Adnan Al

Al W Ani

Neonatal Events Recognition using LBP descriptor and Wavelet Thresholding Technique

Keywords: Local Binary pattern (LBP), wavelet thresholding, distance metric, preterm events recognition I

this paper presents an approach for preterm events recognition using local Binary pattern LBP and wavelet thresholding. Unlike conventional approaches which adopt contact measurement of vital signal and develop models for monitoring the preterm in neonatal intensive care unit (NICU), our approach describes non-contact monitoring vital signal based on thermal video as a new premature pain infant profile (PPIP). An interest clinical vital signal is face temperature of neonate. In this study, we collaborate with premature Infant events 'pain and normal states' detection and recognition during daily care monitoring. The proposed approach is composed of a thermal video analysis component and an activity recognition component. A video analysis component contains features descriptor using histogram of Local Binary Pattern LBP in the first experiment, and applying wavelet thresholding technique on approximation wave coefficients of histogram feature in the second experiment. Activity recognition contains classification of premature events using classifiers. We present recognition results by considering a variety of classifiers.

INTRODUCTION

Vital signals are physical quantities measured from body and can be used to determine the physiological behaviors and statues. Monitoring of vital parameters is an important factor in neonatal intensive care unit. Examples of this signal include heart rate, breathing rate, body temperature and blood pressure. Vital signs are used in neonatal intensive care to help diagnose the condition of a baby in a critical state. The state of condition monitoring of an infant cannot be observed directly, but different states of health are associated with particular patterns of measurements [START_REF] Quinn | Bayesian Condition Monitoring in Neonatal Intensive Care[END_REF]. Given observations of the respiration rate, blood sampling, and body temperature and so on, reasoning can therefore be made about the operation of the underlying physiological systems-e.g. whether they are functioning normally, or whether there seems to be evidence of some pathology. Most of vital signs measurements are taken by using contact probes. The measurements received by the cotside PC are affected not only by the physiological condition of the infant, Youssef CHAHIR GREYC-CNRS (UMR 6072), University of Caen Lower Normandy Caen, France youssef.chahir@unicaen.fr but also by the state of the recording equipment. Measurements are frequently corrupted with occasional patterns, caused by particular clinical procedures or changes to probes or equipment. The most obvious cause of occasional readings is a probe disconnection. When probes become physically disconnected from the baby, readings will tend to fall to zero. Further details on physiological monitoring procedures in the NICU are available, for example, in [START_REF] Rennie | A Manual of Neonatal Intensive Care[END_REF].

Relevant previous work on monitoring in intensive care, applied to the types of patterns based on contact probes are broadly categorized into three fields. Work based on statistical time series analysis was explored by some inserters. A useful reviews of some of the applications of statistical time series analysis to intensive care monitoring is given by [START_REF] Fried | Pattern Recognition in Intensive Care OnlineMonitoring[END_REF] [3] and [START_REF] Hoare | Automatic artifact identification in anaesthesia patient record keeping: a comparison of techniques[END_REF]. By contrast, another body of work is based on using domain knowledge to fonnulate high-level representations of particular patterns or situations, then to find suitable abstractions of the data in order to apply some matching rules. In this type of work, the goal is to describe what is happening. A more extreme example of the idea of abstracting data and the descriptions of clinical experts is given by [START_REF] Miksch | Utilizing Temporal Data Abstraction for Data Validation and Therapy Planning for Artificially Ventilated Newborn Infants[END_REF]. At the most specific level, there has been work on identification of particular individual patterns in monitoring data, for example to diagnose infection or particular respiratory problems. An example of this work is reported by [START_REF] Griffin | Toward the earl ear diagnosis of neonatal sepsis and sepsis-like illness using novel heart rate analysis[END_REF].

In general, thermal video analysis has significant challenges, it excite some researchers interesting to develop a relevant techniques for example human activity detection and recognition using standard dataset. Attempts were explored by researchers to develop approaches to detect and recognize human activities from thermal video can be found in [START_REF] Aren | feature based person detection beyond the visible spectrum[END_REF][11][12][START_REF] Mark | A two-stage template approach to person detection in thermal imagery[END_REF][START_REF] Wang | Improved detection and classification in Thermal images[END_REF]. The implementation details of these approaches are beyond the scope of this paper.

Medical thermal imaging (also known as Digital Infrared Thermal Imaging DITI or Medical Infrared Imaging) uses ultra-sensitive thennal imaging camera to produce high resolution diagnostic images of the body. These images can be used to detect areas of temperature changes associated with areas of high metabolic activity, inflammation and enhanced circulation. This makes the images useful in diagnosing pain and injury, circulatory pathology and in monitoring treatment. Recently, thermal imaging was introduced as non-contact probe in neonatal intensive care for condition monitoring. For instance, thermal video can be used to maintain thermal signature of baby's skin, as well as thermal video analysis depend on temperature signature of object under study. Moreover, Dynamic shape of recorded temperature specifies the texture characteristics of thermal image and it is used to detect meaningful behavior of the target.

As mentioned, to overcome the limitation of using the contact probes in NICU, thermal video works more efficiently by deriving and using information of local thermal signature from infants' body. However, this kind of imaging present body configuration in form of thermal pixels, also, it has remote accesses facility, and may be used as visual alarm in condition monitoring. There are attempts in neonatal condition monitoring based non-contact measurements, including neonatal respiratory monitoring based on thermal video [START_REF] Garbey | Contact-free measurements of cardiac pulse based on the analysis of thermal imagery[END_REF], and Contact-free measurements of cardiac pulse based on the analysis of thermal imagery [START_REF] Abbas | Neonatal non-contact respiratory monitoring based on real time infrared thermography[END_REF].

Recently detection and recognition physiological events in neonatal based thermal video have been little explored. In this work, we report a method of preterm physical responses detection and recognition. The motivation in this work is to explore the power of Local Binary Pattern and wavelet thresholding technique as local thermal descriptors for neonates' events detection. We have made an improvement on the features description by adopting pairwise distance between feature vectors. For instance, Hausdorffs distance function and Entropy distance functions are introduced to improve the features representation. To evaluate our method we employ a support vector Machine SVM, and K nearest neighbor, classifiers. Moreover, we recognize neonates' pain response using variety of classifiers. The purpose of using multiple classifiers is to provide a comparison between the feature descriptions, because there were no experiments and methods were focused on the neonatal events recognition based on thermal imaging using NICU dataset environment. Experiments show that the recognition task achieves reasonable results on NICU dataset based thermal video.

The paper is organized as follows. Section 2 presents the outline of the method, section 3 describes problem formulation, where the proposed method is elaborated from features descriptions to evens recognition by a variety of classifiers. We proceed to sections 4 and 5 to explain experimental setups and results respectively. Section 6 concludes the paper.

II. METHODOLOHY

Our approach is composed of two stages to obtain the local description of the infant's events. The first stage is to describe local thermal features by using LBP and then concatenate these features into one dimensional histogram vector. To make the histogram more efficient, we have evaluated the similarity matrix between histogram features vectors using Hausdorffs and entropy distance function, respectively. In the second stage, a feature descriptor is obtained by producing an approximation coefficients threshold of histogram vectors which are computed using wavelet transform WT. As in the first stage, similarity matrices are adopted for improving the feature descriptor. Fig. l shows the basic steps of our method. The first step defines ROI area around face of object. Then local patch of size k*k*t is defined. LBP is computed in second step. And the classification task is performed in the last steps.

III. PROBLEM FORMULATION

In this work, local feature descriptions using LBP and subsequent contributions are described. The feature description from LBP is subject to some variation. With the use of wavelet threshold technique, we can improve the feature description which leads better recognition accuracy.

A. Local Binary Pattern Descriptor LBP has originally been proposed for texture analysis and classification [START_REF] Ojala | Multiresolution gray scale and rotation invariant texture classification with local binary patterns[END_REF]. Recently, it has been applied on face recognition [START_REF] Ahonen | Face Description with Local Binary Patterns. Application to Face Recognition[END_REF][8], and facial expression recognition [START_REF] Shan | Facial Expression recognition based on Local Binary Patterns. A comprehensive study[END_REF].

Where, n is the number of different labels produced by the LBP operator. Having constructed the histogram feature of local patch, histograms from these planes are concatenated into a single histogram vector H= {Hl ,H2., .... Hn}. Fig. 2 shows example of extracting histogram features vector from local patch of video sequence and denote this LBPH. Figure 3 illustrates example result of LBPH extracted from subject example showed in figure 2.

B. Pair wise distance representation

The objective of this section is to utilize the remarkable discriminative ability of the similarity based representation. More specifically, we have improved the above descriptor by using pairwise distance function. In order to accomplish that, the histogram features is transformed into similarity space. Moreover, as each video is represented by a LBPH, the distance function is used to compute the similarity value between two sets histogram vectors. Several distance metric methods have been developed to compute the distance between two sets of vectors [START_REF] Bryant | Metric Spaces: Iteration and[END_REF].

Here, a task where new events are discriminated on the rule of pairwise recognition to events of a training set is adopted. The general mathematic formulation for similarity space is illustrated as follows:

We denote by d(hj,hj) the distance between two histogram vectors, the similarity matrix is defmed as in [START_REF] Charbonnier | On-Line Segmentation Algorithm for Continuously Monitored Data in Intensive Care Units[END_REF] Where, Q specifies the distance function used to compute the similarity matrix. Furthermore, let X and Y be two non empty subsets of a metric space. We define their Hausdorff distance as in. dH(Xy)=max{supxcX in/yc Y d(x,y) ,SUP y c Y inixc xd(x,y)). (4) Where sup represents the supremum and inf the infimum similarly, Entropy function is also introduced to evaluate the discriminative power and efficiency for feature description improvement. The entropy distance between two random variables can be defined to be the difference between their joint entropy and their mutual information as

DlX Y)= H(X Y) -H(X; Y). (5)
Where, H(X,Y)= �;P(x,y) logllp(x,y), is the joint entropy of X,Y.

For the final step of the feature extraction, linear Discriminant analysis performed on the pairwise feature set. Basically, LDA is based on the class specific information which maximize the ratio of between-class scatter and the within-class scatter matrix. the LDA algorithm looks for the vectors in the embedding space to create the between classes discrimination.

Thus, utilizing LDA on the pairwise features, robust feature space can be obtained that discriminate the set vectors of each class.

C. Wavelet Thresholding of Histogram Features

Feature description is the most important information for preterm events recognition; it is used to distinguish one kind of physiological event different from another kind of event.

As described in the last section, the LBP approach to event recognition involves extracting histogram feature vector from images sequences. We believe that wavelets may be a better choice to improve feature description so we propose to use wavelet multi-resolution analysis [22], and wavelet thresholding technique [START_REF] David | Ideal spatial adaption via wavelet shrinkage[END_REF]. More details of wavelet signal analysis can be found in [START_REF] At | A wavelet tour of signal processing[END_REF].

Our goal is to apply wavelet thresholding or wavelet shrinkage technique on extracted approximation coefficients of histogram vector, the resulting feature define the feature description based wavelet threshold we call this LBPWT. In our implementation, multi-levels wavelet is used to encodes histogram features vector H= {h" .... hn} as approximation 12 components , and the result is vector containing an approximation wave coefficients KQ). It is observed that features of the approximation components change smoothly, which is a suitable property for discrimination. The approximation components are also known to be a robust and distortion tolerant feature space for many pattern recognition applications. The histogram vector is decomposed to a certain level and the coefficients at the lowest level are selected to form feature description vector. One Dimensional Jlevel wavelet decomposition on a vector H= { represents the coefficients by a set of approximation and details components [aj, {d),dz, .... A}j�IJ]. Where h" .... hn} aJ is a low resolution approximation of the original signal, and dj are detail coefficients containing the details of the signal at different scales. Figure 4 shows an example result of wavelet decomposition at two levels, where a wave coefficients and details of the histogram are showed. Note that, for this two levels decomposition all wave coefficients are illustrated in this figure .   One of the advantages of using wavelet thresholding is its potential to deal with noise. wavelet thresholding characterized as decomposition of the signal or into wavelet coefficient with a given threshold value, and shrinking these coefficients close to zero to reduce the effect of noise in the data, then applying thresholding technique to find smoothing version of wavelet components. There exist various methods for wavelet thresholding developed by [START_REF] David | Adapting to unknown smoothness via wavelet shrinkage[END_REF], [START_REF] David | Ideal spatial adaption via wavelet shrinkage[END_REF], [START_REF] Moulin | Wavelet thresholding techniques for power spectrum estimation[END_REF], which rely on the choice of a threshold value. In this experiment, we adopt hard thresholding technique as a threshold function defined as.

T = {I, I xl > t o otherwise ( 6
)
Where t is the threshold value and can be calculated using the formula below

t = (J ..J2 log(n). ( 7 )
where, n being the signal length, (J being signal variance which can be estimated from wavelet coefficients. As a result, the extracted approximation coefficients from wavelet threshold are encoded as a features descriptor. Fig. 5 shows the plot of the thresholding wave coefficients.

: : = 1

IV. EXPERIMENTAL RESULTS

For events recognition experiments, we chose to use the dataset of neonatal in NIUe system based thermal video. The dataset are provided by preterm ANR project. These dataset contains several thermal videos monitoring of the Premature Infants, we encode among of these videos a 20 clips which represent an event of premature pain state, as well as a 20 clips represent a normal state event of premature. Moreover each event was collected from 20 different infants. Altogether, the dataset contains 40 samples of two events class problem. The length of each sample is equal to 20 frames.

A patch of size llxll pixels is defined over infant's face as local interest area. The features vectors and corresponding distances matrices were described in sections 2.2 and 2.3.

For LBP the P parameter is set to P=4. Doubechies wavelet function is used with 3 decomposition levels.

We start the experiments with the recognition task based on traditional LBPH descriptor. Thus, to compare the performance enter the classifiers, pairwise distance based experiments were designed in this connection. For further experiments, features descriptor was encoded as a wavelet threshold-based technique. Conventional classifiers of SVM, and k-NN, are used for recognition task.

A. Results

To evaluate the proposed method, we conduct the recognition results on the dataset described above. In each of our approaches experiment, the training process is done on a 20 samples (neonates), and testing phase was performed on another 20 samples.

Because no available of such methods that are focused on the neonate physiological events recognition, we did not attempt a comparison with other methods. Rather, we provide results only to show that our approach works well on a diverse range of data such as neonates' events recognition based thermal video.

We first applied the LBPH directly with classifiers. The recognition rates of two classifiers are listed in Tablel.Since LBP is considered to be good texture descriptor of face, it seems poor operator as shown in table I. Furthermore, we continued our experiments to the wavelet threshold-based LBP descriptor, and we call this WTLBP. Moreover, WTLBP applied directly with recognizers and the recognition rate is summarized in Table II. Since LDA is a good tool to separate the underlying feature space, therefore, a better feature space is created by applying LDA classification over the pairwise features. Hence, LDA-based experiments over pairwise features are listed in table III As a comparison, the performance of LBPH descriptor in combination with pairwise distance is better in events recognition of premature from thermal video.

V. CONCLUSION

In this paper, we have applied LBP as a descriptor of local-based approach for neonatal activity recognition from thermal video, and shown LBP to be suitable for the description of thermal video containing information about neonates events. We have extended feature descriptor by considering the pairwise distance between histogram features vectors. We showed how the use of pairwise distance based LBP descriptor gave rise to an efficient events descriptor. We further extend LBP descriptor by encounter Wavelet thresholding technique. Furthermore, we applied wavelet Thresholding on LBP histogram by compute the threshold value from wavelet coefficients. The experimental results reveal that LBP tend to be good candidate for events description and recognition. The best accuracy has been obtained by using the pairwise metrics between histogram vectors set.

  We denote a video sequence as S = {I),Iz, ... , In }, where Ik is a r xc image frame. In contrast, treating the video as a spatio-temporal data volume and for entire spatio-temporal location we denote by W(v) the local patch volume v of ROI. Furthermore, denote by LBP (W(v)), or M(v) the LBP of local patch. Hence, using the 2D patch to slide over the video sequence and get the local features. The value of LBP code of a pixel (xc,Yc) within the patch is obtained as in Inout video n Patch extraction Features description

Figure 1 .

 1 Figure 1.method of events-based feature description and recognition.

Figure 2 .

 2 Figure 2. Histogram Features extraction from Local patch

Figure 3 .

 3 Figure 3. Concatenated Histogram vector, (top) pain response,(bottom) normal response.

.Figure 4 .Figure 5 .

 45 Figure 4.Wave coefficients of illness state (top panel) detiales dl and d2 components, (nottom panel) apprixination component.

  , showing both the Hausdorffs distance function and Entropy function experiment based methods. The experiments results show that Hausdorff distance outperforms over the Entropy distance and LBP over WTLBP. In summary, by combining the LBPH and pairwise distance, we can obtain better features to represent thermal signature in thermal sequence.

TABLE I .

 I RECOGNITION RATE (%) OF DIRECT LBPH

	Method	K-NN	SVM
	LBPH	80	65

TABLE n .

 n RECONITION RATE (%) OF DIRECT WT LBP

	Methods	k-NN	SVM
	WTLBP	65	75

TABLE TIT .

 TIT RECONITION RATE (%) OF APPLAYING LDA OVER PAIRWISE

	FEATURES VALUE
	methods	k-NN	SVM
	LBP+Hausdorf. LBP+ Entropy WTLBP+Hausdorf. WTLBP+ Entropy	75 80 50 50	70 85 85 50

ACKNOWLEDGEMENTS

The authors wish to thank ANR Preterm, for providing datasets of neonatal conditions monitoring of daily care.

The first author would like to thank his employer, university of AL Anbar for their continuous supporting during study time.


S Alkama
email: sadiaalkama@mail.ummto.dz

Y Chahir

D Berkani

Sadia Alkama -Corresponding

‡ Daoud Berkani
email: daoud.berkani@enp.edu.dz

LABEL MAPS FUSION FOR THE MARGINAL SEGMENTATION OF MULTI-COMPONENT IMAGES

Keywords: marginal segmentation, fusion of label maps, multi-component image, Self Organization Maps

In this paper, we propose a new technique for merging the label maps obtained by the marginal segmentation of a multi-component image. In the marginal segmentation, each component of the multi-component image is independently segmented by labeling the pixels of the same class with the same label. Therefore the number of label maps corresponds to the number of components in the image. It is then necessary to merge them in order to have a single label map, i.e. a single segmented image. In the most merging techniques, the compatibility links between these maps are performed a priori by making the correspondences between their labels. However the various components are segmented and labeled independently, label maps are considered as independent sources. It is then difficult to establish the relationship compatibilities between labels. The method we propose does not a priori assume any compatibility links. The label maps are combined by superposition. Unfortunately, an over-segmentation is produced. To cope with this problem, the insignificant regions and classes are eliminated. Finally, classes are grouped by using hierarchical agglomerative clustering algorithm. Tests performed on color and satellite images show the effectiveness of this method and its superiority compared to the vector segmentation. The self-organizing map is used during the segmentation process in both marginal and vector segmentations.

Introduction

Image segmentation is a field of research which is still expanding. The techniques of image segmentation were first developed for gray-level images (monochrome or mono-component), then they were extended to the multi-component images which have a higher dimension and are provided by more complex vision systems. The multi-components images provided by these sensors are used in various sectors such as in medical field, remote sensing, quality control, etc. These images can be color, multi-spectral, medical, etc.

The segmentation is a critical step in image processing because it affects the quality of the interpretation and of the decision-making. It consists in regrouping the pixels of the image in regions according to their characteristics or features. Several approaches can be used for this purpose. The techniques based on the pixel classification approach consist in assigning a class number to each pixel of the image. The result of this operation is a segmented image called a label map where each pixel is represented by one label which corresponds to the class number in which this pixel has been assigned. Note that the problems of segmentation and classification are closely linked and both words can be used to mean the same thing as all pixels within the same class and which are connected form a region of the image.

Our interest in this paper is the multi-component image segmentation. Three approaches are used to segment the multi-component images [START_REF] Cheng | Color image segmentation: advances and prospects[END_REF][START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF][START_REF] Plataniotis | Color image processing and applications[END_REF]. The first one, called scalar approach, consists in segmenting a single monochrome image obtained by merging all components of the multi-component image. The so-called vector approach considers each pixel as a vector where each element corresponds to a component value and only one processing is applied to this image. The approach described as marginal consists in applying the same segmentation technique independently to each component of the image. This last technique provides a set of label maps where the number of maps is equal to the number of components in the image. These label maps must be merged in order to provide a single label map.

Contrary to the vector approach where many works deal with this field [START_REF] Alkama | Markovian approach using several Gibbs energy for remote sensing images segmentation[END_REF][START_REF] Bhattacharya | Wavelets-based clustering techniques for efficient color image segmentation[END_REF][START_REF] Hema | Automatic MR Brain tumor detection using possibilistic C-Means and K-means clustering with color segmentation[END_REF][START_REF] Holota R | Colour image recognition based on single-layer networks of Min/Max nodes[END_REF][START_REF] Wu M.-N | MRI brain lesion image detection based on colorconverted K-means clustering segmentation[END_REF][START_REF] Kudelka | Orthophoto feature extraction and clustering[END_REF][START_REF] Xue | A new method of color map segmentation based on the self-organizing neural network, emerging intelligent computing technology and applications with aspects of artificial intelligence[END_REF][START_REF] Oscar | An adaptive unsupervised approach toward pixel clustering and color image segmentation[END_REF], few works has been devoted to the marginal segmentation where the major difficulty lies in the fusion of label maps. The works dealing with label maps fusion often merge the binary maps which are edge/no-edge maps obtained by using a contour detection. The merge of edge/no-edge maps is often performed by logical operators such as "or" and "and" [START_REF] Busin | Color spaces and image segmentation[END_REF][START_REF] Harrabi R | Color image segmentation by multilevel thresholding using a two stage: Optimization approach and fusion[END_REF][START_REF] Rosenfeld | Digital Picture Processing[END_REF] or by statistical analysis of correspondences between these maps [START_REF] Giannarou | Fusion of edge maps using statistical approaches[END_REF].

When a label map contains more than two labels the merging problem becomes more difficult. Some authors [START_REF] Charrier | Segmentation d'images couleur par la théorie de l'évidence[END_REF][START_REF] Lezoray | Segmentation d'images couleur par coalescence non supervisée d'histogrammes 2D et fusion de régions selon la théorie de Dempster-Shafer[END_REF] perform this fusion by using the evidence theory which has been originally introduced by Dempster [START_REF] Dempster | A generalization of bayesian inference[END_REF], and further developed by Shafer [START_REF] Shafer | A Mathematical theory of evidence[END_REF]. One difficulty of this theory is in the choice of the modeling mass functions [START_REF] Colot | Evidential segmentation scheme of multi-echo MR images for the detection of brain tumors using neighborhood information[END_REF]. Another problem with this technique is in establishing the compatibility links between the labels of various maps. In fact, the various components of the image are segmented and labeled independently since the label maps are considered as independent sources. There is no guarantee that the same label is assigned to the same area of interest in these different maps. To complete the fusion by the evidence theory, the correspondence between the labels must be made in advance.

The fusion of the label maps can be performed also by using the majority-vote rule [START_REF] Mitchell | Image fusion: theories, thechniques and application[END_REF]. This technique starts by establishing the correspondence of labels in the different label maps. Then, the fusion of these label maps, which are semantically equivalent, is performed by assigning to each pixel in the final map the label that occurs most frequently in the original label maps.

Other authors have treated the fusion of label maps differently [START_REF] Hemelatha | Segmentation by blended partitional clustering for different color spaces[END_REF][START_REF] Ioannou | Fuzzy data fusion for multiple cue image and video segmentation[END_REF][START_REF] Kurugollu | Color image segmentation using histogram multithresholding and fusion[END_REF][START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF][START_REF] Kumar | Segmentation by K-means clustering indifferent color spaces[END_REF][START_REF] Du | Cluster ensemble-based image segmentation[END_REF]. For example, Kurugollu et al. [START_REF] Kurugollu | Color image segmentation using histogram multithresholding and fusion[END_REF] propose a semi-marginal color image segmentation by a multi-thresholding of the RG, RB and BG histograms. The fusion of three label maps is conducted in two successive steps. The first step performs the concordance of labels in the three maps by assigning the same value for the labels having a maximum of occurrences. The next step performs the maps fusion by assigning for each pixel label that is most repeated in its 5 × 5 neighborhood. Lezoray and Charrier [START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF] use a morphological clustering, on the two-dimensional histograms RG, RB and BG, to create three label maps. Then, they eliminate in each map the regions which are sized less than a structuring element of size 3 × 3. Thereafter, they superpose these maps. The fusion map thus generated produces a large number of the labels and regions. A region merging technique is then performed by using a spatial adjacency graph where the adjacent and similar regions are merged.

The fusion of label maps is also involved in the combination of several different segmentations of the same image produced by different parameter settings of the same segmentation algorithm or by different segmentation algorithms [START_REF] Franek | Image segmentation fusion using general ensemble clustering methods[END_REF][START_REF] Hemelatha | Segmentation by blended partitional clustering for different color spaces[END_REF][START_REF] Jawale | Fusion based edge detection and segmentation of color spaces[END_REF][START_REF] Samuel Varaprasad Raju | Edge detection and segmentation by fusion of histogram-based K-means clusters in different color spaces[END_REF]. Combining multiple segmentations can be viewed as a special case of the cluster ensemble problem, i.e., the concept of combining multiple data clustering for the improvement of the final clustering result [START_REF] Mignotte | A precision-recall criterion based consensus model for fusing multiple segmentations[END_REF]. For example, Franek et al. [START_REF] Franek | Image segmentation fusion using general ensemble clustering methods[END_REF] produce N segmentations of an image by varying some parameters or by using different segmentation algorithms. They after generate a super-pixels image (regions image) by combing these N segmentation label maps. They eliminate small regions before they use an ensemble clustering method to reduce the number of objects. Because of eliminating small super pixels before some pixels are unlabeled. These pixels are simply merged to the neighboring region with the smallest color difference.

The fusion of label maps is also used in the combination of the segmentation maps obtained by different segmentations on a same image with different color spaces [START_REF] Ma | Segmentation by fusion of self-adaptive SFCM cluster in multicolor space components[END_REF][START_REF] Harrabi R | Color image segmentation using multi-level thresholding approach and data fusion techniques: application in the breast cancer cells images[END_REF][START_REF] Mignotte | Segmentation by fusion of histogram-based K-means clusters in different color spaces[END_REF]. The fusion model proposed in [START_REF] Mignotte | Segmentation by fusion of histogram-based K-means clusters in different color spaces[END_REF] and [START_REF] Harrabi R | Color image segmentation using multi-level thresholding approach and data fusion techniques: application in the breast cancer cells images[END_REF] combines the individual input segmentations by applying a K-means algorithm where each pixel is characterized by a set of local label histogram values given by each input segmentation. The same strategy with the spatial FCM clustering, instead of K-means, is used in [START_REF] Ma | Segmentation by fusion of self-adaptive SFCM cluster in multicolor space components[END_REF].

We propose in this paper a new fusion technique of the label maps. This procedure is simple to implement, fast and can be used in various computer vision applications. It is fully automatic contrary to other techniques that perform the fusion by using the evidence theory or the ensemble clustering approach. Recall that to complete the fusion by using the evidence theory or the majority-vote, the correspondence between the labels must be made in advance, usually by an expert user and rarely is it performed automatically. In the proposed fusion procedure, this tedious step is eliminated and the fusion is fully automatic and no correspondence between the labels is needed. Furthermore, some techniques like in [START_REF] Franek | Image segmentation fusion using general ensemble clustering methods[END_REF][START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF] remove small regions in each label maps before the fusion step. This procedure is then computed as many times as there are components in the image. After combining the maps, a new removing procedure of the small regions can also be used. This downstream processing is computationally expensive and removes regions which will be removed in the upstream processing. To save time and because an upstream processing is more relevant than a downstream processing, in our proposed method only an upstream processing is performed. Indeed, the downstream processing processes each component independently of the other components, while the upstream processing involves the interaction of spectral components because it did on the combined component. The other originality of the proposed fusion procedure lies in how the pixels belonging to the small (insignificant) regions and small (insignificant) classes removed, are assigned to the remaining significant classes.

Before the fusion, the classification algorithm SOM (Self Organization Maps) is used to segment independently each component of the multi-component image. This algorithm has been widely used and demonstrated its effectiveness in the field of the image segmentation [START_REF] Anitha | An efficient Kohonen-fuzzy neural network based abnormal retinal image classification system[END_REF][START_REF] Awad | Segmentation of satellite images using Self-Organizing Maps[END_REF][START_REF] Jiang | SOM ensemble-based image segmentation[END_REF][START_REF] Kanimozhi | Brain MR image segmentation using self organizing map[END_REF][START_REF] Mautner | Processing and categorization of Czech written documents using neural networks[END_REF][START_REF] Ramirez | Self organizing maps in seismic image segmentation[END_REF]. In the proposed fusion procedure, the label maps are combined into a single map by assigning for the same "label combination" of label maps the same label in this resulting map. Conversely, different "label combinations" will have different labels in the resulting map. In this new and single map, the number of regions and classes (labels) are very high. Insignificant regions and classes are then eliminated by assigning efficiently their corresponding pixels to others classes which are considered as significants. Finally, the hierarchical agglomerative clustering algorithm is used to group the remaining classes until reach the desired number of classes. The results obtained by this marginal segmentation technique are compared with those obtained by a vector segmentation technique using the same SOM algorithm.

The remainder of this paper is organized into five sections. The proposed marginal segmentation is cursory described in the Section 2. Section 3 is devoted to the SOM classification algorithm used in the first phase of proposed segmentation. The steps of the proposed fusion method are detailed in Section 4. The different results, their assessments and a discussion are given in Section 5. We conclude with a conclusion in Section 6.

Proposed marginal segmentation

In the marginal segmentation approach, the components of the image are processed separately. The number of components depends on the kind of the multi-component image. For example, it is equal to three in the case of the color images and it can be higher in the case of the multi-spectral images.

The marginal segmentation is made in two successive phases which are the monochrome independent segmentation of each component and the fusion of label maps obtained in the previous phase.

In the first phase, any gray-level image segmentation technique can be used. In this paper, the SOM algorithm is chosen to segment each component of the image because of its effectiveness proved in the field of the image segmentation [START_REF] Awad | Segmentation of satellite images using Self-Organizing Maps[END_REF][START_REF] Jiang | SOM ensemble-based image segmentation[END_REF][START_REF] Kanimozhi | Brain MR image segmentation using self organizing map[END_REF][START_REF] Ramirez | Self organizing maps in seismic image segmentation[END_REF]. This algorithm is presented in the next section. Each component of the multi-component image is segmented by the SOM algorithm independently of others components. A label map of each component is then generated by assigning to the pixels of the same class a same label and to the pixels belonging to different classes different labels. We obtain then as much label maps as there has components in the image. For example, for the color images, we obtain three label maps.

The second phase of this strategy is very delicate. Some works deal with the label maps fusion [START_REF] Busin | Color spaces and image segmentation[END_REF][START_REF] Charrier | Segmentation d'images couleur par la théorie de l'évidence[END_REF][START_REF] Kurugollu | Color image segmentation using histogram multithresholding and fusion[END_REF][START_REF] Lezoray | Color image segmentation using morphological clustering and fusion with automatic scale selection[END_REF]. The most of them need a priori the knowledge of compatibility links between the label maps. In this paper we propose a new fusion technique to merge the label maps. This technique do not a priori assume any compatibility link between labels. It consists of four steps which are illustrated in Fig. 1. To distinguish the different changes in these steps, an illustration on a color image is presented. The detail of this phase is given in Section 3. Note that the label maps are displayed as color images where each label (i.e. class) is represented by the average color of all pixels having this label (i.e. assigned to this class) and the boundaries are deliberately indicated in bold by white color.

Segmentation by self-organizing maps

Topographic maps or self-organizing maps (SOM) are neural networks that are used for unsupervised learning. They were introduced for the first time by T. Kohonen in 1981 [START_REF] Kohonen | Self organization and associative memory[END_REF][START_REF] Kohonen | Self Organizing Maps[END_REF]. Since then, many works deal with the SOM algorithms especially in the image processing and image segmentation [START_REF] Anitha | An efficient Kohonen-fuzzy neural network based abnormal retinal image classification system[END_REF][START_REF] Araujo | Local adaptive receptive field self-organizing map for image color segmentation[END_REF][START_REF] Mautner | Processing and categorization of Czech written documents using neural networks[END_REF][START_REF] Wehrens R | Self-organising maps for image segmentation[END_REF]. The most important feature of these maps is their ability to self-organize observations into groups.

Before developing the principle of self-organizing maps, it is necessary to introduce some notations. Let Υ be the set of the observations of D dimensions, Υ ⊂ R D . The self-organizing map is a neural network that consists of two layers (see Fig. 2):

• An input layer, which is the subset Y = {y i ; i = 1, . . . , n} of Υ consisting of n elements of a learning set. In our case, Y represents a multi-component image containing the pixels y i characterized by D features. It can also represent one component of a multi-component image in the case of a marginal segmentation, in this case D is equal to 1. In this input layer, all states of all neurons are then forced to the values of the observations y i .

• A 2D computational layer, noted φ, which is formed of lattice neurons that are forming the map. This neural set is denoted W = {ω c ; c = 1, . . . , p} and formed by p vectors of Υ, which are D-dimensional. Each of these neurons is connected to all elements of the input layer.

Let F be an allocation function defined as an application of Y to the set {1, . . . , p} (F : Y → {1, . . . , p}). This function F is used to assign to each input vector y i ∈ Y a neuron with the index c selected from the set {1, . . . , p} and designated by the weight vector ω c , such as the vector ω c is the most similar to y i .

F (y i ) = arg min c ∥y i -ω c ∥ 2 . ( 1
)
During the learning phase of the network, the weight ω c of the winning neuron c is modified as well as weights of the neurons of its neighborhood. The distances δ(c, r) which link the neuron c to the other neurons r of the map allow to vary the relative influence of the various neurons [START_REF] Kohonen | Self Organizing Maps[END_REF].

Fig. 1 General scheme of the proposed marginal segmentation approach: (a) Original image. Marginal segmentation into 7 classes of the components: (b) red (c) green (d) blue. (e) Combination map (187 classes, 9063 regions). (f ) Label map without insignificant regions (90 classes, 388 regions). (g) Label map without insignificant classes (73 classes, 314 regions). (h) Final label map (7 classes, 86 regions).

Recall that the distance δ in φ of any pair of neurons (c, r) of this map is defined as the length of the shortest path between c and r on φ. For example, in Fig. 2 the distance between r and c is δ(c, r) = 4.

This relative influence of the various neurons is quantified by the neighborhood function V T (δ(c, r)) which forces the weights of neurons located in the neighborhood of neurone c to get their values near to the input vector y i . The more a neuron is far from the best matching neuron, the less the variation is important. The function of neighborhood used in this paper is parameterized by a temperature factor T in order to take into account the size of the neighborhood and is given by

V T (δ) = exp(- δ T ).
Fig. 2 Representation of a 2D topographic map of Kohonen.

The self-organizing map algorithm minimizes the cost function noted J T som [START_REF] Kohonen | Self Organizing Maps[END_REF] given by

J T som (W ) = ∑ yi∈Y ∑ c ∈C V T (δ(c, F (y i )))∥y i -ω c ∥ 2 .
The minimum is obtained by setting to zero the derivative of J T som (W ). In the stochastic version of Kohonen, it is not required to find the global minimum of J T som (W ), it is enough to decrease its value. Thus, at the t-th iteration, the weight c of a neuron is modified according to

ω t c = ω t-1 c + µ t ∂J T som ∂ω t-1 c , where ∂J T som ∂ω c = 2 ∑ yi∈Y V T (δ(c, F (y i )))(y i -ω c ).
The neuron weights are updated by using the following equation:

ω t c = ω t-1 c -µ t V T (δ(c, F (y i )))(ω t-1 c -y i ), (2)
where µ t is a decreasing function according to the iterations t. In this work we use

µ t = 1 √ t .
The Kohonen algorithm is summarized in Algorithm 1.

The function V T of neighborhood is parameterized by a temperature factor T in order to take into account the size of the neighborhood. For large values of T , an observation y i changes a large number of neuron weights. On the contrary, for Algorithm 1 Kohonen self-organizing map algorithm [START_REF] Kohonen | Self organization and associative memory[END_REF].

{1. Initialization phase} Choose the φ structure, the size of the map and the initial p neuron weights W 0 (randomly).

Set the values of T max and T min and the number of iterations N iter , let t = 0. repeat {2. t iterative step} Choose an observation y i (usually randomly).

T ← T max ( T min T max ) t N iter -1
{Calculate the new value of T } For this parameter, perform the following two phases: Affectation phase: affect the observation y i to the neuron F t (y i ) defined by the relation (1) Minimization phase: change the values of W t by the relation [START_REF] Anitha | An efficient Kohonen-fuzzy neural network based abnormal retinal image classification system[END_REF].

t ← t + 1 {3. Repeat the step 2 iteratively until t = N iter .} until t = N iter small values of T , V T (δ(c, r)) is negligible if c ̸ = r:
an observation influences only the calculation of the winner neuron weight, ω c . At the beginning of the learning process, the size of the neighborhood is fairly large, but it is made to shrink during learning. This ensures that the global order is obtained already at the beginning, whereas towards the end, as the neighborhood gets smaller, the local corrections of the neuron weights in the map will be more specific. For that, the factor T decreases during learning from T max to T min . In this paper the size of Kohonen map is τ × τ , then T max is set to τ and T min to 1 (with τ = 10 ).

The self-organization, as we described it, does not solve classification problems. Each observation is assigned to a neuron of the map, independently of any notion of class. The classification problem is then just the labeling of each neuron of the map by a number class. The number of neurons is generally greater than the desired number of classes, the labeling can be done by grouping suitably these neurons. In this paper, we propose a grouping procedure based on the hierarchical agglomerative clustering algorithm [START_REF] Jain | Algorithms for clustering data[END_REF]. Because of the topology of the map, only the neighbor neurons and the neighbor sub-groups of neurons in the Kohonen map are grouped.

After this grouping procedure, we obtain finally the desired number of neurons, namely K. Each of these neurons is represented by one number noted k with k = 1, . . . , K. The label map is created by assigning for each pixel the number of the neuron which it is assigned (it should be noted that the word "map" in the self-organization map (SOM) should not be confused with the word "map" in the label map).

The vector segmentation by the SOM algorithm provides one label map noted T while the marginal segmentation provides many label maps, each corresponds to one component of the image. In this case, they are noted T i with i = 1, . . . , D, where D is the number of image components (channels). Fig. 3 shows the results of the vector segmentation and the marginal segmentation of the image "Peppers"

(a) (b1) (b2) (b3) (c) (d1) (d2) (d3)

Fusion of label maps

The first phase of the marginal segmentation produces D label maps (see the previous Section). The second phase of the marginal segmentation consists in the fusion of these label maps. In this section we propose a new fusion technique, which consists in four steps:

1. combination by superposition of marginal maps, 2. elimination of insignificant regions, 3. elimination of insignificant classes, 4. grouping of classes.

Combination by superposition of marginal maps

Let us have some D marginal label maps, identifying the components of some image. The goal of the first step is to create, from the label maps T 1 , T 2 , . . . , T D obtained during the marginal segmentation phase, a new label map noted T f1 , such that

T f1 = K ∨ i=1 T i , ( 3
)
where ∨ is an operator which performs the combination by superposing the marginal label maps T i , i = 1, . . . , D. This combination consists in generating the same label in T f1 for the same combination of labels in the maps T i , and different labels for different combinations. An example of the combination by superposition of three label maps (T 1 , T 2 , T 3 ) is illustrated in Fig. 4. Each label map T i has three labels (K = 3), see Fig. 4(a), (b), (c), and the T f1 produced label map has six labels (classes), see Fig. 4(e). The correspondence between the six labels in T f1 and the combination of labels in (T 1 , T 2 , T 3 ) is given in Fig. 4(d).

1 1 2 2 1 1 2 2 3 3 2 2 3 3 2 2 (a) 2 2 2 3 2 2 3 3 1 1 3 3 1 1 3 2 (b) 3 3 3 1 3 3 3 1 2 2 1 1 2 2 1 1 (c) (1, 2, 3) → 1 (2, 2, 3) → 2 (2, 3, 1) → 3 (2, 3, 3) → 4 (3, 1, 2) → 5 (2, 2, 1) → 6 (d)
Unfortunately, the combination by superposition as proposed here produces an over-segmentation of the image. Indeed, if we have K classes in each map T i , the combination procedure produces M 1 classes in T f1 map with K < M 1 < K D . This number, usually high, induces a large number of regions. For instance, in the example of Fig. 1, each T i label map has 7 classes while the T f1 map contains 187 classes and 9063 regions.

Elimination of insignificant regions

To cope with the problem of the over-segmentation, we begin by eliminating very small regions because they are assumed to be insignificant regions (holes and noises) and can't really correspond to any object in the image. Note that the regions are constituted of the adjacent pixels belonging to the same class. They are determined by using a connected component analysis procedure from the label class map T f1 . The corresponding region map is noted

R with R = ∪R i (R i indicates the i-th region) and R i ∩ R j = ∅ for i ̸ = j.
The insignificant regions are the areas with sizes that don't exceed 0.06 % × n pixels (n is the image size). This threshold value is chosen experimentally after several tests with different color images and satellite images. For example, for an image of 128 × 128 size, the threshold value is equal to 9 and for an image of 256 × 256 size, it is equal to 39.

The eliminated regions are generally merged to neighbored regions. However in this paper we propose another strategy which consists in assigning the pixels of the eliminated regions to classes which contain pixels neighborhood to these eliminated regions. This new strategy is performed as follows.

For each insignificant region R i , we compute its mean color y i by using the pixel values of this region,

y i = 1 n i ∑ j∈Ωi y j ,
where n i is the number of pixels in the region R i and Ω i is the set of the indices of pixels constituting the region R i .

After that, we seek in the T f1 label map, the classes of neighborhood pixels of this region R i . Let Γ i be the set of these classes, Γ i = {C k : C k is the class of neighboring pixels to the region R i }.

For each class C k of Γ i (labeled k in T f1 map), we compute its mean color m k as

m k = 1 n k ∑ j∈C k y j .
The pixels of the insignificant region R i are then labeled by the index of that class C k of Γ i , which has its mean color closest to the mean color of this region. Let us denote this index as l. It can be obtained as

l = arg min k ∥y i -m k ∥ 2 .
At the end of this step, we get another label map noted T f2 which contains M 2 classes (M 2 ≤ M 1 ) with a reduced number of regions. For the example in Fig. 1, the 187 classes in T f1 becomes 90 in T f2 and the 9063 regions in T f1 becomes 388 in T f2 .

The algorithm describing this procedure is given in Algorithm 2 and an illustrative example is given in Fig. 5. Fig. 5(a) shows the label class map T f1 and Fig. 5(b) shows its corresponding region map. The region R 4 is considered as insignificant. It can be merged to one of the classes of its neighborhood among the set {C 1 , C 2 , C 3 , C 5 }. If the mean color of C 2 is supposed closest to the mean color of the region R 4 , then the pixels of this region are assigned to C 2 (Fig. 5(c)).

Algorithm 2 Algorithm of elimination of insignificant regions.

T f2 ← T f1 Decompose the T f1 map (class map) into a region map R Find all insignificant regions in the region map R (i.e. their size does not exceed 0.06 % of the image size) for all insignificant regions do Find the classes which have pixels neighboring to this insignificant region Among these classes, find the one that have a mean color nearest to the mean color of this insignificant region Join the insignificant region to this class (i.e. give to the pixels of the insignificant region in T f2 the same label of the class found before) end for

C 2 C 1 C 3 C 4 C 4 C 5 C 2 (a) R 2 R 1 R 3 R 4 R 5 R6 R 7 (b) C 2 C 1 C 3 C 4 C 5 C 2 (c)

Elimination of insignificant classes

In the previous step, the number of regions is substantially reduced, but it can still be high. In order to reduce this number once again, we propose to eliminate all the classes which have a number of pixels relatively small. Indeed, we consider that the classes with a number of pixels less than 0.5% × n are non-significative. This threshold value is also determined after several tests on different color and satellite images. For an image of 128 × 128 size, this value is equal to 81 and for an image of 256 × 256 size, it is equal to 327.

The pixels of these insignificant classes are assigned to remaining classes by using the same rule described in the previous section. More precisely, the regions formed by the adjacent pixels and belonging to an insignificant class are determined. Then, the pixels of each of these regions are affected to the class of its neighborhood pixels which has a mean color closest to the mean color of this region. The results of this procedure is another label map denoted T f3 , where the number of classes is M 3 with M 3 ≤ M 2 . The number of classes M 3 as well as the number of regions in T f3 is often reduced. In the example in the Fig. 1, the number of classes 90 in T f2 becomes 73 in T f3 and the number of regions 388 in T f2 becomes 314 in T f3 . This procedure is summarized in the Algorithm 3. The example in the Fig. 6 illustrates the steps of this procedure. The class C 2 , composed of three regions (Fig. 6(a)), is supposed insignificant. Each of these three regions will be treated independently by using the same rule described in the previous section. The rightmost region of C 2 will obviously assigned to class C 5 , the left-most region to the class C 4 and the region which is in the center, will be assigned to the class that has a mean color closest to the mean color among the three classes C 3 , C 4 , C 5 . In this example it is assumed that it is the class C 5 (see Fig. 6(b)).

C 1 C 3 C 2 C 2 C 5 C 4 C 2 (a) C 1 C 3 C 5 C 4 (b)

Algorithm 3 Algorithm of elimination of insignificant classes.

T f3 ← T f2 Find the insignificant classes, i.e. those having a size less than 0.5 % × n for all insignificant classes do Find the corresponding regions for all corresponding regions do Find the neighboring classes to this region Among these classes, find the one that have a mean color nearest to the mean color of this region Join this region to the class found before (i.e. give to the pixels of this region in T f3 the same label of the class found before) end for end for Although only significative classes and significative regions remain at the end of this procedure, the number of classes can be larger than the desired number of classes. To leave to the desired class number, a grouping of classes procedure is performed in the next step.

Grouping of classes

The last step of the proposed fusion technique aims to group iteratively the M 3 classes which have the closest mean color until achieve the desired number of classes K (K ≤ M 3 ). This grouping procedure is performed by using the hierarchical agglomerative clustering algorithm [START_REF] Jain | Algorithms for clustering data[END_REF] which is outlined in Algorithm 4. The results of this procedure is a final segmented image noted T f4 , see Fig. 1.

The number of classes and regions in T f4 is greatly reduced. In the example in the Fig. 1, the number of classes 73 in T f3 becomes 7 in the final label map T f4 and the number of regions 314 in T f3 becomes 86.

Algorithm 4 Algorithm of class grouping.

T f4 ← T f3 while the number of classes in T f4 is greater than K do Find the two classes that are the most similar in T f4 Label them with the same class number in T f4 Readjust the labels in T f4 end while

Experiment results and discussion

In this section, we will evaluate the performance of the proposed marginal multicomponent image segmentation. To assess its effectiveness, we compare the results of this technique with those of the vector segmentation based on the same classification algorithm SOM.

This evaluation is based on the criterion proposed by Borsotti et al. [START_REF] Borsotti | Quantitative evaluation of color image segmentation results[END_REF]. It is an unsupervised evaluation criterion, which does not require any "ground truth" and the quality of segmentation results is estimated from statistics calculated on each detected area. It is initially developed for the color imagery and can be applied to the multi-spectral imagery by extending the dimension. Moreover the Borsotti et al. function does not require any adjustment parameter, it gives an indication on the quality of the results which is in adequacy with our visual perception and it avoids the inconvenient of its predecessors functions like the Liu and Yang function [START_REF] Liu | Multiresolution color image segmentation[END_REF] and their revised version [START_REF] Borsotti | Quantitative evaluation of color image segmentation results[END_REF][START_REF] Zhang | A survey of evaluation methods of image segmentation[END_REF]. Indeed, the Liu and Yang function tends to evaluate very noisy segmentations favorably when the number of regions built is important and their revised function is not sensitive enough to small segmentation differences [START_REF] Borsotti | Quantitative evaluation of color image segmentation results[END_REF][START_REF] Zhang | Image segmentation evaluation: A survey of unsupervised methods[END_REF][START_REF] Zhang | A survey of evaluation methods of image segmentation[END_REF].

The Borsotti et al. function is defined by

C R = √ N R 10 4 n NR ∑ r=1 ( E 2 r 1 + log(card(B r )) + R(B r ) 2 card(B r ) 2 )
,

where N R is the number of regions obtained in the segmented image, n is the image size, E r the sum of distances between the pixels of the region B r in input image and the multi-component values attributed to the region B r in the segmented image and R(B r ) is the number of regions having exactly an area equal to that of B r .

The first term in the sum is high only for the non-homogeneous regions (typically, large ones), while the second is high only for the regions whose area B r is equal to the area of many other regions in the segmented image (typically, small ones). This function penalizes the segmentation that produces many regions and having non-homogeneous regions. The lower the C R value, the better the segmentation.

Two types of multi-component images are used to conduct this evaluation. The first one contains color images which are presented by three color components. The second type is constituted of one multi-spectral image coming from Meteosat MSG2 satellite. The components of this image correspond to five infra-red channels of this satellite (see [36] and [START_REF] Alkama | Markovian approach using several Gibbs energy for remote sensing images segmentation[END_REF]). Fig. 7 shows the results of the segmentation of six color images (one synthetic and five real). The original color images are presented on the first column, the results of the vector segmentation are presented on the second column and those of the proposed marginal segmentation are given on the last column.

Fig. 8 shows the results of the segmentation of a Meteosat MSG2 satellite image. This image describes the north-west African region. It presents different cloudy areas and non-cloudy areas (lads, sea, . . . ). The five infra-red channels of this image are displayed in gray levels (see Fig. 8(a) to Fig. 8(e)). The segmented image by the vector approach is shown in Fig. 8(f) and the one provided by our method is given in the Fig. 8(g). The segmentation results are displayed with false colors. Let us note that the colors are affected randomly to classes, this implies that the same color in the segmented images obtained by the marginal and vector approaches does not correspond necessarily to the same class.

The values of the Borsotti function are estimated on all test images and are grouped in the Tab. I. The number of classes K as well as the number N R of the detected regions by each segmentation method are specified in Tab. I. From the results of vector and marginal segmentations displayed in Fig. 7 and Fig. 8, we can see that the proposed marginal technique provides good results. Indeed, for example, in the case of the synthetic color image, many pixels of the orange square region are badly assigned to the yellow and pink regions when we use the vector segmentation, whereas the proposed marginal segmentation affects them correctly. We also find that the little green circle is confused with the large circle in the case of the vector segmentation, whereas in the case of the marginal segmentation just some pixels of this object are misclassified. We can also cite the case of the plane image where a part of the sky is badly detected by the vector segmentation and it is convenably detected by the marginal segmentation. The improvement of results of the marginal segmentation comparatively to the vector segmentation is also observed on the other images in Fig. 7. This observation is confirmed by the values of Borsotti criterion C R given in Tab. I, where they are always better for the marginal segmentation. As regards the Meteosat satellite image, we can see that the clouds are well detected in both cases (the different blue ones and the purple one in the case of the vector segmentation and the different blue ones without the darkest and the clear green in the case of the marginal segmentation). However, we remarque, in the case of the vector segmentation, that many low size regions (even that have one pixel size) are detected. This is a disadvantage which is eliminated by the proposed marginal segmentation. The Borsotti function given for this image in Tab. I is also clearly improved by our marginal segmentation.

In the marginal approach, the dependence between the components is completely ignored. At prior, we can expect to best results with the vector segmentation since all the dependencies between the components are taken into account. However, after experiment we found, in spite of this, the proposed marginal technique provides better results than those of the vector segmentation. We conclude that the developed fusion technique is effective due to different processing steps notably, to the step where the small regions are eliminated. These regions are assimilated to noise and, as stipulated by Borsotti et al. [START_REF] Borsotti | Quantitative evaluation of color image segmentation results[END_REF], they penalize their function. Effectively, when we observe the results of the Tab. I, we note that the number of detected regions N R is reduced in the marginal segmentation comparatively to the vector segmentation. The proposed fusion technique always removes the insignificant regions and classes and reveals only the most important regions and classes.

The originality of the proposed fusion procedure lies in the two procedures of elimination of insignificant regions and classes and especially how the pixels belonging to these removed regions and classes are assigned to the remaining significant classes.

Indeed, the elimination of the insignificant regions and classes allows to find, at the end of the fusion procedure and after the class grouping step, only the significant classes. For example, if these two steps are not performed, some small classes (which correspond to noise) can be founded in the final result and several classes corresponding to various areas of interest can be grouped, giving then a bad segmentation.

A priori, we would think that the elimination of the insignificant classes may be sufficient, but this can leave small regions (which correspond to the noise). Indeed, a significant class, which will not be eliminated by this step, can be formed by several regions, where some of them may be insignificants.

The succession in which the insignificant regions and classes are eliminated does not matter because the final result is substantially identical. Indeed, in these two steps, the elimination is performed by assigning the regions to the appropriate classes.

During the elimination of insignificant classes, each region of these classes is treated independently. The pixels of these regions are not necessarily assigned to the same significant class. Indeed, if we observe the example in Fig. 6, it seems obvious that the three regions of the insignificant class C 2 will be added to different significant classes.

In this paper, we compared the results obtained by using the proposed marginal fusion procedure with those of the vector segmentation to establish the effectiveness of the proposed fusion method for the marginal segmentation. It is obvious that segmentation algorithm used in the marginal segmentation and in the vector segmentation must be the same. In this paper, the segmentation algorithm is performed by using Self Organizing Map (SOM) and fine-tuned with Hierarchical Agglomerative Clustering (HCA) algorithm. Others classical classification algorithms like Expectation-Maximization (EM), Fuzzy C-Means (FCM), k-means, Markov Random Field (MRF) can also be used. Preliminary works, which are not given in this paper, show the efficiency of the SOM comparatively to the above cited algorithms. Other methods using the SOM algorithm combined with another algorithm such as Fuzzy C-Means (FCM) [START_REF] Ortiz | Segmentation of brain MRI using SOM-FCM-based method and 3D statistical descriptors[END_REF], Learning Vector Quantization (LVQ) [START_REF] Demirham | Segmentation of tumor and edema along with healthy tissues of brain using wavelets and neural networks[END_REF], Hybrid Genetic Algorithm (HGA) [START_REF] Awad | Multicomponent image segmentation using a genetic algorithm and artificial neural network[END_REF] can also be used. However, it is evident that when one method of segmentation provides better results in vector segmentation, it provides also better results in marginal segmentation but the comparison of the segmentation methods is not the purpose of this paper.

Conclusion

In this paper, we used two approaches to segment multi-components images, the marginal approach and the vector approach. The same SOM algorithm is used to segment the components of the image in the case of the marginal approach and the multi-component image in the case of the vector approach. In the marginal approach, we developed a new method for the fusion of label maps.

To assess the effectiveness of the proposed marginal segmentation, several tests are performed on two types of the multi-components images, color and satellite images.

The quantitative evaluation, performed on these images, shows that the marginal technique proposed provides better results comparatively to the vector approach.

Although, in its structure, the marginal approach ignores the dependency that exist between the different components, neglecting therefore the information that can participates in improving the performance of treatments, we observe that the results obtained by this proposed marginal approach are much better than those obtained by the vector approach. We conclude that the developed fusion technique is effective due to its different processing steps, notably to the manner in which the small and insignificant regions and classes, produced by the superposition step, are eliminated then reassigned.

Fig. 3

 3 Fig. 3 Segmentation by the SOM algorithm. (a) Original image, (b1) red component, (b2) green component, (b3) blue component, (c) T vector label map, (d1) T 1 marginal label map of the red component, (d2) T 2 marginal label map of the green component, (d3) T 3 marginal label map of the blue component.

Fig. 4

 4 Fig. 4 An example of combination of three label maps: (a) T 1 label map, (b) T 2 label map, (c) T 3 label map, (d) correspondence of the labels, (e) T f1 label map.

Fig. 5

 5 Fig. 5 Example of elimination of insignificant regions: (a) T f1 label map, (b) R region map, (c) T f2 label map.

Fig. 6

 6 Fig. 6 Example of elimination of insignificant classes: (a) T f2 label map, (b) T f3 label map.

Fig. 7

 7 Fig. 7 The results of the color image segmentation. Rows: (1) Synthetic, (2) Peppers, (3) Plane, (4) Flowers, (5) Church, (6) Elephants. Columns: (a) Original images, (b) Vector segmentation, (c) Proposed marginal segmentation.

Fig. 8

 8 Fig. 8 The results of the segmentation in 15 classes of the Meteosat image taken at noon December 15, 2006. The original image components: (a) IR8.7 (b) IR9.7 (c) IR10.8 (d) IR12.0 e) IR13.4. Segmentation results: (f ) Vector segmentation (g) Marginal segmentation.


Asma Kebbeb

Messaoud Mostefai

Fateh Benmerzoug

Chahir Youssef

Efficient Multimodal Biometric Database Construction and Protection Schemes

Keywords: Biometric databases, multimodal authentication, digital watermarking, cross-section topology

This work proposes an efficient approach for the construction and the protection of a dynamic and evolutionary multimodal biometric database. The last is dedicated to a biometric authentication system operating on a set of connected sites. For a better protection of acquired data, a topological watermarking module is developed to dissimulate the related enrolled person's files links.

Introduction

Currently and for safety reasons, the majority of the governments and institutions bet on biometrics to reinforce the means to check the identity of persons. Thus, one currently attends the progressive substitution of the classical authentication systems by more powerful biometric systems. In general, the latter carry out a search for similarity between multimodal descriptors relating to the person to be identified with those recorded in advance in a multimodal database [START_REF] Jain | Introduction to Biometrics[END_REF]15].

The construction of the latter is often a tiresome process which requires the mobilization of a staff for the database filling with the descriptors of all the persons authorized to reach the controlled site (enrollment). These constraints in the implementation of such systems as well as related data security requirements encouraged us to propose a dynamic and evolutionary approach for the construction and the protection of a multimodal biometric database.

Inspired by the complex human discovery, memorization and authentication process [START_REF] Fàbregas | Faundez M Recognition Performing in a System[END_REF][START_REF] Sinha | Face Recognition by Humans: Nineteen Results All Computer Vision Researchers Should Kno about[END_REF] an original approach for the construction of a selforganized multimodal biometric database is proposed. For a better protection of the acquired biometric data, a topological watermarking module is developed to dissimulate the related enrolled person's files links.

After a brief presentation of the classical biometric authentication system as well as their implementation constraints, we will detail our approach which aims at giving more autonomy to the latter by enabling them to acquire and update automatically the required authentication data. Thereafter, the adopted watermarking scheme for the protection of acquired data will be described and validated by test results. Finally, we conclude with perspectives.

Existing Multimodal Biometric Authentication Systems

In general, supervised sites have several distant access points which require the installation of powerful surveillance networks able to manage efficiently the whole dedicated surveillance equipment. The first systems adopted for this type of architecture were based on smart control access cards [START_REF] Li | An Efficient Biometrics Based Remote User Authentication Scheme using Smartcards[END_REF]. Although, they ensured efficient authentication and provided continuous historical access, the latter could not in any case guarantee that the holder of the required card was truly the owner and even if these last could integrate the photograph of the owner, the checking must be done only by a dedicated person, which is constraining and expensive. This pushed the designers of these kinds of systems to adopt an online approach which consists in performing an in-situ biometric descriptors extracting and comparison with pre-acquired (enrolled) biometric data stored initially in a dedicated database [START_REF] Snelick | Large-Scale Evaluation Multimodal Biometric Authentication State-of-the-art Systems[END_REF].

Both the type and the number of used descriptors are directly related to the chosen modalities. For performance sake, the mono-modal authentication systems were quickly replaced by multimodal authentication systems that are able to carry out a strong authentication based on the exploitation of several modalities such as: Face, voice, iris, fingerprint, signature etc., [12].

Although, they are powerful, these systems frequently exploit and in a non-optimal way static databases (dedicated to the storage of the required descriptors). Things become more complicated if the latter is shared in network between several remote sites (our case). Indeed, besides the slowness of the access to the database, emerge the problem of the confidentiality and the security of the biometric data that are recorded and diffused via the network.

In what follows we will present our approach which aim at proposing on one hand a model of dynamic database construction allowing carrying out fast and targeted research and on the other hand, a robust watermarking scheme able to ensure efficient protection of acquired and shared data.

Biometric Databases Construction

Generally, the adopted process for the construction of biometric databases is based on an off-line First Come First Served principle (FCFS). Once, the database filled, it becomes operational for use in an authentication system. Often and in order to improve the research performances on such bases, one proceeds to an off-line reorganization of acquired data [12]. This constraining approach goes against the real time systems requirements which must be able to collect and to reorganize in a fluid and transparent way the data as they arrive.

If one wishes to make the authentication systems less constraining, more autonomous and able to interact in a natural way with humans, it is necessary to provide them with data collection and reorganization mechanisms inspired by those of the human ones.

The mechanism adopted for the construction of our multimodal database is based on the following findings:

• The audio-visual human memory fills progressively with time and the events with which the person is confronted to during his/her life. • Birds of a feather flock together.

On the basis of these reports, one can consider the construction of biometric authentication systems which at the beginning of their startup do not have any enrolled person in the database. Hence, there is neither distinct enrolment phase nor authentication phase (as it is the case for the whole of the classical authentication systems), but rather of online enrollment or authentication operations. Thus, the result will be:

if detected person then if authorized to be recorded then Enrolment else Authentication

In addition, in order to have online organization of the multimodal database, the multidimensional structure (where each modality is assigned to a dimension) is adopted. For a first approach, we start with a 2D biometric database dedicated to the storage of the image and voice modalities.

Any enrolled person will have four associated files indexed according to a generated person position within a 2D memory position matrix. This last can progressively change with the arrival of new peoples.

The following example (presented in next section) shows the procedure of indexing of nine enrolled persons {P 0 to P 8 } according to their degree of intersimilarity with the enrolled group. The adopted similarity criterion between candidates is based on hausdorff metric [START_REF] Huttenlocher | Comparing Images using the Hausdorff Distance[END_REF] for face modality and HMM with MFCC for voice modality [START_REF] Iqbal | Recognition using HMM with MFCC ATM[END_REF]. The obtained intersimilarity results allow us to order the persons from the most similar (with the high score) to the least similar (with the low score). Finally, a coded index is generated to each enrolled person according to his/her 2D position.

Data Base Protection

Although, the relation between the affiliated person files are dissimulated, these last can be easily replaced or renamed intentionally or not, putting thus in failure the authentication process. In order to, overcome this problem it is essential to place indicators able to detect and prevent such changes.

By exploiting the advances in the field of data security, we will present in what follows the development of a multimodal database protection module founded on digital watermarking techniques. This last will allow a robust dissimulation of an embedded mark within the enrolled person face. A simple checking of this mark will permit to know if any associated person file has undergone a change or not.

Proposed Method

According to the chosen modalities, any enrolled person will be represented with a group of template files necessary for any authentication operation as shown in Figure 2. These files have a common special position with which their indexes were calculated. If a change occurs on one of these files, the new position will be automatically different from the initial position.

In order to detect such changes, we propose to mark the face template of the enrolled person with his/her initial 2D position. Thus, a simple mark lecture and a simple comparison with the position produced by the existing files will indicate if one of these last underwent a change or not.

Existing Watermarking Schemes

The general principle of the different watermarking techniques consist in marking work to be protected with an imperceptible signature which allows an easy authentication of the owner while being robust to attacks (malicious or not) [START_REF] Nasereddin | Digital W Technology Overview[END_REF]. The various watermarking systems suggested in the literature [START_REF] Halder | Techniques for Relational Databases: Survey, Classification and Comparison[END_REF] can be classified in one of the following categories: Those that act directly in the space domain and those that act in the frequency domain [START_REF] Datta | Domain Watermarking: An Overview International[END_REF]. In spite of their simplicity of implementation and computation, spatial methods are generally vulnerable to geometrical attacks. Indeed, these methods are based on the image coordinates to insert and extract the embedded mark. A simple line and/or column crop will make impossible the extraction of the mark. This is why the major people choose frequency methods to embed the mark. These last are invariant vis-à-vis the geometrical attacks. This did not slow down the interest carried to the spatial techniques, which remain by far the fastest and the simplest in comparison with frequency techniques.

Topological Watermarking Scheme

In our case, the chosen watermarking scheme is spatial, additive and with a secret key. It is based on the topology of the image, and allows the embedding of one or more marks in one or more parts of the image located by a topological map containing the related components of a selected cut [START_REF] Bertrand | Image Segmentation through Operators Based Upon Topology[END_REF]. The adopted topological watermarking scheme (presented in Figure 4) is as follow:

1. Conversion of the color image into a gray level image and selection of the required cross section.

Extraction of the related components and generation

of the marking map (used to locate the insertion points in the original image). 3. Generation of a key with the adopted parameters of insertion. 4. Original image watermarking by following the marking map.

Cross Sections Extraction and Selection

A gray level image can be considered as a stacking of several binary plans called cross sections "cuts". Each cross section is a threshold of the image on a given gray level (K). The binary values of a selected cross section are obtained in the following way:

If P(x, y) ≥K then P K (x, y)=0 else P K (x, y)=1
Where, P(x, y) represents a pixel of the image with coordinates x and y and P K (x, y) a binary pixel of the cross section K. Figure 5 shows an example of a cross section extraction from a gray level image. Figure 5-a represents the gray level value of each point. Figure 5b is a representation in topographic relief. Figures 5-c and d represent two cross sections of the image.

Mark Insertion Space

Once the cut chosen, a topological treatment is applied to the image in order to extract connected components [START_REF] Couprie | Topological Operators For Grayscale Image Processing[END_REF]. Their number and size will determine the quantity of information that could be inserted. This task is performed by a statistical module which allows the extraction and the classification of related connected components according to their center and the number of points to be used. Obtained topological map will be used with a secret key to locate insertion points on the original image. The generation of the key depends on the following elements:

• Label of the related used component.

• Size of the mark.

• Selected field of insertion.

• Number of the marked cuts.

• Statistical parameters of selected marked points.

Once the key generated, the mark is inserted following the generated topological map. In order to, improve the robustness of the watermarking against the geometrical attacks, (crop and rotation), the insertion points are sorted according to their distance from the center of the related component Figure 6. These values remain unchanged in case of geometrical attacks. A header code is added to the embedded message to indicate the reading direction during the extraction of the mark.

Insertion of the Mark

Watermarking process consists in forming couples of blocks of fixed size using a sorted list of the insertion points. The insertion of a bit of the mark is made by modifying the difference of averages between two close blocks without deteriorating them. Obtained difference must be equal to one of the two specific values d 0 and d 1 . The first value indicates the insertion of one "0" and the second the insertion of one "1". d 0 is a pseudo-random number generated by the secret key K, whereas d 1 is the sum of d 0 and R/2, where, R is the degree of resistance against high frequency attacks Figure 7. Considering that M A is the average of the block A, and M B the average of the block B, then:

M diff =(M A -M B +R×256) mod R
The term R×256 ensures a positive M diff value. In order to, be in conformity with the marking rules a fixed value µ is added to each pixel of the block A and subtracted from each pixel of the block B. In case of a non-entire value, an error diffusion procedure is applied to the couple of blocks [START_REF] Liu | Fast Two Watermarking without Referring Image and Watermark[END_REF]. The computation rules of µ are as follows:

• In the case of insertion of "1", the rule is:

If M diff <d 0 then M diff =M dif f +R and µ=(d 1 -M diff )/2
• In the case of insertion of "0", the rule is:

If M diff >d 1 then M diff =M diff -R and µ=(d 0 -M diff )/2
The selected component is finally labelled to avoid marking it again.

Example of Image Watermarking

The following example Figure 8, illustrates our approach: First, we proceed to the extraction of interesting cross sections which allows the insertion of

(2) desired mark. The cross section selection is done manually or automatically. In the first case, the user fixes the cross section to be used for watermarking; in the second case, an automatic research process is lunched to find the best suited cross section for the watermarking requirements in terms of quantity of information to be inserted. In this example, marking required the use of the cross section 102 (with K=102) which has been selected according to the size of the embedded mark which is initially of 16 bits (a coded 2 D position). The value of R has an impact on the robustness of the watermarking and the quality of the marked image. More this value is important more the watermarking is robust and more degradation is perceptible.

Extraction of the Mark

Figure 9 shows the mark extraction process. If the key is right, it contains all required information about the environment of insertion. After the extraction of the used cross section, topological treatments are carried out to define the field of insertion of the mark and to reform the blocks used for the insertion of the mark. Knowing the statistical parameters (d 0 and R), the mark can be then regenerated. For the extraction of the embedded bit the difference of the averages between two adjacent rebuilt blocks is computed. If this difference is close to d 0 , then the value "0" is extracted; in the contrary case one "1" is extracted.

The following rules are used for the extraction of the embarked bit:

If |M diff -d 1 |<R/4
then «1» is extracted else «0» is extracted

Tests of Robustness

In this part tests are carried out to study the robustness of the watermarking against the various signal processing attacks: Compression, filtering, noise addition and geometrical transformation (see Table 6). For compression attacks, the Mark was successfully extracted with JPEG attacks of about 50%.

Another type of attacks consists on filtering successively the marked image with a low pass filter or on adding a white Gaussian noise with a null average and a variable deviation σ. We succeeded in decoding the mark at the second iteration (for low pass filtering) and for values of σ going up to 60 (for Gaussian filtering); beyond, the mark is lost.

Traditional geometrical attacks (rotation, the mirror effects and fenestration) have also been tested. For each one of these attacks, the mark has been successfully extracted.

These experiments showed that the length of d 0 must be close to R/4. More precisely, d 0 Must be between R/2 and R/4, (R/4 < d 0 > R/2).

Figure 1 .

 1 Figure 1. Working environment.

Figure 2 .

 2 Figure 2. Enrolled person's associated files.

Figure 3 .

 3 Figure 3. Enrolled persons sample.

Figure 4 .

 4 Figure 4. Topological Watermarking Scheme.

Figure 5 .

 5 Figure 5. Example of cross sections.

Figure 6 .

 6 Figure 6. Connected component parameters.

Figure 7 .

 7 Figure 7. Relation between d 0 , d1 and R.

Figure 8 .

 8 Figure 8. Example of watermarking (R=40, d 0 =11).

Figure 9 .

 9 Figure 9. Extraction of the mark.

Table 1 .

 1 Enrolled persons faces inter-similarities results.

		P0	P1	P2	P3	P4	P5	P6	P7	P8
	P0	100	74	68	52	71	68	59	63	57
	P1	74	100	77	76	66	85	78	68	72
	P2	65	77	100	78	74	72	80	77	68
	P3	57	76	78	100	69	84	87	65	72
	P4	71	66	74	69	100	60	71	76	54
	P5	68	85	72	84	60	100	84	66	66
	P6	59	78	80	87	71	84	100	71	78
	P7	63	68	77	65	76	66	71	100	59
	P8	55	72	68	72	64	66	78	62	100

Table 2 .

 2 Enrolled persons voices inter-similarity results.

		P0	P1	P2	P3	P4	P5	P6	P7	P8
	P0	78	42	34	23	36	28	25	8	20
	P1	43	88	24	13	11	27	15	23	22
	P2	17	11	74	12	24	10	19	36	29
	P3	29	12	18	80	34	32	27	26	21
	P4	28	6	12	11	86	23	16	5	21
	P5	13	36	18	17	11	76	22	11	18
	P6	16	33	23	20	33	17	83	18	21
	P7	39	39	12	22	14	33	13	88	33
	P8	26	27	27	18	23	10	33	16	72

Table 3 .

 3 Enrolled persons faces ordering.

	Face index	0	1	2	3	4	5	6	7	8
	Score	52	62	65	57	54	56	59	59	55
	New Order	P2	P1	P6	P7	P3	P5	P8	P4	P0

Table 4 .

 4 Enrolled persons voices ordering.

	Voice index	0	1	2	3	4	5	6	7	8
	Score	8	11	10	12	4	11	16	12	10
	New Order	P6	P3	P7	P1	P5	P2	P8	P0	P4

Table 5 .

 5 New enrolled persons positions.

	Voice/ Face	0	1	2	3	4	5	6	7	8
	0			P6
	1				P1	P3
	2
	3			P7
	4						P5
	5	P2
	6							P8
	7									P4
	8								P0

Table 6 .

 6 Tests of robustness.

Acknowledgements

This work was supported by the Algerian research ministry through the PNR project (Ref: 42/TIC/2011). The used hardware and Software tools are supported by the MSE Laboratory.

Conclusions and Perspectives

This article presents an efficient biometric database construction and protection scheme. The use of a 2D position matrix allows efficient and rapid localization of enrolled persons as well as a robust protection of their associated files.

The database protection is performed using a spatial watermarking scheme based on cross section topology. The insertion points of the mark are located by a topological map made up of related components of one or more cross sections, allowing thus efficient watermarking on several parts of the image.

Two improvements remain necessary in this work: The optimization of the database content update and the automation of the watermarking process. These improvements are the subject of our current work.