] Mendonça | Ph2: A public database for the analysis of dermoscopic images[END_REF]. PH 2 is a public and free database, built to perform and Based on the given features in table 5.1, intuitively, the most difficult is to recognize the atypical nevus. Thus, for example the asymmetry feature makes a real border between common nevus and melanoma only. The pigment network feature separates more common nevus with a total absent of pigment network to atypical and melanoma.

However the dots/globules features are not descriptive between the three cases. We can observe also that streaks and regression area features are more common in common nevus and atypical nevus than melanoma. Blue-whitish veil discriminates better between benign and malignant compared to other features. Finally, the color increases gradually from common nevus to melanoma.

Another way of reading table 5.1 is horizontally. Indeed, it shows the influence of each sub-feature. For example, the typical Dot/Globules feature is more frequently in common nevus than atypical nevus and almost inexistent in melanoma case. However, the atypical Dot/Globules feature shows an opposite behavior with a high presence in melanoma, less in atypical nevus and rarely present in common nevus. A statistical analysis of the database is performed and compared to a based scoring system used in the hospitals in the next sub-section.

From the table 5.1, it can be seen that:

• Asymmetry makes a border between common nevus and melanomas with 96.25%

fully symmetric for common nevus and 82.5% fully asymmetric for melanoma.

However, for atypical nevus, the asymmetry feature is not significant as shown in the table with 43.75%, 33.75% and 22.5 for asymmetry, symmetric in 1 axis and fully asymmetric, respectively.

• The pigment network feature makes a border common nevus in one side with 100% typical network and in the other side atypical and melanoma with 96.25% and 97.5% respectively for atypical pigment network feature.

• Dots / Globules feature is more typical for common nevus than atypical nevus and melanoma with 57.5%, 10% and 0%, respectively. Then, the opposite behavior is visible for atypical, where it is rare in commons nevus with 6.25% and more present in atypical nevus and melanoma with 40% and 55%, respectively.

• Streaks feature is more discriminating between common nevus in one side and atypical nevus and melanoma in other side when it is present. However, when it is absent, it is very difficult to conclude regarding the percentage of absence of streaks of common, atypical and melanoma, which are 98.75%, 80% and 67.5%, respectively.

• Regression area is describing the common nevus by the total absence, and more it is present, more there is a high probability to get melanoma.

• Blue-whitish veil has the same behavior than regression area, where is more absent for common and atypical nevus and more present for melanoma.

• Color feature is discriminating melanoma if three or more colors are detected with a percentage of 67.5%, and discriminating common and atypical nevus if two colors or less are detected with a percentage of 96.25% and 88.75%, respectively.

Significance of the database

The significance and the representativeness of the database in medical images is one the most challenging task. The information given by the current database contain almost ABCD rule developed by Stolz et al. [START_REF] Stolz | Abcd rule of dermatoscopy-a new practical method for early recognition of malignant-melanoma[END_REF] and used for comparison by Capdehourat et al. [1] and Dolianitis et al. [START_REF] Dolianitis | Comparative performance of 4 dermoscopic algorithms by nonexperts for the diagnosis of melanocytic lesions[END_REF].

The PH 2 database quantifies each pigment following ABCD rule excepting border irregularities. According to Capdehourat et al. [1], the evaluation of ABCD rule follows the scores summarized in the table 1.1 where dermoscopic structures contains pigment network, structures ares, dots, globules and branched streaks. The authors added to these features Blue-whitish veil which is a major criteria of 7-point checklist [1] system.

This scoring system is applied on the features described in table 5.1. It followed the method used by Capdehourat et al. [1] where :

• Asymmetry is evaluated from 0 to 2 , with 0 being fully symmetric, 1 for symmetric in one axis and 2 for fully asymmetric. It has the highest weight factor of

1.3.
• Border is evaluated with score from 0 to 8, drawing eight segments; one point is given for each abrupt pigment cutoff with a weight factor of 0.1.

• Color is evaluated from 1 to 6, attributing one point for each color with a weight factor of 0.5. Colors considered are white, red, black, light brown, dark brown and blue-gray.

• Dermoscopic structures encompass five structures which are: pigment network, structureless area, dots, globules and branched streaks. One point per structure with a weight factor of 0.5.

We notice that there are some differences between extracted features in PH 2 database and ABCD rule. Therefore, the threshold of the scoring system is adapted by removing the contribution of border irregularities. Then, the thresholds 4.75 and 5.45 became 4.50 and 5.20, respectively. Therefore, for each image the obtained score value (S abcd ) of the function given in equation (1.1) is evaluated as follow:

• benign: if the score is S abcd < 4.50,

• clinical doubt: lesion if the score lies between 4.50 ≤ S abcd ≤ 5.20,

• malignant: if the score is S abcd > 5.20.

Figure 5.1: ANOVA test results

There are other characteristic explored in the database, such as blue-whitish veil, not used in ABCD rule, but used in another scoring system which is 7-point checklist [1].

However, the objective evaluation is difficult to be achieved due the visual features characterized depending only on the decision of absence or presence of each characteristic.

The results reported by Dolianitis et al. [START_REF] Dolianitis | Comparative performance of 4 dermoscopic algorithms by nonexperts for the diagnosis of melanocytic lesions[END_REF] are presented in the table 5.2. They are compared to the results obtained from PH 2 database applying ABCD rule. These results show a similar behavior and equivalent results for the three performance metrics which are sensitivity, specificity and accuracy. The threshold of ABCD rule, given in the table ??, applied on PH 2 database was adapted taking in consideration the missing values of border irregularities. Then, the value of the threshold is reduced to 4.5 and 5.20 in place of 4.75 and 5.45 respectively. two methods, given by equation (4. [START_REF] Raquel | Computerized medical diagnosis of melanocytic lesions based on the abcd approach[END_REF], is not performed in the current work. Then, the results obtained using both methods are presented and illustrated.

Segmentation by Inclusion

In this section, equation (4.14) is applied as illustrated. From these examples, it can be seen easily that the algorithm developed follow perfectly the inclusion method explained in section 4.2. The segmentation by inclusion has an effect very important to distinguish between the different lesion darkness regions.

In Figure 5.5, four images are illustrated using the inclusion segmentation method.

The first column of the figure shows the original images segmented, the second column illustrates the results of segmentation and finally the third one shows the different regions segmented accounting the background. In the second column, the size of images is reduced to show better the different lesions. The current method is very sensible to noises and borders inhomogeneity [START_REF] Wang | An efficient local chan-vese model for image segmentation[END_REF], as it can be visible in the sub-figure5.5h. For each image, all parameters used in the illustrated segmentation are given. Therefore, we notice that the parameter ν and dt are different for each image and chosen manually.

These dependent parameters make the method very difficult for the automation.

Segmentation by Separation

The implementation of this second method provides the expected results as shown in figure 4.4. However, the separated cases in the current database are rarely visible due to the fast development of skin lesion [START_REF] Liu | Rate of growth in melanomas: characteristics and associations of rapidly growing melanomas[END_REF]. Knowing that our algorithm in this case searches only the convergence of two separated sets. The following examples in figure 5.6 are chosen to illustrate some possible cases .

Obtained results

The evaluation of the developed method is highlighted by a subjective evaluation performed by three image processing experts into acceptable and unacceptable segmentation. For each acceptable segmentation a 3 choices of evaluation is proposed which are excellent, good and average. Table 5.3 explains how the experts evaluated the proposed method. In the first step, the experts evaluated the segmentation into acceptable and unacceptable, and in the second step they evaluated separately the acceptable ones into excellent, good or average segmentation. The second intermediate evaluation makes in evidence further the possible improvement of the proposed method. For each expert, only the protocol of evaluation is explained without any influence on their evaluation. Table 5.4 reports the results of the subjective evaluation performed by two image processing expert (the first expert and the third expert) and medical expert (the second expert). Thus, from the database used, only 2.38% and 6.98% are evaluated as the unacceptable segmentation by the image processing experts respectively. However the medical expert evaluated 9.30% of images as Unacceptable segmentation. For the excellent segmentation, 96.06%, 48.84% and 13.95% are evaluated by the first, second and the third experts. We can notice that the difference between experts are more visible than unacceptable case. The same difference between the experts is visible for good and average segmentation. It can be seen that for the medical expert, the results of acceptable segmentation is lower than image processing experts. It is explained by the expert that it is not acceptable to miss a malignant parts of the lesion, because to succeed the treatment of cancer they have to treat the whole lesion, and the missing of a small part of lesion can develop other malignant cells. It can be concluded that in hospitals that the false negatives are considered more dangerous than false positives.

Therefore, we can conclude that the proposed method of segmentation highlights the random development of melanoma, it is extended from Chan and Vese model. The objective of current method is to follow the development of the whole lesion and its particular parts of the lesion. The results obtained show an acceptable detection and segmentation over than 90%, and only less than 10% of wrong detection or missed parts in the segmentation. The subjective evaluation is performed by two image processing experts and medical expert. However, to process the current method in a typical CAD system, more developments are needed, specially the automation of all parameters of the model. These points are also discussed in the next chapter in perspective section.

Multi-resolution analysis results

The results presented in this section refer to the method explained in section 4.3.2. To enhance the quality of images used, the computation of the result was forwarded by the hair removing preprocessing using DullRazor Software as detailed in subsection 5.4.2.

Applying the method on a database of 200 dermoscopic images from PH Depending on the variant of LBP operator as explained in section 3.4, we have 59 textural features from LBP u2 , 36 from LBP ri and 9 from LBP riu2 . Indeed, in the experiments only radius R = 1 and eight neighborhood pixels (P = 8) are used.

The evaluation of the proposed method is measured using three performance metrics which are sensitivity (sen), specificity (spe) and accuracy (acc) [START_REF] Emre Celebi | A state-of-the-art survey on lesion border detection in dermoscopy images[END_REF], as given in equations (5.1) to (5.3). The parameter α is added to compensate the difference of images number in the accuracy performance. This parameter is obtained by the following formula:

α = #Benign #M alignant (5.5)
Where #Benign and #M alignant design the number of benign and malignant images respectively. Therefore, α = 2 for the first and second classification (melanoma vs atypical, and melanoma vs common nevus) and α = 4 for the last classification (malignant and benign lesions). The performance results are computed also by accuracy given by equation (5.4).

Equation (5.4) can be also used with different values of the parameter α to give more weight for false negatives or false positives to tolerate or reject some special situations, such as let cancerous patients without treatment which are false negatives. In our case, the α chosen is used just to regulate the difference between benign and malignant lesions. This formulation is equivalent to (sen + spe)/2 used in Barata et al. [START_REF] Barata | Improving dermoscopy image classification using color constancy[END_REF]. In the next section, the results show a significant difference between the two metrics. To detect melanoma lesions, the results are classified into three cases . Firstly, we explored the classification between melanoma and atypical nevus. Secondly, we explored classification performance between melanoma and common nevus and finally we performed the classification between melanoma and the whole benign lesions. Three performance metrics i.e. sensitivity, specificity and accuracy/modified accuracy given by equations (5.1) to (5.4) are computed. For each performance, we compute also 1000 random combinations for the choice of the training and test sets which is the validation method N -random fold cross validation. In the result tables (5.7, 5.8 and 5.9), VP defines the validation performance and Std represents the standard deviation of the thousand combinations used for validation. The results are divided into three categories which are textural features using local binary pattern operator, structural features using wavelet and curvelet coefficients and finally the mixture of textural and structural features.

Hair removing

The preprocessing step is also implemented in the current work to enhance the image quality. Thus, DullRazor1 Software is used for hair removing, it was applied on all the visible hairs as illustrated in figure 5.10. In figure 5.10, two kinds of hair removal are presented, thick and thin, under DullRazor software. It can be seen easily that the skin lesion is more clear and less influenced by the treatment when the hair is thick than thin as illustrated by figures (b) and (d), respectively. Despite that, even in the worst scenario, the lesion is more clear and efficient than before the treatment.

Obtained Results

The recognition of melanoma can be easier or either more difficult depending on the benign lesions set used for classification. Therefore, to reduce this effect of the database, two studies are done for the classification and recognition of melanoma mixed with each set of benign lesions and compared. the other classification is done between melanoma and the whole benign lesions respecting the condition of representativity explained below.

For each classification, 12 evaluation performances are computed. The three variant of LBP operator, wavelet and curvelet coefficients for the non-fusion cases. Six combinations are computed from the fusion of structural features (wavelet and curvelet) with textural ones (LBP variants). Finally, wavelet and curvelet coefficients are mixed, as explored by Li et al. [START_REF] Li | Multifocus image fusion by combining curvelet and wavelet transform[END_REF] for image compression. Table 5.6 summarizes the number of features of the thirteen combinations studied in the current work. Each fusion is done by the concatenation of vectors obtained from each method. The next subsections present firstly the result classification obtained between melanoma and atypical nevus, then melanoma with common nevus and finally between malignant and benign cases.

Melanoma Vs Atypical Nevus

In this part, the classification is focused on the detection and the recognition of melanoma

Melanoma Vs Common Nevus

As mentioned above, the second classification is done only between melanoma and common nevus lesions. Table 5.8 shows the validation performance of sensitivity, specificity and accuracies metrics. Thus, for textural features, LBP ri and LBP u2 show a high performances than LBP riu2 , and it can be seen that LBP ri is more sensitive and less specific than LBP u2 . The textural features performances show that wavelet coefficients discriminate melanoma better than curvelet coefficients and the fusion of the structural and textural features contributes in the reduction of the variability between different combinations in validation step.

It can be seen that the best results validation is performed using wavelet and the fusion of wavelet with different variant of LBP with an accuracy of ≈ 90%. The fusion of wavelet and LBP u2 is the most stable operator showing the smallest standard deviation value for the three me. It can be seen that wavelet is showing better results than the fusion of wavelet and LPB variants. Therefore, it can be concluded that the fusion has not more contribution on the performance metrics, but the fusion is more contributing on the standard deviation of the results obtaining 4.92 for wavelet + LBP u2 compared to 5.65 obtained by wavelet.

Melanoma Vs Atypical and Common Nevus

The last performance of the current study is the classification between malignant (melanoma) and benign (atypical and common nevus) lesions. The results are presented in table 5.9.

Thus, for textural features, it can be seen that LBP ri is more sensitive and more accurate than the two other variants of LBP operator. The highest specificity results are obtained using LBP u2 with a smallest variation compared to the other variants of LBP. The accuracy validation results show 81.76% and 82.10% for LBP ri and LBP u2 respectively, and only 76.84% for LBP riu2 .

For structural features, wavelet coefficients showed a good performances compared to curvelet coefficients with an accuracy performance of 85.54% and 79.85% respectively. These results gives an opposite conclusion to the ones obtained by Abu Mahmoud et al. [START_REF] Abu | Wavelet and curvelet analysis for automatic identification of melanoma based on neural network classification[END_REF] where the authors concluded that curvelet coefficients are more efficient than wavelet ones. This results could depend on the database used or the nature of features extracted (for further studies and comparison, Daubechies 4 wavelet transform is used).

The fusion of the wavelet and LBP u2 increases considerably the specificity and the accuracy performances and only wavelet with LBP u2 for the sensitivity as shown in table 5.9. However the fusion doesn't show a significant effect on sensitivity performance for the fusion of wavelet with LBP ri and LBP riu2 respectively.

The best results for all the performances metrics validation is obtained by the fusion of wavelet coefficients and LBP u2 with 78.93% of sensitivity validation, 93.25 of specificity validation and 86.07% of accuracy validation. It shows also the smallest standard deviation for the thousand combination of random fold-cross validation used. However, it can be seen that the fusion is not contributing on specificity compared to wavelet features but it obtained the same performance over than 93%. The Sensitivity which is the evaluation of the number false negatives is lower approaching a performance of 79%, and it should be improved.

Analysis and comparison

From tables 5.7, 5.8 and 5.9, we can deduce by using the two sets of features (textural and structural) that the detection of melanoma mixed with common nevus is easier as compared with melanoma mixed with atypical nevus, which is expected as the class overlap between melanoma and common nevus is less than that between melanoma and atypical nevus. Thus, in table 5.8 we obtained the same behavior of common nevus comparing to ABCD rule scoring system illustrated in figure 5.3. We can conclude that the detection and the recognition performances of melanoma depends on the kind of the benign lesions used for computation.

The fusion of wavelet and LBP u2 outperforms all the tested methods in the current work, as it can be seen from the results in tables 5.7,5.8 and 5.9.

In general, curvelets have better performances than wavelets. However, in our case, the results obtained show better performances from wavelet coefficients compared to curvelet coefficients in the three tables. These results can be explained by the multitude of singularity points coming from the random development of skin cancer lesions. It could also be expressed by the redundancy of curvelet coefficients which represent the double of the redundancy of wavelet coefficients [START_REF] Jalal | Curvelets and ridgelets[END_REF].

As detailed in section 3.3, wavelets are efficient for singularity points and curvelets are more efficient for the detection or characterization of curves. Therefore, we also evaluate a fusion between the two sets of (wavelet and curvelet) coefficients as Li et al. [START_REF] Li | Multifocus image fusion by combining curvelet and wavelet transform[END_REF] used for image compression. Thus, the results obtained are not showing any significant improvement in the detection and classification of benign and malignant lesions. than those presented in tables 5.7, 5.8 and 5.9. Thus, the validation result step is crucial for the adaptability of the proposed method.

The known ABCD rule, often used in hospitals manually, has achieved an accuracy of 87.5% as in table 5.2. In this work, the proposed automation of the ABCD rule achieved an accuracy of 86.07% as in table 5.10, which is fairly comparable to the result obtained manually. This achievement shows a great potential of developing CAD system for melanoma detection.

In order to show the importance of the cross validation methods for the obtained results, table 5.11 reports the accuracy performance obtained for each combination of the 1000-random fold cross-validation used by the proposed method by intervals. Figure 5.11 illustrates the histograms of the thousand combinations. Thus, a probability of 0.633 to obtain an accuracy greater than 85% and only 0.141 to get an accuracy smaller than 80%, and a probability of 0.279 to get an accuracy greater than 90%. Then, without a cross validation methods, it will be difficult to compare objectively between methods.

To conclude, the proposed method achieved the second objective of the current work which is an exploration of sets of features to make a border between benign and malignant lesions. Thus the method shows a significant set of features describing better melanoma and benign lesions. The set of features includes textural and structural The obtained results are performed and validated using the fusion of different combinations of these features under SVM classifier. They are also compared to the previous results presented in the literature performed on the same free public database PH 2 . The recognition of melanoma were highlighted mixing with common nevus, atypical nevus and the whole benign lesions. The obtained results are validated using n-fold random sampling cross validation method. This validation is to increase the confidence of the obtained results on different databases which is very important in a typical CAD system.

The results show an accuracy performance of 86.07% for melanoma mixed with the whole benign lesions, 85.20% for melanoma mixed with atypical nevus and finally a performance accuracy of 90.17% for melanoma mixed common nevus. In fact, addition to the performance highlighted in this work, an other contribution consists on the dependence of the performances on the diversity of benign lesions. Thus, more there are common nevus cases, more the performances should be better as it can be seen from the results presented in the two tables 5.7 and 5.8 referring to atypical and common nevus,

Implementation

The implementation describes the preprocessing step detailed in section 5.5.1.1 as the first stage of the algorithm and the extraction of features from border irregularities given in section 4.3.3 as the second stage.

Standard view implementation

The single presentation and orientation of malignant and benign melanoma gives the same features characteristics for all images of the database. Therefore, the implementation of the Standard Image Orientation Algorithm (see Algorithm 1) on some skin lesion images (malignant and benign melanoma) is illustrated to show the reorganization and the view standardization of these images. that the irregularities are exploring the small areas locally and the large areas globally.

Obtained Results

Two results are presented in this section, statistical analysis to illustrate the effect of valleys and crevasses concepts introduction, and SVM classification on the obtained features.

Statistical analysis of the results

The number of detected valleys are computed and divided into equidistant segment with length 5 from 0 to 50 as presented in table 5.12. From this table, it can see that To improve these statistical analysis results, the size of the detected valleys and crevasses using different thresholds to discriminate better the benign and malignant lesions is added, as explained in section 4. The result shows a maximum of accuracy of 86.54% given by τ v = 19 with sensitivity of 95.45% and specificity of 80%. it can be seen from this table that the good result of the sensitivity for big values of τ v i.e more than 83% for all τ v ≥ 50. The opposite is seen for the specificity where it gives irregular values when τ ≥ 50, from 68.18% to 81.82%.

For the threshold τ = 0 (Table 5.14), more than 72% of sensitivity, specificity and accuracy performances are obtained. This result represents the information extracted from border features by the proposed method and the effect of these new concepts introduced in this work (valleys and crevasses).

Standard image view contribution

The normalization of the database is one of the keys contributing to result improving of the method proposed. It shows the impact of making all images in the same view.

However the choice of horizontal, vertical or oblique view has no any effect.

CONCLUSIONS AND RECOMMENDATIONS

In this chapter, all research works presented in this thesis are summarized in section 6.1, where the objectives enumerated in section 1.5. Then, The limitations of presented methods and their perspectives are introduced and discussed in section 6.2.

Conclusion

The main aim of this PhD work is to propose a mathematical methods to automate the detection of skin cancer. The main issue of this thesis is to treat the different output images in skin cancer. Therefore, in the current work, the majority of image category acquisition, which are standard camera images and dermoscopy images, are treated to improve the CAD system for skin cancer. The work is separated into two parts following these two categories of input images.

In the current work, two main tasks were treated, firstly the development of an adapted segmentation for skin lesions, and secondly the classification of lesions into malignant and benign cases using a sets of discriminative features. This second part is also divided into two distinguished methods depending on the input image. The approach is evaluated using the subjective evaluation method. The results obtained shows a high performance of the proposed method for the used database. Although, a Jaccard index method could be applied to evaluate the proposed method.

However, the ground truth given for these images shows only the whole lesion and not the specific level lesions basing on the color and intermediary borders. The method answered to the first objective of adaptive segmentation. However, it is not fully automatic due to the manual fixed parameters of the original method.

The main contribution of the proposed approach is more theoretical, and it can be applied on other kind of images. Therefore, it explains the generalization of the model for different more cases than the original model.

Part II: Feature extraction

This second part summarizes the two methods developed to extract the main features of skin lesions for their classification into benign and malignant lesion. Firstly, the border irregularities of lesions applied on standard camera images is explored. Secondly, a new descriptor based on a mixture of structural and textural features is developed. This second approach was applied on dermoscopy images from the free database PH 2 .

1. The first method of feature extraction is based on different combinations of structural and textural features to select the best discriminative set for the classification of benign and malignant lesions. Therefore, for structural features, a multiresolution analysis was explored using wavelet and curvelet transforms. While, the textural features are extracted using local binary pattern operator. The method was also cross validated by n-random sampling cross validation using 1000 random combinations. The method highlights the performances of three skin lesions sets from PH 2 database, which are common nevus, atypical nevus and melanoma.

The results obtained show a higher performances in term of accuracy, sensitivity and specificity in case of wavelet-local binary uniform pattern fusion. This method is answering to the second objective of feature extraction based on the the fusion of structural and textural features. A comparison of these methods with previous work in the literature are highlighted and discussed in the last chapter. All details of proposed methods are explained as suggested in the literature. In addition to that, for all methods proposed, only the free benchmark databases, which are DermIs and DermQuest for standard camera images and PH 2 for dermoscopy images, are used.

Future directions

Despite the several developed approaches, to our knowledge, there is no CAD system available for medical doctors that can perfectly discriminate melanoma. Thus, there is a need to explore new directions in skin cancer detection using images processing.

Therefore, the main directions for further work can be itemized in general and specified perspectives. The specified ones include:

• Minimization of the segmentation proposed for the extension of Chan and Vese model expressed by equation (4.12) using random forest or gradient descent methods. This perspective is one of the main directions of the current work. It present a new view of segmentation in image processing.

• The automation of all parameters of Chan and Vese model and its generalizations.

This issue makes the segmentation using this method very difficult for non-image processing experts. Therefore, the artificial neural network such as Conventional

Neural Network which could be a good compromise method to resolve this issue.

The general perspectives includes some main points about the methodology of work in skin cancer detection domain, such as:

• A systematic validation of all obtained results. We highlighted this point in the fusion of structural and textural features. Thus, it allows for the future work the more visibility for the best direction of research. It increases also the efficiently of results comparison.

• The highlighting of proposed and explored methods in public free database in addition to their private databases such as PH 2 and ISIC (International Skin Images Collaboration in process) databases to easily validate the comparison between methods.

3 :

 3 Comparison and summary of some different methods used for feature extraction and their obtained results . . . . . . . . . . . Table 2.4: Summary of the most used classifiers in skin cancer recognition Table 5.1: Summary of the characteristics of PH 2 database representing the percentage of each sub-feature and between brackets the number of images. . . . . . . . . . . . . . . . . . . . . . . . . . . .Table 5.2: Result of ABCD rule obtained from PH 2 database . . . . . . . . Table 5.3: Subjective evaluation rules. . . . . . . . . . . . . . . . . . . . . Table 5.4: Subjective Evaluation done by image processing expert on the results obtained from the extension of Chan and Vese model by inclusion method . . . . . . . . . . . . . . . . . . . . . . . . . Table 5.5: Subjective Evaluation done by image processing expert on the results obtained from the extension of Chan and Vese model by inclusion method . . . . . . . . . . . . . . . . . . . . . . . . . Table 5.6: Number of features of studied combinations . . . . . . . . . . . Table 5.7: Results obtained for Melanoma Vs Atypical nevus giving Performance validation VP and the standard deviation Std for 1000 random-cross validation under SVM classifier. . . . . . . . . . . X Table 5.8: Results obtained for Melanoma Vs Common nevus giving Performance Validation VP and the standard deviation Std for the 100random-cross validation under SVM classifier. . . . . . . Table 5.9: Results obtained for Melanoma Vs Atypical and Common ne-vus giving Performance validation VP and the standard deviation Std for the 100random-cross validation under SVM classifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Table

13 :Figure 1 . 1 :

 1311 Figure 1.1: Different kinds of skin cancer classified by the Skin Cancer Foundation [2] . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 1 . 2 :

 12 Figure 1.2: Asymmetry of melanoma compared with benign lesion [2]. . .

Figure 1 . 3 :

 13 Figure 1.3: Border irregularity between malignant and benign lesions[2]. .

Figure 1 .

 1 Figure 1.4: Color variation between melanoma and benign lesion [2]. . . .

Figure 1 . 5 :

 15 Figure 1.5: Diameter in melanoma and benign lesion [2]. . . . . . . . . . .

Figure 1 . 6 :

 16 Figure 1.6: Evolving of melanoma over time [2]. . . . . . . . . . . . . . .

Figure 1 . 7 : 7 -

 177 Figure 1.7: 7-point checklist illustration [1]. . . . . . . . . . . . . . . . . .

Figure 3 . 1 :

 31 Figure 3.1: Wavelet representation scale j=0 . . . . . . . . . . . . . . . . .

Figure 3 . 2 :

 32 Figure 3.2: Wavelet representation scale j=0 and j=1 . . . . . . . . . . . .

Figure 3 . 3 :

 33 Figure 3.3: A comparison between wavelet (a) and curvelet (b) [3] . . . . .

Figure 4 . 1 :

 41 Figure 4.1: The zero level set function. The boundary C is illustrated by the ellipse which is equivalent to φ(x, y) = 0 and it separates the domain Ω into 2 regions φ(x, y) > 0 and φ(x, y) < 0. . . .

Figure 4 . 2 :

 42 Figure 4.2: C is represented by the 2 curves {φ 1 = 0} ∪ {φ 2 = 0} which gives 4 distinct regions illustrated in this figure, 3 in the foreground and the background. . . . . . . . . . . . . . . . . . . .

Figure 4 . 3 :

 43 Figure 4.3: C is represented by the 3 curves {φ 1 = 0} ∪ {φ 2 = 0} ∪ {φ 3 = 0} dived it to 8 regions with the background. . . . . . . . . . .

Figure 4 . 4 :

 44 Figure 4.4: C is represented by the 2 curves without intersection between φ 1 and φ 2 . It illustrates one possible case of N = 3. . . . . . .

Figure 4 . 5 :

 45 Figure 4.5: C is represented by the overlapping curves. It is illustrated by φ 2 ⊂ φ 1 which is symetric to φ 1 ⊂ φ 2 . . . . . . . . . . . . . .

Figure 4 . 6 :Figure 4 . 7 :

 4647 Figure 4.6: Four regions using two level set functions φ 1 and φ 2 . . . . . . .

Figure 4 . 8 :

 48 Figure 4.8: Four regions using two level set functions φ 1 , φ 2 and φ 3 using separation-inclusion . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 9 :

 49 Figure 4.9: Four regions using two level set functions φ 1 , φ 2 and φ 3 using inclusion-separation. . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 10 :

 410 Figure 4.10: Four regions using two level set functions φ 1 , φ 2 and φ 3 using total inclusion. . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 11 :

 411 Figure 4.11: Comparison with existing generalization of Chan and Vese model

Figure 4 . 12 :

 412 Figure 4.12: Implementation of the approach using equation (4.13). (a): Original RGB image. (b): Segmentation of the two regions under separability model (equation (4.13)). (c): Global regionbased segmentation. . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 13 :

 413 Figure 4.13: Implementation of the approach using equation (4.14). (a): Original RGB image. (b): Segmentation of the two regions under inclusion model (equation (4.14)). (c): Global regionbased segmentation. . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 14 :

 414 Figure 4.14: Flowchart of structural and textural features fusion proposed in this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 15 :

 415 Figure 4.15: Illustration of the normalization of the images using standard view orientation approach. (a): Original RGB image. (b): The ROI of the lesion. (c): The isolation of the ROI. (d): Reorientation of the ROI to horizontal view. The image is provided from DermIs website (www.dermis.net) under the name of SSM26a. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 16 :

 416 Figure 4.16: Four direction to detect the regular border. Horizontal direction: left to right and right to left. Vertical direction: up to down and down to up. . . . . . . . . . . . . . . . . . . . . . .

Figure 4 . 17 :

 417 Figure 4.17: Illustration of the valley and the crevasse cases: Valley: using only one direction (horizontal or vertical) and Crevasse: Using two directions (horizontal and vertical) . . . . . . . . . . . . .

Figure 5 . 1 :

 51 Figure 5.1: ANOVA test results . . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 2 :

 52 Figure 5.2: Variability of the three classes of the PH 2 database. (1): Common nevus. (2): Atypical nevus. (3): Melanoma. . . . . . . .

Figure 5 . 3 :

 53 Figure 5.3: Results of ABCD rule system applied on PH 2 database. . . . .

Figure 5 . 4 :

 54 Figure 5.4: Illustration of the same image acquired with different distance. (a): LMM8_orig image (kept). (b): LMM8_2_orig image (removed) [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 5 :

 55 Figure 5.5: Implementation of the approach using equation (4.14) on images from DermIs database. (a): Original RGB image SSM18. (b): Segmentation of the two regions with ν = 0.2 and dt = 0.5. (c): Global region-based segmentation. (d): Original RGB image SSM9. (e): Segmentation of the two regions with ν = 0.28 and dt = 1.5. (f): Global region-based segmentation. (g): Original RGB image SSM11. (h): Segmentation of the two regions with ν = 0.07 and dt = 1.5. (i): Global regionbased segmentation. (j): Original RGB image SSM11. (k): Segmentation of the two regions with ν = 0.15 and dt = 0.3. (l): Global region-based segmentation. . . . . . . . . . . . . .

Figure 5 . 6 :

 56 Figure 5.6: Implementation of the approach using equation (4.13). (a): Original RGB image (SSM34). (b): Segmentation of the two regions. (c): Global region-based segmentation.(d): Original RGB image (SSM18). (e): Segmentation of the two regions. (f): Global region-based segmentation . . . . . . . . . . . . .

Figure 5 . 7 :

 57 Figure 5.7: Subjective evaluation examples. (a): Excellent Segmentation. (b):Good Segmentation. (c): Average segmentation.(d): Unacceptable segmentation. . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 8 :Figure 5 . 9 :

 5859 Figure 5.8: Training and test sets selection . . . . . . . . . . . . . . . . .

Figure 5 . 10 :

 510 Figure 5.10: Hair removing with DullRazor software. (a,c): original images. (b,d): Dullrazor software treatment on the original images.

Figure 5 .

 5 Figure 5.11: histogram of the thousand combinations results for accuracy metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figure 5 . 12 :

 512 Figure 5.12: Single orientation of melanoma sample from DermQuest Database [5]. (a): original malignant image NM61. (b): gray level ROI of the oriented ROI of NM61 image. (c) Binary ROI of the oriented ROI of the image NNM61. (d): Original Malignant image (SSM74). (e):gray level ROI of the oriented ROI of SSM74 image. (f) Binary ROI of the oriented ROI of the image SSM74.

Figure 5 . 13 :

 513 Figure 5.13: Single orientation of benign lesions sample from DermQuest Database [5]. (a): original benign image D45. (b): gray level ROI of the oriented ROI of D45 image. (c) Binary ROI of the oriented ROI of the image D45. (d): Original benign image D54. (e):gray level ROI of the oriented ROI of D54 image. (f) Binary ROI of the oriented ROI of the image D54. . . . . . . .

Figure 5 . 14 :

 514 Figure 5.14: Illustration of main stages of border irregularities. (a): Original gray level image. (b): Binary ROI image. (c): valleys areas detected with the edge of the ROI. (d): Valley areas detected (13 elements). (e): Crevasse areas detected with the edge of the ROI. (f): Crevasse areas detected (3 elements). . . . . . . .

Figure 5 . 15 :

 515 Figure 5.15: Accuracy of standard view and original images using border features presented in the current method. blue (up) : proposed standard view images, red (down): Original images. . . . . . .

Figure 1 . 1 :

 11 Figure 1.1: Different kinds of skin cancer classified by the Skin Cancer Foundation [2]

Figure 1 . 5 :

 15 Figure 1.5: Diameter in melanoma and benign lesion [2].

  Figures from 1.2 to 1.6 illustrate the five rules of ABCD/ABCDE rules showing

Figure 1 . 7 : 7 -

 177 Figure 1.7: 7-point checklist illustration [1].

  Abbas etal.[START_REF] Abbas | A feature-preserving hair removal algorithm for dermoscopy images[END_REF].(2011)

  Various classifiers are used in CAD systems for skin cancer recognition. Artificial Neural Network and Support Vector Machine are the most common used. Commonly, skin cancer lesions are classified following two or three classes which are benign / malignant and nevus / atypical / melanoma. The different metric performances used for each classifier makes harder the comparison between the results of the different proposed methods. In addition to that, the absence of a large public available benchmark dataset accompanied by the ground truth and the diagnosis from several dermatologists makes really hard, even impossible to compare objectively the approaches developed in the literature. This chapter presents the theoretical background of the explored methods in the current work which is divided into three main parts. Section 3.2 provides total variation theory of Mumford and Shah and Chan and Vese model well, used for segmentation in image processing[START_REF] Bar | Mumford and shah model and its applications to image segmentation and image restoration[END_REF][START_REF] Duan | Some fast projection methods based on chan-vese model for image segmentation[END_REF]. The multiresolution analysis is presented in section 3.3. It provides an overview of the history of multiresolution analysis and the need of the development of new applications. It starts by introducing Fourier transform, followed by wavelet and ridgelet and finally by curvelet transforms. Section 3.5 gives an introduction of the mathematical background of the two used classifiers, Artificial Neural network and Support Vector Machine. Finally, this chapter ends by a short summary

  4) where C is a given curve in the domain R and c 1 , c 2 are the averages of I inside and outside C. Using this formulation, the function F C (C) is minimized on the boundary of the object.

  H and the dirac function δ 0 given in equation (3.7), the curve C and the areas inside and outside the level set function φ given in equation (3.6) are expressed by equation (3.8)

Figure 3 . 1 :Figure 3 . 2 :

 3132 Figure 3.1: Wavelet representation scale j=0

. 44 )

 44 Fast Discrete Curvelet Transform (FDCT) via wrapping was introduced by Candes et al. in their second generation of curvlet [160]. This implementation is based on wrapping of Fourier samples with a 2D image as input in a Cartesian array form f [m, n] where 0 ≤ m ≤ M , 0 ≤ n ≤ N , M and N are the dimension of the array (image).

. 45 )Figure 3 . 3 :

 4533 Figure 3.3: A comparison between wavelet (a) and curvelet (b)[3]

Figure 3 .

 3 Figure 3.3 illustrates the advantages of curvelet transform in curve detection com-

  Ojala et al.[START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classification with local binary patterns[END_REF] introduced uniform pattern and invariant rotation local binary pattern. The uniform pattern variant indexed by LBP u2 keeps only the pattern contains in maximum 2 transition 0/1 and/or 1/0, this variant contains 59 combinations. The invariant rotation variant pattern indexed by LBP ri has the same configuration for all rotations, it contains 36 combinations. The invariant rotation uniform pattern variant is an intersection of the uniform patterns LBP u2 and the invariant rotation variant LBP ri > It represents only the uniform patterns which has the same configuration in all rotations, then it contains 9 combinations.

1 . 3 .

 13 It started by the Total Variation theory, explaining the Mumford and Shah function and the minimization developed by Chan and Vese. This theory is primordial to explain the extension of Chan and Vese model proposed in the next chapter for skin lesion segmentation. 2. Then, it is followed by the multiresolution analysis theory, where wavelet and curvelet transforms are introduced to be used in the next chapter. It provides also the the multiresolution analysis development starting by Fourier transform into curvelet transform explaining more the main task and limitations of each transform. The third part provides the Local Binary pattern theory. This method is mixed with multiresolution analysis and used for feature extraction to discriminate melanoma. 4. The fourth (i.e. last part) provides the statistical classification methods to separate the skin cancer into two or more different sets, explaining more the theory of SVM and ANN classifiers. Then, it provides the statistical validation methods referring some methods used in skin cancer area, and finally, it provides the most used performance metrics in skin cancer.

  as a boundary of an open subset ω of Ω (i.e ω ⊂ Ω and C = ∂ω), in what follows, inside(C) denotes ω and outside(C) denotes the region Ω\ω. The segmentation problem presented in[START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF] is to solve the following minimization problem:inf u,C Ω (u -u 0 ) 2 dxdy + µ Ω\C |∇u| 2 dxdy + ν|C| (4.1)where µ, ν are fixed parameters to weight the different terms in the energy given by equation (4.1), u 0 : Ω → R is a given bounded image-function, u is an optimal approximation of u 0 and |C| is the length of curves making C.A given C = ∂ω (the boudary of open set ω ∈ Ω) is presented implicitly as the zero Lipscitz continuous function φ : Ω → R such that φ(x, y) < 0 in ω, φ(x, y) > 0 in Ω \ ω and φ(x, y) = 0 on ∂ω. Using the following Heaviside function H(z).

Figure 4 . 1 :

 41 Figure 4.1: The zero level set function. The boundary C is illustrated by the ellipse which is equivalent to φ(x, y) = 0 and it separates the domain Ω into 2 regions φ(x, y) > 0 and φ(x, y) < 0.

. 6 )

 6 Figures (Fig.4.2) and (Fig. 4.3) illustrate the cases 2 and 3 zero level sets function

  Figures (Fig.4.2) and (Fig. 4.3) illustrate the cases 2 and 3 zero level sets function respectively. Ellipses and circles represent the curve C and the different classes of φ i .

Figure 4 . 2 :

 42 Figure 4.2: C is represented by the 2 curves {φ 1 = 0} ∪ {φ 2 = 0} which gives 4 distinct regions illustrated in this figure, 3 in the foreground and the background.

Figure 4 . 3 :

 43 Figure 4.3: C is represented by the 3 curves {φ 1 = 0} ∪ {φ 2 = 0} ∪ {φ 3 = 0} dived it to 8 regions with the background.

Figure 4 . 4 :

 44 Figure 4.4: C is represented by the 2 curves without intersection between φ 1 and φ 2 . It illustrates one possible case of N = 3.

  Figure 4.5: C is represented by the overlapping curves. It is illustrated by φ 2 ⊂ φ 1 which is symetric to φ 1 ⊂ φ 2 .

u 1

 1 represents the first choice of the zero level set function, u 2 (1 -u 1 ) represents the second zero set level function excluding u 1 (it pushes to the separability of the two level set functions and reduces the intersection to an empty set), then(1 -u 1 )(1 -u 2 )represents the image background. This combination is an extension of Chan and Vese model for N = 3 not developed by Vese and Chan[START_REF] Luminita | A multiphase level set framework for image segmentation using the mumford and shah model[END_REF] and neither by Li et al.[START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF].For the energy F 32 given in equation (4.14) illustrated in figure 4.5, knowing that φ 1 ⊂ φ 2 the background defined by (1 -u 1 )(1 -u 2 ) can be defined only by (1 -u 2 ).

Figure 4 . 6 :

 46 Figure 4.6: Four regions using two level set functions φ 1 and φ 2 .

  sets. It is equivalent to the first case developed in the current study for the detection of 3 regions illustrated by figure 4.4.

Figure 4 . 7 :

 47 Figure 4.7: Four regions using three level set functions φ 1 , φ 2 and φ 3 using the total separation method

Figure 4 .

 4 Figure 4.11 illustrates the generalization of the proposed method compared to the ones developed in the literature. We can see that, in the proposed method, all possible situation are studied to segment efficiently the lesions.

Figure 4. 11 :

 11 Figure 4.11: Comparison with existing generalization of Chan and Vese model

Figure 4 . 12 :Figure 4 . 13 :

 412413 Figure 4.12: Implementation of the approach using equation (4.13). (a): Original RGB image. (b): Segmentation of the two regions under separability model (equation (4.13)). (c): Global region-based segmentation.

Figure 4 . 14 :

 414 Figure 4.14: Flowchart of structural and textural features fusion proposed in this work.

Algorithm 1 Figure 4 . 15 :

 1415 Figure 4.15: Illustration of the normalization of the images using standard view orientation approach. (a): Original RGB image. (b): The ROI of the lesion. (c): The isolation of the ROI. (d): Reorientation of the ROI to horizontal view. The image is provided from DermIs website (www.dermis.net) under the name of SSM26a.

  Figure 4.16 illustrates the four directions applied in the proposed

Figure 4 . 16 :

 416 Figure 4.16: Four direction to detect the regular border. Horizontal direction: left to right and right to left. Vertical direction: up to down and down to up.

Figure 4 . 17 :

 417 Figure 4.17: Illustration of the valley and the crevasse cases: Valley: using only one direction (horizontal or vertical) and Crevasse: Using two directions (horizontal and vertical)

Figure 4 .

 4 Figure 4.18: p-norms illustration

  compare the evaluation of several systems. The database was built up through the joint collaboration between Universidade do Porto, Técnico Lisboa, and the Dermatology service of Hospital Pedro Hispano in Matosinhos, Portugal. The acquisition of images was obtained under the same conditions. They are 8-bit RGB color images with a resolution of 768 × 560 pixels. The database contains a total of 200 dermoscopic images divided into 160 benign lesions and 40 melanomas. The benign lesions contain 80 common nevi and 80 atypical nevi. The quality, resolution and dermoscopic features of images are highlighted in the current database. Every image was segmented manually and diagnosed by several dermatologists. It contains also the clinical diagnosis and dermoscopic criteria such as asymmetry, color and presence of typical and atypical structures.

Figure 5 . 2 :

 52 Figure 5.2: Variability of the three classes of the PH 2 database. (1): Common nevus. (2): Atypical nevus. (3): Melanoma.

Figure 5 . 3 :

 53 Figure 5.3: Results of ABCD rule system applied on PH 2 database.

Figure 5 .

 5 Figure 5.3 describes the results of ABCD rule (blue) of the whole database and the mean of each class (red). Descriptively, using ABCD rule results, the graph shows more stability in common nevus lesion than the two other cases (atypical nevus and melanoma).

5. 2 . 3

 23 Standard Camera Images DatabaseThe standard camera image database is provided from two dermatology website, Dermatology Information System (DermIS) [4] and Dermquest[5]. The database contains a total of 206 images where 118 are melanomas cases and 87 are benign lesions. DermIS contains 69 images divided into 43 melanomas and 26 benign lesions and DermQuest contains 137 images divided also into 76 melanomas and 61 benign lesions. Recently (2014) Amelard et al. [105] used this database in his work. The DermQuest database shows a redundancy of some images due the different acquisition of the same image changing the distance and the view of acquisition. To avoid a confusion and make independence between lesions, only clear images are chosen. Therefore, 40 images are deleted where 38 are melanomas and 2 are benign lesions.

Figure 5 .

 5 Figure 5.4 illustrates one case of redundant images. In this cases the image in figure 5.4a is kept and the other in figure 5.4b is deleted in the database. Thus, the new database contains 166 images divided into 99 melanomas and 67 benign lesions.

Figure 5 . 4 :

 54 Figure 5.4: Illustration of the same image acquired with different distance. (a): LMM8_orig image (kept). (b): LMM8_2_orig image (removed) [4].

Figure 5 .

 5 5 presents 4 image examples showing different segmentations obtained.

Figure 5 . 5 :

 55 Figure 5.5: Implementation of the approach using equation (4.14) on images from Der-mIs database. (a): Original RGB image SSM18. (b): Segmentation of the two regions with ν = 0.2 and dt = 0.5. (c): Global region-based segmentation. (d): Original RGB image SSM9. (e): Segmentation of the two regions with ν = 0.28 and dt = 1.5. (f): Global region-based segmentation. (g): Original RGB image SSM11. (h): Segmentation of the two regions with ν = 0.07 and dt = 1.5. (i): Global region-based segmentation. (j): Original RGB image SSM11. (k): Segmentation of the two regions with ν = 0.15 and dt = 0.3. (l): Global region-based segmentation.

Figure 5 . 6 :

 56 Figure 5.6: Implementation of the approach using equation (4.13). (a): Original RGB image (SSM34). (b): Segmentation of the two regions. (c): Global region-based segmentation.(d): Original RGB image (SSM18). (e): Segmentation of the two regions. (f): Global region-based segmentation

Figure 5 .

 5 Figure 5.7 illustrates an example of the four qualities segmentations explained in table 5.3. Due to the missing of information in the ground truth, it is very difficult to evaluate

Figure 5 . 7 :

 57 Figure 5.7: Subjective evaluation examples. (a): Excellent Segmentation. (b):Good Segmentation. (c): Average segmentation.(d): Unacceptable segmentation.

( 1000 )

 1000 combinations of training and test sets are chosen randomly from the database. Thus, each image is used in average 700 times for training and 300 times for tests. An unbiased standard deviation (Std) for the thousand combinations is also computed for the three performance metrics.The evaluation is performed between the three sets of skin lesions (common nevus, atypical nevus and melanoma). Thus, to get a representative training set from the benign lesions, 70% of each set are chosen separately as illustrated in figure5.8. Two cases are computed and analyzed in this study, a separate case which is the recognition of melanoma mixed only with common nevus or atypical nevus. The second case is to recognize melanoma mixed with the whole benign lesions respecting the representativity of common and atypical nevus in training and test sets.

Figure 5 . 8 :

 58 Figure 5.8: Training and test sets selection

  T N T P + F N + T N + F P (5.3) Where T P (True Positives) defines the melanoma classified as melanoma, T N (True Negatives) defines the non melanoma classified as non melanoma, F P (False Positives) and F N (False Negatives) are the non melanoma and melanoma which are not classified on the right set respectively. Equation (5.3) depends on the number of benign and malignant lesions. To remove this dependence, we estimate the accuracy in the following way: â cc = αT P + T N αT P + αF N + T N + F P (5.4)

Figure 5 .

 5 Figure 5.9a presents the evolution of the modified accuracy ( â cc) depending on different values of α, from 0.1 to 5, fixing other variables (sensitivity, specificity, malignant number and benign number). While, Figure 5.9b illustrates the dependence of the accuracy metric (eq.(5.3)) on malignant and benign number, presented by the dark curve.By varying the β value from 0.1 to 5 in M = βB, where M is malignant number, B is benign number, we can see easily that the accuracy (acc) is strongly dependent on those quantities. The blue color line presents the modified accuracy ( â cc), with α = 1/β, to compensate the difference between malignant and benign number.

Figure 5 . 10 :

 510 Figure 5.10: Hair removing with DullRazor software. (a,c): original images. (b,d): Dullrazor software treatment on the original images.

Figure 5 .

 5 Figure 5.11: histogram of the thousand combinations results for accuracy metric

Figure 5 . 12 :

 512 Figure 5.12: Single orientation of melanoma sample from DermQuest Database [5]. (a): original malignant image NM61. (b): gray level ROI of the oriented ROI of NM61 image. (c) Binary ROI of the oriented ROI of the image NNM61. (d): Original Malignant image (SSM74). (e):gray level ROI of the oriented ROI of SSM74 image. (f) Binary ROI of the oriented ROI of the image SSM74.

Figure 5 . 13 :

 513 Figure 5.13: Single orientation of benign lesions sample from DermQuest Database [5]. (a): original benign image D45. (b): gray level ROI of the oriented ROI of D45 image. (c) Binary ROI of the oriented ROI of the image D45. (d): Original benign image D54. (e):gray level ROI of the oriented ROI of D54 image. (f) Binary ROI of the oriented ROI of the image D54.

Figures 5 .Figure 5 . 14 :

 5514 Figures 5.12 and 5.13 show the effect of making images in the same orientation. It can be seen easily that the border in binary image representation is a good descriptor between malignant and benign lesions. It can seen also that the area between pigment and its box is minimized. As mentioned above, the performances of this standardization are presented in section 5.5.2.3 and illustrated in Fig.5.15 in comparison with the original view.

Figure 5 .

 5 Figure 5.14 describes the different steps of valleys and crevasses detection. This example shows well the different sizes of valleys and crevasses. It can be seen easily

3 . 3

 33 and summarized by equation (4.31). Therefore, a machine learning via SVM training and classifier are applied on the feature set obtained. The obtained results are presented in subsection below (subsection:5.5.2.2).5.5.2.2 SVM classification on border irregularity featuresSupport Vector Machine (SVM) classifier is used on a database of 166 skin lesions images (67 benign lesions and 99 malignant melanoma), it is applied on different integer values of the threshold τ v (τ v ∈ [0, 100]) as given in equation (4.31). The other threshold τ c mentioned in the equation is fixed empirically to 2.5. This choice reduces considerably the complexity of the algorithm and time running. Thus, the features extracted are used as input for the SVM classifier with linear kernel following 70% (69 malignant, 45 benign) for the training and 30% (30 malignant, 22 benign) for the test. Table5.14 shows different results for τ v ∈ (0,[START_REF] Rigel | The evolution of melanoma diagnosis: 25 years beyond the abcds[END_REF][START_REF] She | Combination of features from skin pattern and abcd analysis for lesion classification[END_REF][START_REF] Nabin | An overview of melanoma detection in dermoscopy images using image processing and machine learning[END_REF][START_REF] Kiani | E-shaver: An improved dullrazor R for digitally removing dark and light-colored hairs in dermoscopic images[END_REF][START_REF] Delgado | Independent histogram pursuit for segmentation of skin lesions[END_REF][START_REF] Tony | Active contours without edges[END_REF][START_REF] Ma | Multi-scale descriptors for contour irregularity of skin lesion using wavelet decomposition[END_REF][START_REF] Pesaresi | A new approach for the morphological segmentation of high-resolution satellite imagery[END_REF][START_REF] Deb | A fast and elitist multiobjective genetic algorithm: Nsga-ii[END_REF] adding to that the optimum value of τ v showing the best results.

Figure 5 .

 5 Figure 5.15 shows the effect of preprocessing step. The intermediate contribution of the standard view presented in section 4.3.3.1 using the same training and test sets on SVM classifier. The graph illustrates the accuracy performance of the same database between the original orientation and the proposed standard view. Therefore, from the graph it can be seen easily that the accuracy for all thresholds (from 0 to 100), shows greater results in standard view than the original images. The maximum of accuracy in original is only 78.85% compared to standard view images which is 86.54%.

Figure 5 . 15 :

 515 Figure 5.15: Accuracy of standard view and original images using border features presented in the current method. blue (up) : proposed standard view images, red (down): Original images.

6. 1 . 1

 11 Part I: Segmentation methodIn this part, the research on the segmentation of skin lesion is focused on the development of new approach of skin lesion segmentation based on Chan and Vese Model. It has the particularity to segment the the random development of melanoma lesion. This approach is applied and evaluated on skin cancer coming from standard camera images given in DermIs and DermQuest databases. One of Chan and Vese model particularities is its high sensibility to different edges and colors. The skin cancer is recognized principally by sets of rules defined by dermatologists and researchers which are ABCD rule and 7-point checklist. Our proposed approach can be considered as a specialization in one side and a generalization in other side of Chan and Vese model. Therefore, a choice of one specific combination treats the segmentation deeply compared to the original Chan and Vese model. In the second view, all the combination of Chan and Vese model are treated in the current approach.

2 .

 2 The second method of feature extraction is based on the border irregularities behavior. The method explored a new concept of border representation, where two kinds of features are extracted from the border, which are valleys and crevasses geometrical forms. These two new concepts can considered as first and second level of lesion border irregularities. These features are learned by SVM classifier with linear kernel. The results obtained show a higher performances of classification compared to the literature's results using the same database. This idea of characterization of border could be implemented in a typical flow of ABCD rule method, it represents more variability than the method based on eight segments from the border used currently in ABCD rule. The challenge fixed in the third objective , which is the exploration of the border irregularities in formation of, is achieved.

Table 2 .

 2 1: Comparison of different used methods on hair-removal task . . .

Table 2 .

 2 2: Comparison and summary of some different methods used for segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 2 .

 2

Table 5 .

 5 12: Number of detected area in equidistant segments using first level of irregularity (horizontal vertical). Valley geometrical forms

Table 5 .

 5

  . . .

		P DE	Partial Differential Equation
		P H 2	PH 2 Database
			LIST OF ABBREVIATIONS
		P P R	Positive Predictive value
		RGB	Red Green Blue channel
	ABCD ROC	Asymmetry, Border, Color, Diameter Receiver Operating Characteristic
	Acc	ROI	Accuracy metric Region Of Interest
	AN N	SCF	Artificial Neural Network Skin Cancer Foundation
	AN OV A SIF T	Analysis Of Variance Scale Invariant Feature Transform
	AU C	Sen	Area Under Curve Sensitivity metric
	CAD	Spe	Computer Aided Diagnosis Specificity metric
	CIE	International Commission on Illumination SP AM Sequential Pattern Mining
	CN N	SP T	Convolutional Neural Network Steerable Pyramids Transformation
	DCT	SSA	Discrete Cosine Transform Stacked Sparse Auto-Encoder
	DF T	Std	Discrete Fourier Transform Standard deviation
	DW T	SV M	Discrete Wavelet Transform Support Vector Machine
	EM		Expectation Minimization
	Ep		Error probability
	F CM		Fuzzy C-Mean
	F DCT		Fast Digital Curvelet Transform
	F F T		Fast Fourier Transform
	F N		False Negative
	F P		False Positive
	F P R		False Positive Rate
	GP AC		Graph Partitioning Active Contours
	GV F		Gradient Vector Flow
	ISIC		International Skin Imaging Collaboration
	JRC		Joint Reverse Classification
	kN N		k-Nearest Neighbor
	LBP		Local Binary Pattern
	M LR		Multi-scale Lesion-biased Representation
	N P R		Negative Predictive value
			XVI	XV

Table 1 .

 1 1: ABCD rule with the interval values of p i and the weight factor w i of each component[1].

	Feature	Description	Points p i	Weight factor w i	sub-score range
	Asymmetry One value of 0.5 for each axis.	0 -2	1.3	0 -2.6
	Border	Eight segment, one value of 1 for each abrupt pigment cutoff.	0 -8	0.1	0 -0.8
		One value of 1 for each color:
	Color	white, red, light brown, dark brown,
		blue-gray.

Table 1 .

 1 1 expresses the description of each feature of the system and gives their different point values and weight factors.

75 then the pigment is benign 4.75 ≤ S abcd ≤ 5.45 then the pigment is clinically doubful S abcd > 5.45 the pigment is malignant

Table 1 .

 1 2: The major and minor criteria of 7-point checklist and the different weights for each criterion[1].

	Major criteria	Score	Minor criteria	Score
	Atypical pigment network	2	Irregular streaks	1
	Blue-whitish veil	2	Irregular pigmentation	1
	Atypical vascular pattern	2	Irregular dots/globules	1
			Regression structures	1

Table 2

 2

	.1 summarizes some methods used for hair detection and inpainting steps
	with the results obtained for each one. Most of the presented methods in this table had
	compared their result to DullRazor software.
	Table 2.1: Comparison of different used methods on hair-removal task
	Method	Hair detection	Restoration	Database	Results
	DullRazor
	[38].

  applied another generalization of Chan and Vese Model developed by Li et al.[START_REF] Li | Multiphase soft segmentation with total variation and h 1 regularization[END_REF] (see chapter 4). Using ABCD rule for feature extraction and SVM classifier on a database of 4240 benign and 232 malignant moles, the performance evaluation was conducted using a 10-fold cross-validation and it performed a true detection rate over than 98% for all 10 tested cases. Another extension of the model is presented recently by Kang et al.[START_REF] Ha | Multiphase image segmentation via equally distanced multiple well potential[END_REF].

In 2009, Silviera et al.

[START_REF] Silveira | Comparison of segmentation methods for melanoma diagnosis in dermoscopy images[END_REF]

compared 6 methods of segmentation, adaptive thresholding (AT), gradient vector flow, adaptive snake (AS), level set of Chan and Vese model (C-LS), expectation-minimization level set (EM-LS) and fuzzy-based split-and merge (FBSM) algorithm. The comparison shows that the best result of false positive rate (FPR) of 2.55% is given by C-LS method, but the results are lower for true detection rate (TDR) of 83.39% comparing to Adaptive snake with a TDR of 95.47%. In 2015, an extension of Chan and Vese model applied on dermoscopic images is developed

[START_REF] Adjed | Segmentation of skin cancer images using an extension of chan and vese model[END_REF]

,

Table 2 .

 2 2: Comparison and summary of some different methods used for segmentation

	Authors		Segmentation		Database	Results
			method
	Abbas et al.	Region-based Active	320 images TDR of 92.17% and FPR of
	[47] (2011)	Contours [59]			5.62%
	Safi	et	Multipahse	seg-	4472	Accuracy of 98.57% with a
	al.	[63]	mentation with TV	images	TDR of 99.1%
	(2011)		and H 1 regulariza-
			tion [64]
	Casttilejos	Wavelet Transform
	et al. [68]	mixed with three
	(2012)		variants of FCM
						88.9%
	Ma	et	Wavelet decomposi-
	al.	[71]
	(2013)
	Ganster et al.	Gray-scale morpho-	4000	Around 96% of correct seg-
	[83] (2001)	logical segmentation	images	mentation.

algorithm 50 images AUC value over then 0.96 Clawson et al. [99] (2009) Harmonic wavelet transform [100] 30 images With ground truth of two experts: 1St-Acc: 93.3%, Sen: 50%, Spe: 100%. 2nd-Acc: 93.3%, Sen: 95.2%, Spe: tion bank [72] 134 images Spe: 90.32%, Sen: 83.33% and Area of ROC: 89.07%.

  ] proposed a multi-scale lesion-biased representation (MLR) and performed the classification under joint reverse classification (JRC) model. The results obtained on a database of 200 dermoscopic images are 87.50 of sensitivity, 93.13% of specificity and 90.31 of accuracy. However, the authors did not cross validate the obtained results of the proposed method. Recently, Li and Shen[START_REF] Li | Skin lesion analysis towards melanoma detection using deep learning network[END_REF] used deep learning network to detect melanoma. Applying straight-forward CNN algorithm for segmentation and lesion index calculation unit for classification. On ISIC database containing 2750 images, the method showed an accuracy of 92.2%, a sensitivity of 78.9% and a specificity of 97.5%. On the same database, Gal et al.[START_REF] Gal | Deep bayesian active learning with image data[END_REF] and Lopez et al.[START_REF] Lopez | Skin lesion classification from dermoscopic images using deep learning techniques[END_REF] proposed a bayesian convolutional neural network and convolutional neural network, respectively, Gal et al. obtained an AUC of 0.75 and Lopez et al. obtained an accuracy of 81%.It can be seen that the most of recent contributions of skin cancer recognition are

	Authors Authors feature extraction feature extraction Database Database obtained results obtained results
			method method
	Sadghi et al. Codella et al. Spatial arrangement combination	945 images Accuracy of 78.3% with AUC of 1279 An accuracy of 76%, a sensi-
	[127] (2013) [137] (2017) and orientation of hand-coded feature	od 83.2% for absent/present images tivity of 82% and a specificity
			streak lines to detect extractors,	sparse-	and an accuracy of 83.6% of 62%.
			regular and irregular coding methods,	with AUC of 88.9% for regu-
			streaks	SVMs, with fully	lar/irregular.
	Takruri et al.	Wavelet and curvelet CNN	448 images Wavelet: Acc: 87.1%, Sen:
	[128] (2014)	features		86.4% and Spe:	88.1%.
						Curvelet: Acc: 83.6%, Sen:
						76.9% and Spe: 85.4%
	Cavalvanti	Computerization of	220 images An accuracy of 93.63%, a sen-
	et al. [129]	ABCD rule		sitivity of 94.92% and a speci-
	(2011)					ficity of 91.46%
	Amelard	Multi-stage illumina-	206 images An accuracy of 81.26%, a sen-
	et al. [105]	tion algorithm		sitivity of 84.04% and a speci-
	(2014)	Authors	feature extraction	Database ficity of 79.91%. Obtained results
	Sabbaghi	method SIFT mixed with	814 images With SVM An accuracy of
	Codella et al. et al. [130] color identification Sequential	Pattern	2624	Accuracy of 93.1%, Sensitiv-85%, and with SSA an ac-
	(2016)	[122] (2015) algorithm Mining	under	images curacy of 95% a sensitivity ity of 94.9% and specificity of
			SVM	and	SSA	92.8% of 94.9% and a specificity of
		Abuzaghleh classifiers. Fast Fourier trans-	200 images 90.6%, 91.3% and 97.7 of ac-95.4%.
	Bi	[118] (2014) et MLR method under form mixed with 200 images An accuracy of 90.31%, a sen-curacy of common, atypical
	al.	[132]	discrete JRC model for classi-	cosine	and melanoma resp. sitivity of 87.50% and a speci-
	(2016)		transform fication.	ficity of 93.13%.
	Li	Abbas et al. et CNN algorithm for Combination	of 2750	1039	Sensitivity of 89.28%, speci-An accuracy of 92.2%, a sen-
	al.	[121] (2013) [133] segmentation and le-color-related feature images	images sitivity of 78.9% and a speci-ficity of 93.75% and area un-
	Two classifiers are used to evaluate the proposed method. Firstly, they employed linear and Treeble Pyramid der AUC of 0.986. (2017) sion index calculation ficity of 97.5%.
	SVM for the classification step, and secondly, they used Stacked Sparse Auto-Encoder transformation unit for classification.

(SSA) neural network variant. The results achieved by these methods on a database of 814 images are 85% and 95% of accuracy for SVM and SSA, respectively. Bi et al. [132In the same idea, Esteva et al. [136] applied a deep convolutional neural network on a database of 129450 clinical images into 2, 032 different diseases. Their results were compared to 21 board-certified dermatologists. Table 2.3: Comparison and summary of some different methods used for feature extraction and their obtained results developed in feature extraction area such as presented in table 2.3. However, the results

are still should improved specifically the decrease of false negative cases such as the results obtained by Li et al.

[START_REF] Li | Skin lesion analysis towards melanoma detection using deep learning network[END_REF]

using CNN method. Another problematic can be seen in the literature is that most of contributions are not validating their obtained results such as Cavalvanti et al.

[START_REF] Pablo | Automated prescreening of pigmented skin lesions using standard cameras[END_REF]

and Bi et al.

[START_REF] Bi | Automatic melanoma detection via multi-scale lesion-biased representation and joint reverse classification[END_REF]

. Therefore, there is a need to develop and adapt a new approach of feature extraction following a rigorous methodology of work by validation and parameters highlighting.

  are the most used for classification of skin cancer images. The mathematical theory of these two classifiers are explained in the next chapter. Thus, the SVM and the ANN classifiers divide the dataset into two sets, one for training and the other for tests. In most of cases, 70% of the data is used for training and 30% is used for tests. The SVM classifier was used in[19, 56, 63, 104-106, 111, 118, 119, 122, 126, 130, 140-146] and ANN was used in[START_REF] Ma | Analysis of the contour structural irregularity of skin lesions using wavelet decomposition[END_REF][START_REF] Abu | Wavelet and curvelet analysis for automatic identification of melanoma based on neural network classification[END_REF][START_REF] Zhou | A new method describing border irregularity of pigmented lesions[END_REF][START_REF] Yue | Skin lesion classification using relative color features[END_REF][START_REF] Codella | Deep learning, sparse coding, and svm for melanoma recognition in dermoscopy images[END_REF][START_REF] González-Castro | Automatic classification of skin lesions using geometrical measurements of adaptive neighborhoods and local binary patterns[END_REF][START_REF] Sabbaghi | A deep bag-of-features model for the classification of melanomas in dermoscopy images[END_REF][START_REF] Surowka | Different learning paradigms for the classification of melanoid skin lesions using wavelets[END_REF][START_REF] Ilias | Characterization of digital medical images utilizing support vector machines[END_REF][START_REF] La | Learning methods for melanoma recognition[END_REF][START_REF] Iyatomi | An improved internet-based melanoma screening system with dermatologist-like tumor area extraction algorithm[END_REF][START_REF] Dreiseitl | A comparison of machine learning methods for the diagnosis of pigmented skin lesions[END_REF]. In addition

to these two classifiers, there are also many other classifiers used in melanoma recognition such as the k-Nearest Neighbor (kNN) classifier

[START_REF] Ganster | Automated melanoma recognition[END_REF][START_REF] Pablo | Automated prescreening of pigmented skin lesions using standard cameras[END_REF][START_REF] Barata | Two systems for the detection of melanomas in dermoscopy images using texture and color features[END_REF]

, Discriminant

Table 2 .

 2 4 summarizes the different classifier utilized in the literature for classification and recognition of melanoma. As already mentioned above, it can be seen easily from the table that the most used classifiers are SVM and ANN.

Table 2 .

 2 4: Summary of the most used classifiers in skin cancer recognition

	Classifier	Author references
	Support Vector Machine	[19,56,63,104-106,111,118,119,122,126,128,
		140-146]
	Artificial Neural Network	[71,75,91,106,111,112,122,125,143,144,146-
		148, 151]
	k-Nearest Neighbor	[83, 129, 140, 146]
	Decision Trees	[1, 8, 99, 129]

  The choice of the descriptor to use and/or to develop for feature extraction is more difficult and more complicate than other steps. Unlike segmentation, where the objective is to find the border lesion, the descriptor's objective is to develop an adaptive method to discriminate widely the lesions. It can be textural, statistical, structural or geometrical features. In skin cancer images, many feature extraction methods are formulated and developed from the two scoring systems used by clinicians in the hospitals, ABCD rule and 7-point checklist. Other methods also used different mathematical tools and descriptors such as Fourier, wavelet and curvelet coefficients. The major limitation of ABCD rule and 7-point checklist is that the two systems are based on visual interpretation, which is subjective between dermatologists. The cancerous lesions are random biological phenomena manifesting various structures in sizes, shapes and densities.

Table 5 .

 5 1 summarizes all the given characteristics in PH 2 database, where sub-

feature is describing the different cases of each feature, for example, fully asymmetry is a sub-feature of Asymmetry. The table shows the percentage of the presence / absence of each sub-feature. For each percentage, the number of images is noted between brackets. The table is to be read by columns, thus for example, the common nevus is 96.25% fully symmetric, 2.5% is symmetric in one axis and only 1.25% is fully asymmetric and melanoma is 12.5% fully symmetric, 5% symmetric in one axis and 82.5% fully asymmetric. The table shows the dominant characteristics for each feature. It represents the cross table between characteristics and skin lesions diagnosis.

Table 5 .

 5 1: Summary of the characteristics of PH 2 database representing the percentage of each sub-feature and between brackets the number of images.

	Database characteristics	Common	Atypical	Melanoma
			Nevus (80)	Nevus (80)	(40)
		Fully symmetric	96.25% (77)	43.75% (35)	12.5% (5)
	Asymmetry	Symmetric in 1 Axe	2.5% (2)	33.75% (27)	5% (2)
		Fully Asymmetric	1.25% (1)	22.5% (18)	82.5% (33)
	Pigment	Typical	100% (80)	3.75% (3)	2.5% (1)
	network	Atypical	0% (0)	96.25% (77)	97.5% (39)
	Dots / Globules	Absent Typical Atypical	36.25% (29) 57.5% (46) 6.25% (5)	50% (40) 10% (8) 40% (32)	45% (18) 0% (0) 55% (22)
	Streaks	Absent Present	98.75% (79) 1.25% (1)	80% (64) 20% (16)	67.5% (27) 32.5% (13)
	Regression	Absent	100% (80)	95% (76)	47.5% (19)
	area	Present	0% (0)	5% (4)	52.5% (21)
	Blue-whitish	Absent	100% (80)	92.5% (74)	25% (10)
	veil	Present	0% (0)	7.5% (6)	75% (30)
		1 color	42.5% (34)	25% (20)	0% (0)
		2 colors	53.75% (43)	63.75% (51)	32.5% (13)
	Color	3 colors 4 colors	3.75% (3) 0% (0)	11.25% (9) 0% (0)	27.5% (11) 32.5% (13)
		5 colors	0% (0)	0% (0)	7.5% (3)
		6 colors	0% (0)	0% (0)	0%

Table 5 .

 5 2: Result of ABCD rule obtained from PH 2 database

	Diagnositic Parameter	Doliantilis et al. [35]	PH 2 Database
	Sensitivity	77.5%	77.5%
	Specificity	80.4%	97.5%
	Accuracy	73.2%	87.5%
	Applying Analysis of Variance (ANOVA) on the vector obtained by ABCD rule
	on the H 0 (same population) against H 1 (different classes). The P-value obtained is
	less than 0.01 as given in the Matlab table reported in figure 5.1. Then, the hypothesis

H 0 is significantly rejected. Thus, the database presents significantly heterogeneous population (more than two classes).

Table 5 .

 5 3: Subjective evaluation rules.

	Evaluation		Description
		Excellent	It separates perfectly the two regions and improvement
			needed.
	Acceptable	Good	It separates very well the two regions but it can be im-
			proved
		average	It separates the two regions with small missed parts
			where the improvement of the segmentation is required.
	Unacceptable		It cannot not recognize the two regions or big parts of the
			lesion are missed.

Table 5 .

 5 4: Subjective Evaluation done by image processing expert on the results obtained from the extension of Chan and Vese model by inclusion method

	Segmentation quality	First expert	Second expert Third expert
	Excellent segmentation	69.06%	48.84%	13.95%
	Good segmentation	21.42.%	23.26%	55.81%
	Average segmentation	7.14%	18.60%	23.26%
	Unacceptable segmentation	2.38%	9.30%	6.98%

Table 5 .

 5 5 reports the results of experts for the two cases of evaluation, acceptable and unacceptable. It can be seen that more than 90% of segmentations are evaluated as acceptable by the three experts. Furthermore, these performances are obtained not only for the detection of lesion ROIs but also for the segmentation of the different development of moles in the skin lesion, which is the main objective of the proposed method.

	Table 5.5: Subjective Evaluation done by image processing expert on the results ob-
	tained from the extension of Chan and Vese model by inclusion method
	Segmentation quality	First expert	Second expert Third expert
	Acceptable segmentation	97.62%	90.70%	93.98%
	Unacceptable segmentation	2.38%	9.30%	6.98%

Table 5 .

 5 6: Number of features of studied combinations

			Features			features
	Features	Methods		Fusion	Methods
			number			number
		LBP ri	36		LBP ri + Wavelet	100
	Textural Features	LBP riu2	9	Fusion of	LBP riu2 +Wavelet	73
		LBP u2	59	textural and	LBP u2 +Wavelet	123
	Structural	Wavelet	64	structural	LBP ri + Curvelet	99
	Features	Curvelet	63	features	LBP riu2 +Curvelet	72
	Wavelet + Curvelet	127		LBP u2 +Curvelet	122

  mixed only with atypical nevus, those presented by the second and the third columns in the table 5.1. The results obtained are given in the table 5.7. Therefore, for textural features, the best performances are obtained by LBP u2 followed by the LBP ri , and the worst result are obtained by the LBP riu2 . For structural features, wavelet shows better results then curvelet for all metrics performances used. The fusion of textural and structural features gives better results in wavelet coefficients with LBP operator and it shows a smallest standard deviation for the variability of validation results expressed by the variable Std. Wavelet with LBP u2 improves the three metrics used and gives the best results compared to all the methods and method combinations studied. The fusion of curvelet coefficients with LBP operator improves the sensitivity, specificity and accuracy metrics compared to curvelet and LBP separately. However, wavelet with LBP shows better results than curvelet with LBP.From this first study, the dominant features are expressed LBPP u2 and wavelet methods with an accuracy validation of 80.85% and 84.23%, respectively. It can be seen that the results obtained by the fusion of LBP u2 and wavelet shows the best performance with an accuracy validation of 85.20%. However, wavelet with LBP ri and LBP riu2 is showing a result lower the wavelet method. In the other case, the fusion is of curvelet and and LBP variants is showing a better results than LBP and curvelet separately. It can be seen also that the the low results are obtained by th LBP riu2 variant, it can be explained by the few features used in this method (see table 5.6). Finally, the fusion of

wavelet and curvelet, which is the last case studied in the table 5.7, is not showing any increase of performance, oppositely it shows lower performance than wavelet features.

Table 5 .

 5 7: Results obtained for Melanoma Vs Atypical nevus giving Performance validation VP and the standard deviation Std for 1000 random-cross validation under SVM classifier.

	Performances Metrics	Sensitivity (sen)	Specificity (spe)	Accuracy (Acc)		Accuracy ( Ãcc)
	Features	Methods	VP	Std	VP	Std	VP	Std	VP	Std
	Textural Features	LBP ri LBP riu2 LBP u2	77.44% 11.88 81.97% 8.04 74.17% 12.09 73.19% 9.29 76.55% 12.32 85.15% 7.35	80.46% 5.82 73.51% 6.77 82.28% 5.56	79.70% 6.30 73.68% 6.83 80.85% 6.31
	Structural	Wavelet	79.47% 12.93 88.99% 7.10	85.79% 6.07	84.23% 6.84
	Features	Curvelet	73.10% 13.56 82.01% 7.56	79.04% 6.14	77.56% 6.85
	Fusion of	Wavelet + LBP ri	78.13% 12.08 88.63% 6.90	85.11% 5.49	83.38% 6.42
	Structural and	Wavelet + LBP riu2	77.51% 12.37 88.22% 5.80	84.62% 5.80	82.86% 6.81
	Textural Features	Wavelet + LBP u2	81.84% 11.29 88.57% 6.80	86.31% 5.48	85.20% 6.24
		Curvelet + LBP ri	79.08% 12.50 85.69% 7.34	83.49% 5.72	82.38% 6.08
		Curvelet + LBP riu2	76.15% 13.31 82.84% 7.66	80.61% 6.25	79.49% 6.83
		Curvelet + LBP u2	78.75% 11.89 86.83% 6.89	84.14% 5.51	82.79% 6.30
	Wavelet + Curvelet	78.97% 12.84 85.51% 7.14	83.98% 6.01	82.24% 6.87

Table 5 .

 5 8: Results obtained for Melanoma Vs Common nevus giving Performance Validation VP and the standard deviation Std for the 100random-cross validation under SVM classifier.

	Performances Metrics	Sensitivity (sen)	Specificity (spe)	Accuracy (acc)		Accuracy ( ã cc)
	Features	Methods	VP	Std	VP	Std	VP	Std	VP	Std
	Textural Features	LBP ri LBP riu2 LBP u2	82.28% 11.11 84.29% 7.71 78.92% 12.07 77.68% 8.35 80.82% 12.56 87.80% 6.78	83.62% 5.72 78.09% 6.16 85.47% 5.74	83.29% 5.88 78.30% 6.40 84.31% 6.70
	Structural	Wavelet	88.47% 10.36 91.99% 5.67	90.81% 5.23	90.23% 5.65
	Features	Curvelet	80.80% 12.25 84.53% 7.63	83.29% 6.20	82.66% 6.58
	Fusion of	Wavelet + LBP ri	88.82% 9.44	90.95% 5.93	90.24% 4.97	89.88% 5.15
	Structural and	Wavelet + LBP riu2	88.91% 10.06 91.45% 5.85	90.60% 4.99	90.17% 5.54
	Textural Features	Wavelet + LBP u2	89.25% 9.26	90.80% 5.59	90.28% 4.76	90.02% 4.92
		Curvelet + LBP ri	81.25% 11.36 85.68% 7.30	84.20% 5.76	83.47% 5.25
		Curvelet + LBP riu2	81.64% 11.93 85.34% 7.40	84.11% 6.23	83.49% 6.53
		Curvelet + LBP u2	82.86% 11.12 87.17% 6.86	85.73% 5.48	85.02% 6.03
	Wavelet + Curvelet	87.73% 10.57 90.40% 6.99	89.51% 5.68	89.06% 6.19

Table 5 .

 5 9: Results obtained for Melanoma Vs Atypical and Common nevus giving Performance validation VP and the standard deviation Std for the 100random-cross validation under SVM classifier.

	Performances Metrics	Sensitivity (sen)	Specificity (spe)	Accuracy (acc)		Accuracy ( ã cc)
	Features	Methods	VP	Std	VP	Std	VP	Std	VP	Std
	Textural Features	LBP ri LBP riu2 LBP u2	78.07% 12.35 86.14% 4.80 77.74% 11.29 75.95% 5.92 74.13% 13.01 89.40% 4.52	84.53% 3.89 76.31% 4.67 86.34% 3.82	82.10% 5.90 76.84% 6.02 81.76% 6.28
	Structural	Wavelet	77.56% 13.17 93.50% 3.48	90.31% 3.44	85.54% 6.54
	Features	Curvelet	70.42% 14.50 89.29% 4.91	85.52% 4.41	79.85% 7.18
	Fusion of	Wavelet + LBP ri	75.42% 13.68 93.46% 3.65	89.85% 3.52	84.41% 6.79
	Structural and	Wavelet + LBP riu2	76.73% 13.49 93.47% 3.59	90.12% 3.44	85.08% 6.67
	Textural Features	Wavelet + LBP u2	78.93% 11.95 93.25% 3.61	90.34% 3.27	86.07% 6.32
		Curvelet + LBP ri	72.35% 13.34 90.56% 4.41	86.92% 3.81	81.46% 6.55
		Curvelet + LBP riu2	70.30% 14.76 89.19% 4.72	85.38% 4.24	79.74% 7.13
		Curvelet + LBP u2	72.67% 12.88 91.09% 3.99	87.40% 3.61	81.88% 6.46
	Wavelet + Curvelet	76.16% 14.11 93.13% 3.68	89.74% 3.95	84.64% 6.99

Table 5 .

 5 10: Comparison of the results of proposed approach with the results of recent methods in the literature using the same database

	Method	Method used	sensitivity specificity accuracy
		The authors used color and shape geometry
	Abuzaghleh	features using Fast Fourier Transform (FFT)
	et al. [118]	and Discrete Cosine Transform (DCT). SVM	-	-	90.6%
	(2014)	classifier is used on PH 2 Database for 75% for
		training and 25% for test.
	Bi al. [132] et (2016)	The authors used multi-scale lesion-biased cross validate the obtained results. representation under joint reverse classifica-tion on PH 2 . However, the authors did not	87.50	93.13	90.31%
		Four algorithms to extract color constancy
	Barata et	(Gray World, max-RGB, Shady of Gray and
	al. [141]	General Gray World). SVM classifier with	92.5%	76.3%	84.3%
	(2015)	the χ 2 kernel is used for classification on PH 2
		database.
		A fusion textural and structural features. Re-
	Proposed method	sults of random sampling cross-validation un-for classification on PH 2 database with 70% der SVM classifier with the linear kernel used	78.93%	93.25%	86.07%
		for training and 30% for test.

Table 5 .

 5 10 presents a comparison of the proposed method with recent works on classification and recognition of melanoma using the same database PH 2 . Our proposed method shows the highest performance in terms of specificity and accuracy compared to Barata et al.[START_REF] Barata | Improving dermoscopy image classification using color constancy[END_REF], showing a validated result of 93% and 86% respectively. Although accuracy is higher for Abuzaghleh et al. proposition[START_REF] Abuzaghleh | Automated skin lesion analysis based on color and shape geometry feature set for melanoma early detection and prevention[END_REF] and Bi et al.[START_REF] Bi | Automatic melanoma detection via multi-scale lesion-biased representation and joint reverse classification[END_REF], they did not perform any validation comparing neither the current work validated by n-random sampling cross validation, nor k-fold cross validation used byBarata et al. In addition to this, the Abuzaghleh et al.[START_REF] Abuzaghleh | Automated skin lesion analysis based on color and shape geometry feature set for melanoma early detection and prevention[END_REF] used 75% of the database for training in place of 70% frequently used in the literature. The authors used the fusion of fast Fourier transform with discrete cosine transform, and their results are still less efficient than the proposed method due to the lack of validation of their results. Table5.11 and figure

Table 5 .

 5 11: Comparison of the results of proposed approach with the results of recent methods in the literature using the same database In addition the this, the authors did not present sensitivity and specificity performances, and no information on training and test sets is presented. Therefore, it is difficult to reproduce the same result for comparison. Furthermore, knowing that the benign lesions are heterogeneous[2], then, if we choose some special configurations of training and test sets we could present higher results

	Acc < 65%	65% ≤ Acc < 75% 75% ≤ Acc < 85% 85% ≤ Acc < 95% Acc ≥ 95%
	2	37	328	585	48
	5.11 are showing the importance of validation, where wa can choose a specific training
	and test sets to obtain higher result.

Table 5 .

 5 13: Number of detected area in equidistant segments using second level of irregularity (horizontal vertical). Crevasse geometrical forms

		malignant melanoma	benign melanoma (67
	number of elements
		(99 images)	images)
	0 sets	6 (≈ 6.1%)	27 (≈ 40.3%)
	[1-2]	38(≈ 38.4%)	24 (≈ 47.1%)
	[3-4]	26 (≈ 26.3%)	12 (≈ 17.9%)
	[5-6]	12(≈ 12.1%)	2 (≈ 3%)
	[7-8]	7(≈ 7.1%)	1 (≈ 1.5%)
	[9-10]	7 (≈ 7.1%)	1 (≈ 1.5%)
	[11-12]	1 (≈ 1%)	0 (≈ 0%)
	[12-...]	2 (≈ 2%)	0 (≈ 0%)

Table 5 .

 5 14: Result of SVM classifier using the extracted features following the different values of the threshold τ v .

	τ	sensitivity	specificity	accuracy
	0	73.33%	72.73%	73.08%
	10	60%	95.45%	75%
	19	80%	95.45%	86.54%
	20	80%	90.91%	84.61%
	30	86.67%	77.27%	82.69%
	40	80%	68.18%	75%
	50	86.67%	68.18%	78.85%
	60	83.33%	72.73%	78.85%
	70	86.67%	72.73%	80.77%
	80	83.33%	81.82%	82.69%
	90	86.67%	63.64%	76.92%

Table 5 .

 5 [START_REF] Stolz | Abcd rule of dermatoscopy-a new practical method for early recognition of malignant-melanoma[END_REF] presents the results of classification using different thresholds τ v . The results are performed following three performance metrics which are accuracy (acc), sensitivity (sen) and specificity (spe).

DullRazor software is available on http://www.dermweb.com/dull_razor/

ACKNOWLEDGEMENTS

Firstly, I would like to thank the two universities that were part of this joint supervision, Université d'Evry Val d'Essonne, Paris Saclay and Universiti Teknologi PETRONAS, for the opportunity they gave me to be part of their Ph.D program. They both collaborated and contributed to the succeed of this Ph.D study.

For N = 3, the following formula of M k n is obtained:

(4.9)

Equation (4.9) can be written by zero level set function φ and the Heaviside function H used in Chan and Vese model:

(4.10)

The existence of soft segmentation developed in equation (4.8) requires to satisfy two constraints. The first one requires that each membership function u i belongs to the interval [0, 1]. Then, the second is the constraint of summation of all the soft membership functions to be one [START_REF] Jianhong | A stochastic-variational model for soft mumford-shah segmentation[END_REF] as given by equation (4.11) below:

In the formula (4.9), we notice M 3 3 depends only on the membership function u 1 . The interrogations of how and why M 3 can be independent of u 2 using zero level set functions are explained in the next section. The development and the illustration of all possible configurations for the detection of 3 regions is also done.

Proposed Extension of Chan and Vese model

Unlike the generalizations of Chan and Vese model developed only for one configuration, in this current work, the objective is to find for each N , with 2 m-1 ≤ N < 2 m (⇒ N ∈ N), all the possible configurations. This objective will help to segment further the details of skin cancer images.

The idea of this work is to complete the segmentation with unfixed number of zero

Standard image orientation

Different illumination conditions, skin tones, hairs on the skin and varying the angle of image acquisition, add noise to this images. These artifacts make the feature extraction more challenging. Thus, a preprocessing is required to remove these additional noises.

Once the noise is removed, there is a need to present all the images in one standard view. Hence, in the current study, a conversion of the images into one common view is presented. Thus, the approach to normalize the images is presented.

The proposed method is applied when the region of interest (ROIs) are detected and boxed using bounding box and coordinates of ROIs from the binary images of ground truth given in the database. The dimensions of the bounding box depend on the size of the abnormal region itself. The ROI used are extracted manually, and taken as ground truth to show the contribution of the current approach.

To resolve this issue and standardize the size, the following strategy is adopted:

• Firstly, the minimization of the unwanted area using rotation of the ROIs from 0 to 180 degrees. Then, the box of ROI containing small area is selected.

• Secondly, horizontal (or vertical) orientation of boxes is chosen for standard view. Figure 4.15 illustrates the reorientation and the choice of direction on our database. It can be seen that ROI box is minimized to contain only the lesion.

The image provides from DermIs website (www.dermis.net) under the name of SSM26a.

The algorithm 1 summarizes the different steps of the standard image orientation method.

Segmentation of Images Results

The obtained results of the extension of Chan and Vese Model proposed in section 4.2 are presented in this section. The implementation of the developed method on different images is presented in the next subsection (5.3.1), then an evaluation of the segmentation is presented in subsection 5.3.2.

The algorithm is implemented in the whole database of malignant and benign lesions presented in section 5.2.3. The following figures illustrate different image segmentations showing visually more and less accurate cases. As mentioned in the literature, the most difficult of the original method is to provide the best parameters of the model to get attended segmentation. Therefore, for each presented image, the two parameters ν and dt are given. An exhaustive table for the whole database is given in the end of the section. The minimization given in equation (4.12) is not implemented in the current work. The reasons are discussed and some methods are suggested in perspectives and future directions.

To remove different noises, the segmentation is applied on cropped and resized image focused on the lesions. It makes the subjective evaluation of experts more confident when the border are formally recognized by the naked eyes.

Implementation

The two methods developed for detection of the three regions illustrated by figures 4.4 and 4.5 are applied and implemented on standard camera images in the database described in subsection 5.2.3. Therefore, two extended models are applied defined by equations (4.13) and (4.14) representing the separation and the inclusion of the two sets φ 1 and φ 2 respectively.

In this section, the methodology of implementation is presented, the different parameters used and the illustration of some images presenting the advantages and limitations of the method are also highlighted. As mentioned above, the minimization of these

Results of Border features

The results presented in this section refer to the method developed in section 4.3.3 applied on a database of 166 standard camera images detailed above in section 5.2.3.

Therefore, the proposed method extracts the irregularity border features exploring valleys and crevasses concepts illustrated in figure 4.17. Depending on the number and size of valleys and crevasses detected, for each image 8 different features are extracted, as summarized by equation (4.31). Then, using this set of features, the classification is performed utilizing Support Vector Machine (SVM) with linear kernel.

In the current section, the standard image orientation step is also implemented to normalize all images of the database in the same and common view. This normalization is summarized in algorithm1 and illustrated below in section 5.5.1.1.

Different implementations are explored with the proposed method, one with and the other one without the preprocessing (standard image view) step described above.

A comparison between the original and standard image view is also done. The main method of the current work includes the preprocessing step. The following points enumerates the procedure of implementation:

1. Implementation of the proposed method in its integrity using the both algorithms presented in subsections 4. Therefore, two kinds of results are presented. Firstly, the main result given by the whole algorithm using border features presented in the previous section. The second result shows the intermediate contribution of standard view images and the effect of the preprocessing step on the proposed method. 4 (≈ 4%) 0 (≈ 0%) [START_REF] Carli | Pattern analysis, not simplified algorithms, is the most reliable method for teaching dermoscopy for melanoma diagnosis to residents in dermatology[END_REF][START_REF] Emre Celebi | Lesion border detection in dermoscopy images[END_REF][START_REF] Lee | Dullrazor R : A software approach to hair removal from images[END_REF][START_REF] Wighton | Dermascopic hair disocclusion using inpainting[END_REF][START_REF] Kiani | E-shaver: An improved dullrazor R for digitally removing dark and light-colored hairs in dermoscopic images[END_REF] 4 (≈ 4%) 0 (≈ 0%) [START_REF] Taghi | An effective hair removal algorithm for dermoscopy images[END_REF][START_REF] Nhi H Nguyen | Segmentation of light and dark hair in dermoscopic images: a hybrid approach using a universal kernel[END_REF][START_REF] Xie | Pde-based unsupervised repair of hair-occluded information in dermoscopy images of melanoma[END_REF][START_REF] Fiorese | Virtualshave: automated hair removal from digital dermatoscopic images[END_REF][START_REF] Huang | A robust hair segmentation and removal approach for clinical images of skin lesions[END_REF] 4 (≈ 4%)

for N (v) > 25, malignant melanomas present 30% of the database valleys against less than 5% for benign melanoma. In the same time, for the number of detected valleys [1 to 5] 13.4% are found for benign melanoma and only 2% for malignant melanoma.

Using valleys concepts, around 50% of the data can be selected and classified. However from 11 to 25 valleys detected number is almost the same between benign and malignant melanoma. We conclude from this table that the malignant melanoma has more chances to contains more valleys than benign lesions.

Table 5.13 presents the number of crevasses detected with segment length of 2 from 0 to 14. Thus, from the table the absence of crevasses in benign lesions presents around 40% compared to malignant melanoma where only 6% without any crevasse are detected. Even if the crevasses exist in benign melanoma, in average, there are more in malignant than benign ones. In the other side, melanoma cases contain more crevasses with around 23% against 6% for benign lesion when N (c) > 5. From this table, the conclusion is that benign lesions contains less crevasses than malignant cases.

The two tables (5.12 and 5.13) describe perfectly the idea of border irregularity of ABCD rule with more deep analysis and study. The introduction of the two concepts (valleys and crevasses) as first and second level of border irregularity feature increases the detection and helps more the understanding of the feature itself.

In this subsection, the obtained results are compared with the method used by Amelard et al. [START_REF] Amelard | Melanoma decision support using lighting-corrected intuitive feature models[END_REF] (2014). Using the same database from dermQuest [5] and DermIs [4], our results outperforms significantly those presented by Amelard et al. as shown in Table 5.15 with an accuracy of 86.26% obtained by the proposed method to an accuracy of 81.26% obtained by Amerald et al.

In addition to that, as mentioned above, a preprocessing of the database is also done to clean all the redundant images as illustrated by figure 5.4 where the same image were acquired at different distance.

81.26%

Proposed method

Border irregularity features on standard view images

86.54%

Thus, by the proposed method, the border of pigment lesions is studied to discriminate the malignant and benign lesions on standard camera images. Therefore, the border irregularity of each pigment are deeply explored. In the literature, most of methods studied the irregularities following the two axis x and y giving some score as used in ABCD rule. The proposed method extracts a small set of features containing 8 irregularity border features. The obtained results are encouraging and showing higher performances comparing to the literature on the same database.

To conclude, in the current work, two ideas are proposed and explored. Firstly, the introduction of valleys and crevasses concepts for the irregularity of lesion borders, and secondly the standard view of the whole database with its impact on the result as it