Rahma Boukadida

Yaroub Elloumi
email: yaroub.elloumi@esiee.fr

Mohamed Akil

Mohamed Hedi Bedoui

MAS-PDR: Mobile-Aided Screening System for Proliferative Diabetic Retinopathy

Keywords: Fundus images, Neovascularization, Smartphone captured fundus image, Mobile-Aided-Screening (MAS) system, Mobile Health, Random Forest (RF)

NeoVascularization (NV) occurs in the Proliferative Diabetic Retinopathy (PDR) stage, where the development progress of new vessels presents a high risk for severe vision loss and blindness. Therefore, early NV detection is primordial to preserve patient's vision. Several automated methods have been proposed to detect the NV on retinograph-captured fundus images. However, their employment is constrained by the reduced ophthalmologist per person ratio and the expensive equipment required for image capturing.

This paper presents a novel method for NV detection in smartphone-captured fundus images. The implementation of the method on a smartphone device having an optical lens for fundus capturing leads to a Mobiles -Aided-Screening system of PDR (MAS-PDR). The challenge is to ensure accurate and robust detection even with the moderate quality of fundus image, with a reduced execution time. Within this objective, we identify the major criteria of neovascularized vessels which are tortuosity, width, bifurcation and density. Our main contribution consists in proposing a sharp feature to reflect each criterion on reduced computational complexity processing. Therefore, the feature set is provided to a random forest classifier in order to deduce whether the fundus image is in the PDR stage.

A dataset raised from publicly databases is used on a 10-cross validation process where average accuracy of 98.69%, sensitivity of 97.73% and a specificity of 99.12% are achieved. To evaluate the method robustness, the same experimentation is repeated after applying motion blur filters to the fundus image dataset, where 98.91% accuracy, 96.75% sensitivity, and 100% specificity are deduced. Moreover, NV screening is performed under three seconds when executed in smartphone devices demonstrating the appropriateness of our suggested method to MAS-PDR.

Introduction

Diabetes is a worldwide disease with more than 415 million of patients, according to a report of the international diabetes federation [START_REF] Boittiaux | L'essor du diabète dans le monde[END_REF]. This number is expected to increase over the next decades to reach 642 million diabetics in 2040 [START_REF] Boittiaux | L'essor du diabète dans le monde[END_REF][START_REF] Sabanayagam | Incidence and progression of diabetic retinopathy: a systematic review[END_REF]. Diabetic Retinopathy (DR) is a serious complication of diabetes which affects nearly 30% of diabetes patients [START_REF] Pan | Characteristics of Neovascularization in Early Stages of Proliferative Diabetic Retinopathy by Optical Coherence Tomography Angiography[END_REF]. Moreover, the WHO has estimated that DR is the main responsible for 37 million cases of blindness throughout the world [START_REF] Ting | Diabetic retinopathy: global prevalence, major risk factors, screening practices and public health challenges: a review: Global burden of diabetic eye diseases[END_REF]. The DR can be divided into Non Proliferative Diabetic Retinopathy (NPDR) and Proliferative Diabetic Retinopahy (PDR). The latter is the most severe stage of DR, which corresponds to 9% of DR-affected people [START_REF] Pan | Characteristics of Neovascularization in Early Stages of Proliferative Diabetic Retinopathy by Optical Coherence Tomography Angiography[END_REF]. This stage is characterized by the proliferation of new abnormal blood vessels due to the extensive lack of oxygen in the retinal capillaries [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF]. The Neovascularization (NV) can rapidly progress early PDR to advanced PDR that cause bleeding, fibrous proliferation, vitreous hemorrhage and retinal detachment, hence posing a high risk for severe vision loss and blindness [START_REF] Ting | Diabetic retinopathy: global prevalence, major risk factors, screening practices and public health challenges: a review: Global burden of diabetic eye diseases[END_REF][START_REF] Chalakkal | Fundus retinal image analyses for screening and diagnosing diabetic retinopathy, macular edema, and glaucoma disorders[END_REF] . The detection of NV in early stage in order to stop or delay its progression leads to avoid vision loss and blindness.

NV diagnosis is based on examining fundus images, such as the ones shown in Fig. 1. However, a delay in the diagnosis of patients on the PDR stage is registered. The first cause corresponds to the limited ratio of human and material resources per person required for fundus image acquisition and diagnosis. Besides, patients with PDR must mobilize to be diagnosed, which might be restricted due to the elderly DR patients and the geographical remoteness. In the literature, a lot of work has been proposed to detect NV [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF][START_REF] Agurto | Detection of neovascularization in the optic disc using an AM-FM representation, granulometry, and vessel segmentation[END_REF][START_REF] Welikala | Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification[END_REF][START_REF] Huang | Automatic detection of neovascularization in retinal images using extreme learning machine[END_REF][START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Silkar | Detection of neovascularization in retinal images using mutual information maximization[END_REF][START_REF] Agurto | A multiscale decomposition approach to detect abnormal vasculature in the optic disc[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF][START_REF] Gupta | Local characterization of neovascularization and identification of proliferative diabetic retinopathy in retinal fundus images[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF]. However, they are dedicated to classical fundus images, requiring ophthalmologists, capture equipment and patient mobility at the same time. Consequently, the proposed methods for NV diagnosis cannot retrieve the delay of NV diagnosis.

The overuse of smartphones [START_REF]Number of smartphone users worldwide[END_REF] and their growing performance in terms of processing, portability, storage capacity and image quality lead to be used in medicine, especially for ophthalmic screening. Various mobile digital retinal screening devices, such as iExaminer, D-EYE and Paxos digital ophthalmoscopes, have been suggested [START_REF] Wu | Comparison Study of Funduscopic Examination Using a Smartphone-Based Digital Ophthalmoscope and the Direct Ophthalmoscope[END_REF][START_REF] Russo | A Novel Device to Exploit the Smartphone Camera for Fundus Photography[END_REF][START_REF] Panwar | Fundus Photography in the 21st Century-A Review of Recent Technological Advances and Their Implications for Worldwide Healthcare[END_REF]. Those low-cost devices are composed by optical lens and designed to be attached to a smartphone. The smartphone captured fundus images are legible between 86% and 100% on average and have an accepted quality between 93% and 100% [START_REF] Akil | Detection of retinal abnormalities using smartphone-captured fundus images: a survey[END_REF]. In addition, several clinical studies have approved the ability to detect DR from smartphone-captured fundus images [START_REF] Prasanna | Decision Support System for Detection of Diabetic Retinopathy Using Smartphones[END_REF][START_REF] Bourouis | An intelligent mobile based decision support system for retinal disease diagnosis[END_REF][START_REF] Monjur | Smartphone Based Fundus Camera for the Diagnosis of Retinal Diseases[END_REF]. However, those images are characterized by a moderate quality, caused by the handheld aspect of the capture process. Within this context, several methods have been put forward and implemented into smartphones to detect ocular pathologies, such as DR grading [START_REF] Bourouis | An intelligent mobile based decision support system for retinal disease diagnosis[END_REF][START_REF] Majumder | A deep learning-based smartphone app for real-time detection of five stages of diabetic retinopathy[END_REF] and glaucoma screening [START_REF] Martins | Offline computer-aided diagnosis for Glaucoma detection using fundus images targeted at mobile devices[END_REF][START_REF] Guo | Yanbao: A Mobile App Using the Measurement of Clinical Parameters for Glaucoma Screening[END_REF].

Our objective consists in proposing a novel method that detects NV from smartphone-captured fundus images. The implementation of the method as an app on a smartphone associated with a mobile retinal screening device leads to propose Mobile-Aided-Screening (MAS) of PDR. The first challenge is to ensure an accurate detection even with the downgraded quality of smartphone-captured fundus images. The second challenge is to perform screening in a reduced time with respect to the clinical employment, despite the limited capacity of smartphone architectures.

The paper is organized in the following way. Section 2 discusses the related work. The suggested method for NV detection is presented in section 3. The evaluation of the proposed method using different fundus image databases and performance parameters is done in section 4, followed by conclusion in the last section.

Automated Methods for PDR Detection

Related work

Several automated methods for NV detection have been put forward in the literature. Some methods have aimed at NV screening while others have targeted the segmentation of neovascularized vessels, as detailed respectively in the following sub-sections. On the other hand, NV occurs on the Optic Disc (OD) before propagating into the whole retina. Accordingly, we observe that a lot of related work, whether for NV screening or vessel segmenting, has detected NV in the OD region, named "NV in optic Disc (NVD)". Others have focused on the neovascularized vessels in the whole retina, called "NV Elsewhere (NVE)". These methods are described respectively in each subsection.

NV screening methods

The method proposed by Agurto et al. [START_REF] Agurto | Detection of neovascularization in the optic disc using an AM-FM representation, granulometry, and vessel segmentation[END_REF] selected the OD, enhanced the sub-image quality and segmented its vessels. After that, the features were extracted by applying the Amplitude-Modulation Frequency-Modulation (AM-FM) and granulometry, which were used to respectively analyze the vessel tortuosity and width. Finally, the partial least squares classifier was performed to deduce NV. In [START_REF] Agurto | A multiscale decomposition approach to detect abnormal vasculature in the optic disc[END_REF], a set of 1248 features were extracted from the OD through the AM-FM , fractal analysis and granulometry to model the vessel tortuosity, density and width. Then, the Support Vector Machine (SVM) classifier was performed to classify whether the fundus image was on the NVD stage.

For NVE screening methods, a study detailed in [START_REF] Huang | Automatic detection of neovascularization in retinal images using extreme learning machine[END_REF] presented a pixel wise classification method. A set of features was extracted for each pixel of the preprocessed image, which reflected the tortuosity and the retina texture through the standard deviation filters, the anisotropic Gaussian filters, the Gabor matched filters and the differential invariant filters with multiple scales. Thereafter, the feature set was provided to the extreme learning machine to classify the fundus image as normal or neovascularized. To enhance the computational performance, the proposed method was implemented in parallel where two map-reduce models are employed respectively for feature extraction and training [START_REF] Huang | Automatic Parallel Detection of Neovascularization from Retinal Images Using Ensemble of Extreme Learning Machine[END_REF]. The work described in Yu et al. [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF] consisted in extracting of 42 features: 34 reflecting the vessel shapes, five modeling the fractal dimension analysis and three representing granulometry analysis. After that, the recursive feature elimination algorithm is applied to select the set of the 18 optimal features. Thereafter, the SVM was used to classify whether the retinal image was neovascularized or not. Gupta et al. [START_REF] Gupta | Local characterization of neovascularization and identification of proliferative diabetic retinopathy in retinal fundus images[END_REF] proposed a method to identify NVE regions in the retinal image. A set of 525 features was extracted from each patch based on vessel density, width and tortuosity and on the retina texture. Thereafter, a Random Forest (RF) classifier was utilized to train the labeled patches. The method suggested in Hassan et al. [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF] segmented the whole retinal vessel tree. Afterwards, the number and area of vessels were quantified. The fundus image was then split into regions where each was tested through the area and number values to deduce whether it contained neovascularized vessels.

Segmentation methods of neovascularized vessels

The method described in [START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF] focused on segmenting the abnormal vessels that belonged to the OD. In this context, several features were extracted from each segmented vessel to model the length, the width, the tortuosity and the density on it specific area. Other features were extracted from the whole vessel tree, which corresponded to the vessel number and the retina texture. Then, the SVM classifier intercepted the feature set to categorize a vessel as normal or neovascularized. The work described by Silkar et al. [START_REF] Silkar | Detection of neovascularization in retinal images using mutual information maximization[END_REF] propounded a method for the segmentation of neovascularized vessels inside the OD and elsewhere in the retina. In the first stage, the entire vessel map was split into two trees containing respectively the thick and thin vessels. After that, a threshold based on tortuosity and density was performed to the thin vessel tree in order to distinguish between normal and neovascularized ones.

The work described by Akram et al. [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF] proceeded to segment the retinal vessel tree and extract features from each vessel to model their density, the number of vessels, the vessel tortuosity, the vessel width and the retina texture. Then, a multi-level m-Mediods classifier was used to differentiate normal and abnormal blood vessels. In [START_REF] Welikala | Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification[END_REF], the fundus image was segmented using two approaches. From both vessel tree results, each vessel was distinguished in order to extract four features that were related respectively to the density, tortuosity and number of vessels and to the area. Those features were used to classify vessels into healthy or NV ones using the SVM. Finally, a vessel was considered as NV if it was classified as NV in both segmented vessel trees.

Critical study

The blood vessels converge from the optic nerve head into the whole retina. Hence, the abnormal vessels start to appear on the OD, which correspond to the early stage of PDR. Therefore, to screen the PDR, it is meaningful to detect NV on the OD rather than the whole retina.

The methods always segment the retina vessel. For the methods that target the neovascularized vessel segmentation, each vessel is extracted separately from the vessel tree in order to be classified. However, the methods aiming for NV screening proceed to extract summary features from the whole vessel tree [START_REF] Welikala | Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification[END_REF][START_REF] Huang | Automatic detection of neovascularization in retinal images using extreme learning machine[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF] or from each tree region [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF][START_REF] Agurto | Detection of neovascularization in the optic disc using an AM-FM representation, granulometry, and vessel segmentation[END_REF][START_REF] Silkar | Detection of neovascularization in retinal images using mutual information maximization[END_REF]. Those features may distort the detection by considering microvascular structures or vascular lesions, such as the ones occurring in the mild DR or in the wet aged macular degeneration stages, as abnormal vessels.

The NV detection approach are differentiated between methods in terms of considered vessel properties. Therefore, we study the existing methods in order to identify the NV properties, as indicated in Table 1. We deduce that some properties are more used than others, which are tortuosity, width and density, which are intrinsically related to the morphology of the new abnormal vessels. Moreover, NV occurs through ramification from existing vessels. Thus, the vessel number increases in terms NV, which is closely related to the branch number, where both properties are used in [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF][START_REF] Welikala | Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification[END_REF][START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF].

Although NV leads to the addition of new vessels, the vessel length has a weak correlation with NV. This results in several bifurcations rather than extending the length of initial ones. Correspondingly, the length feature is infrequently extracted. Furthermore, the retinal texture features are always correlated with the other morphological properties of NV.

We distinguish that few methods have extracted the four main NV properties. Among them, the work described in [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF] aimed to segment the neovascularized vessels, which relied on using higher computational complexity processing. Accordingly, they required higher execution times of 5.83 and 6.5 minutes, respectively. Similarly, the method put forward in [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF] lied to extract 42 heavy processing features. Then, a feature selector was applied to identify 18 relevant ones to be used for classification. However, it was fail to outperform the detection performance of existing methods while the result required 8.74 seconds. As a consequence, increasing the size of feature set did not necessarily increase the detection performance.

Automated Method for PDR Detection

Approach principle

Our objective is to propose an automated method for detecting NV from retinal images captured by mobile devices. First of all, NV occurs on the OD before the whole retina. Moreover, the smartphone capture device has a limited field of view which does not allow modeling all retinal components. Therefore, to anticipate the detection of NV, our method ensures an early detection of NVD. Thus, the first step consists in automatically identifying and locating the OD.

The fundus images captured by smartphones are frequently blurred, noised, and have a non-balanced contrast. Subsequently, the OD will be enhanced through a pre-processing step. Since NV results in new vessels, we propose to segment the blood vessel tree belonging to the OD. In contrast to the existing methods for NV detection, we choose to deduce NV based on each vessel separately rather than using the whole vessel tree, in order to ensure higher accuracy and robustness.

Our challenge is to extract a set of features adequately reflecting the NVD without confusing with healthy images. Accordingly, our main contribution consists in extracting features related to the four morphological properties of NVD that are respectively the vessel tortuosity, the thinned width, the number of branches and the increased vessel density. In the last step, a classifier is utilized to classify whether the OD image contains NVD or not. Those processing steps are depicted in Fig. 2, which are respectively described in the following sections.

Pre-processing

The method proposed in [START_REF] Pourreza-Shahri | Computationally efficient optic nerve head detection in retinal fundus images[END_REF] insures locating the OD based on circularity and intensity through applying the radon transform. The method achieved a higher accurate performance, where an accuracy of 100% is performed to locate OD in the public DRIVE database. We note that this method is able to be configured with the aim of locating a sub-image having the same OD size. Thereafter, this method is extended to be provide a mobile computer aided system for OD detection [START_REF] Elloumi | A mobile computer aided system for optic nerve head detection[END_REF]. The processing was optimized to reduce complexity where the same detection accuracy is performed through 1.3 second in smartphone device. Therefore, the method proposed by [START_REF] Elloumi | A mobile computer aided system for optic nerve head detection[END_REF] will be implemented which extract the OD sub-image in order to remove it from the fundus image.

Our objective is to segment the vessels that require the explicit modeling of vessels with respect to their background. Therefore, we extract the green channel as performed in several methods aiming for blood vessel tree segmentation [START_REF] Deshpande | Single image motion deblurring: An accurate PSF estimation and ringing reduction[END_REF][START_REF] Cai | Blind motion deblurring using multiple images[END_REF][START_REF] Aras | Segmentation of retinal blood vessels for detection of diabetic retinopathy: A review[END_REF][START_REF] Dash | A thresholding based technique to extract retinal blood vessels from fundus images[END_REF][START_REF] Moccia | Blood vessel segmentation algorithms -Review of methods, datasets and evaluation metrics[END_REF][START_REF] Akil | Computationally efficient blood vessels segmentation in fundus image on shared memory parallel machines[END_REF], as illustrated in Fig. 3(b1) and Fig. 3(b2). Thereafter, due to the handheld aspect of the smartphone, the fundus images are always blurred and noised [START_REF] Akil | Detection of retinal abnormalities using smartphone-captured fundus images: a survey[END_REF]. Thus, we apply the point spread function to the OD sub-image to enhance the image quality [START_REF] Deshpande | Single image motion deblurring: An accurate PSF estimation and ringing reduction[END_REF][START_REF] Cai | Blind motion deblurring using multiple images[END_REF] . Then, the Contrast Limited Adaptive Histogram Equalization (CLAHE) approach [START_REF] Chalakkal | Automatic segmentation of retinal vasculature[END_REF] is applied, where the pre-processed OD is shown in Fig. 3(c1) and Fig. 3(c2).

Vessel segmentation

NV entails abnormal thin vessels where a segmentation step remains crucial for NVD detection. The new vessels are less visible and have lower contrast than the normal ones, as illustrated in Fig. 3(a2). For this, we invert the gray level of the preprocessed image using the Black-hat morphological operator, as indicated in Fig. 3(d1) and Fig. 3(d2). Then, we segment the vessels through the "Otsu thresholding" [START_REF] Muramatsu | Automated segmentation of optic disc region on retinal fundus photographs: comparison of contour modeling and pixel classification methods[END_REF][START_REF] Nakagawa | Recognition of optic nerve head using blood-vessel-erased image and its application to production of simulated stereogram in computer-aided diagnosis system for retinal images[END_REF] where the final result is shown in Fig. 3(e1) and Fig. 3(e2). NV consists in adding new vessels with specific forms. For this purpose, we extract each vessel through the detection contour processing, which is explained as a curve joining all continuous points having the same intensity [START_REF] Kumari | Automatic License Plate Recognition Using OpenCV and Neural Network[END_REF].

Feature extraction

Tortuosity feature

Tortuosity is a morphological property of the retinal vessels. It can be defined as a non-smooth appearance of the vessel's course [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF][START_REF] Grisan | A Novel Method for the Automatic Grading of Retinal Vessel Tortuosity[END_REF]. NV increases the vascular tortuosity, as illustrated in Fig. 1(b). This rise occurs as a result of the elevated blood pressure [START_REF] Cheung | Retinal Vascular Tortuosity, Blood Pressure, and Cardiovascular Risk Factors[END_REF][START_REF] Paul | Significance of Asymmetric Retinal Vasculature Tortuosity -Report of 10 Consecutive Cases[END_REF][START_REF] Kubicek | Morphological Segmentation of Retinal Blood Vessels and Consequent Tortuosity Extraction[END_REF].

Several studies have demonstrated that the increased vessel tortuosity correlates with the severity of DR. The clinic-based study described in [START_REF] Sasongko | Retinal vascular tortuosity in persons with diabetes and diabetic retinopathy[END_REF] studied the difference of tortuosity in relation with DR, where it was deduced that the arteriolar tortuosity grew with the rise in the DR severity. The work described in [START_REF] Zhu | Tortuosity of Retinal Main and Branching Arterioles, Venules in Patients With Type 2 Diabetes and Diabetic Retinopathy in China[END_REF] indicated that the retinal vessels became tortuous either locally and/or over an extended area during retinal progression. Furthermore, these small vessels were more susceptible to become tortuous during the retinal NV stage. For this reason, we will extract a value that reflects the tortuosity to classify the OD sub-image as healthy or NVD.

Indeed, the more a vessel is tortuous, the greater the distance between the vessel extremities is. For this, we calculate the T tortuosity for each vessel, which is considered as the ratio between the vessel length L and the Euclidean distance D between the two vessel extremities [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF][START_REF] Mustafa | A review on the diabetic retinopathy assessment based on retinal vascular tortuosity[END_REF], as indicated in equation 1.

T = L D ⁄ (1)
where length L is calculated using the modified "Riks" method [START_REF] Riks | An incremental approach to the solution of snapping and buckling problems[END_REF]. For example, the vessel illustrated in Fig. 4(a The objective of this section is to generate a single feature related to the tortuosity of the whole vessel tree. The idea is to deduce the feature value from the T ones corresponding to all vessels belonging to the OD subimage. In fact, a healthy image can contain vessels where most of them have a low tortuosity. For NV, several vessels with higher tortuosity are added. We proceed to illustrate the vessel distribution in terms of tortuosity, as presented in Fig. 5. We deduce that the distribution of tortuosity for a healthy image is asymmetrical to the left, which indicates that small values of tortuosity correspond to 80% of the vessels, as shown in the Fig. 5(a). In contrast, the distribution of tortuosity for an NVD image is asymmetrical to the right, which indicates that high tortuosity values are most frequent, where 80% of vessels have higher tortuosity values, as given in Fig. 5(b).

(a1) (b1) (c1) (d1) (e1) (a2) (b2) (c2) (d2) (e2)
Our main idea consists in extracting a feature that reflects the distribution of vessel tortuosity. The mean of the vessels is an inadequate value for modeling tortuosity related to NV. For this, we employ the skewness which models the symmetrical degree of a distribution [START_REF] Mardia | Measures of multivariate skewness and kurtosis with applications[END_REF]. The skewness feature 𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 reflects the tortuosity distribution, as indicated in equation 2.

𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 = ∑ ( - ) ⁄ (2)
where Moy represents the average of the tortuosities, E represents the standard deviation, N represents the total number of vessels, and T represents the tortuosity of a vessel. For instance, the tortuosity skewness of a healthy image is equal to 0.91, while it is equal to -0.35 for a neovascularized image.

Width feature

NVD is characterized by the appearance of new vessels in the OD that have a thin width [START_REF] Agurto | Detection of neovascularization in the optic disc using an AM-FM representation, granulometry, and vessel segmentation[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF] as represented in Fig. 1(b). Multiple studies have primarily focused on the association between the retinal vascular width and the risk of DR where Wong et al. [START_REF] Wong | Retinal Arteriolar Narrowing, Hypertension, and Subsequent Risk of Diabetes Mellitus[END_REF] showed that the DR were associated with narrowing arterioles. Additionally, Nguyen et al. [START_REF] Nguyen | Retinal Arteriolar Narrowing Predicts Incidence of Diabetes: The Australian Diabetes, Obesity and Lifestyle (AusDiab) Study[END_REF] concluded that the retinal arteriolar caliber might be smaller with the increasing DR severity. For this purpose, we extract a feature that reflects the width in order to classify the image as healthy or NVD, as proceeded by the method in [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Gupta | Local characterization of neovascularization and identification of proliferative diabetic retinopathy in retinal fundus images[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF].

We determine the width L for each vessel in terms of pixels. The main processing idea consists in progressively thinning and quantifying the vessel width. Both steps are repeated until the vessel is disappears. Thus, the morphological "Erosion" transformation is iteratively applied, whose structuring S element size is initialized at 1 and incremented by 1 at each iteration. The processing is turned off when the vessel sub-image becomes entirely black, as indicated in algorithm 1. Thereafter, the vessel width L is deduced in terms of the structuring element, as calculated in equation 3.

L = S -1 (3)
where S represents the size of the structuring element. Figure 6 illustrates the vessel sub-images after each Erosion application. The structuring element size is increased from 1 to 8, whose vessel width L is equal to 7.

Image input h = 1 h = 2 h = 3 h = 4 h = 5 h = 6 h = 7 h = 8
Fig. 6 Erosion results in terms of structuring element sizes

The objective of this section is to generate a single feature deduced from all L width vessels of the OD sub-image. Therefore, we proceed to illustrate the vessel distribution in terms of width, as depicted in Fig. 7. We deduce that the width distribution for a healthy image is asymmetrical to the right, where vessels having a width above 2 represent 80% of all vessels, as shown in Fig. 7(a). In contrast, the width distribution for an NVD image is asymmetrical to the left, where 80% of the vessels have a width value below 2.5, as provided in Fig. 7(b). Our main idea consists in extracting a single width feature that reflects the distribution of the vessel width. Similarly, we compute a feature of width skewness Skewness between all the vessels in order to model the width distribution, as indicated in equation 4.

Skewness = ∑ ( - ) ⁄ ( 4
)
where Moy is the average width, E is the standard deviation, N represents the total number of vessels, and L represents the width of a vessel. For example, the width skewness of the healthy image is equal to -0.63, whereas it is equal to 0.49 for the NVD image.

Number of branches

The retina contains four major arteries and veins that develop from the optic nerve head in order to propagate respectively in the inferior, nasal, superior and temporal regions. All other vessels fork from those major vessels through bifurcation nodes. When NV occurs, several new vessels appear especially in the OD. Consequently, a neovascularized OD has a high number of branches. As indicated in the work proposed by Pan et al. [START_REF] Pan | Characteristics of Neovascularization in Early Stages of Proliferative Diabetic Retinopathy by Optical Coherence Tomography Angiography[END_REF], the neovascularized vessel branch duplicated frequently in all directions, as depicted in Fig. 1(b). For this purpose, we extract a value that reflects the number of branches in order to classify the image as healthy or NVD [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF]. We want to identify the number of branches NB for each vessel by applying the gift wrapping Algorithm. This latter allows computing the convex hull [START_REF] Sharif | A new Approach to Compute Convex Hull[END_REF] that generates a polygon whose encompasses the vessel [START_REF] Amiraj | Implementation of Hand Detection based Techniques fo Human Computer Interaction[END_REF], as shown in the vessel modeled in Fig. 8. As a result, the number of branches of the vessel is deduced, which corresponds to the number of the polygon sides. Thereafter, we deduce bifurcation by computing the total number of branches NB of all vessels, as calculated in equation 5.

NB = ∑ NB (5)

where NB represents the number of branches of a vessel, and N represents the total number of vessels. For instance, the number of branches for the healthy OD of Fig. 3

Blood vessel density

NV is characterized by the appearance of new vessels due to a significant lack of oxygen in the retinal capillaries [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF]. The new vessels are denser than the normal blood vessels [START_REF] Welikala | Automated detection of proliferative diabetic retinopathy using a modified line operator and dual classification[END_REF][START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF]. Therefore, we extract a value that reflects the density of blood vessels in order to classify the image as healthy or NVD. For this purpose, we calculate the density of all blood vessels D in the OD, which is considered to be the ratio between [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Silkar | Detection of neovascularization in retinal images using mutual information maximization[END_REF] the vessel area and the OD area, as indicated in equation 6.

D = x1 x2 (6)

where x1 is the number of all vessel pixels, and x2 is the total number of OD pixels. For the healthy OD shown in Fig. 1(a), the vessel density is equal to D = 0.20. In contrast, the neovascularized OD in Fig. 1(b) has a vessel density equal to D = 0.27.

Classification

The classifier must provide a higher performant classification based on the extracted features. This performance is to be ensured even when using a reduced size of dataset for training. Moreover, the classifier should be characterized by a lower complexity in order to be adequate for a mobile implementation [START_REF] Prasanna | Decision Support System for Detection of Diabetic Retinopathy Using Smartphones[END_REF][START_REF] Saki | Smartphone-based real-time classification of noise signals using subband features and random forest classifier[END_REF]. For this purpose, we select classifiers that attest those criteria, which are the SVM and the RF classifiers. For each classifier, the provided results depend on the manner in which their parameters are initialized. Therefore, we describe both classifiers in the following sub-sections where we focus on their parameters.

Thereafter, we perform an experimental study, as detailed in section 5.2, where each classifier is employed with different parameters, as done in [X, Y]. Thereupon, the classifier achieving the better detection performances is identified to be integrated on our proposed method.

SVM

The SVM is an automatic learning algorithm used for data classification, which is widely used for binary classification [X]. The principal objective of SVM is to determine an optimal hyperplane that separates the training data into classes, by maximizing the geometric margin between each other [START_REF] Kavzoglu | A kernel functions analysis for support vector machines for land cover classification[END_REF][START_REF] Abe | Support Vector Machines for Pattern Classification[END_REF][START_REF] Ahmed | A survey of network anomaly detection techniques[END_REF]. Many related works [START_REF] Agurto | A multiscale decomposition approach to detect abnormal vasculature in the optic disc[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF] used the SVM classifier to detect the NVD where optimal performances have been achieved. The hyperplane generation depends of the used kernel that can be polynomial, Radial Basis Function (RBF) and sigmoid function [START_REF] Karatzoglou | Support Vector Machines in R[END_REF]. All kernels have common parameter called the cost ∁ and the slope gamma γ. The SVM classifier provided adequate performance when a reduced training dataset is used. Moreover, the SVM complexity is equal to 𝐦𝐚𝐱(𝒅𝒂𝒕𝒂 × 𝒗𝒆𝒄), 𝒅𝒂𝒕𝒂²) [START_REF] Ayinala | Low complexity algorithm for seizure prediction using Adaboost[END_REF]59], where 𝒅𝒂𝒕𝒂 is the number of images used on the training process and 𝒅 is feature set size, hence requiring a constant execution time.

RF

The RF [START_REF] Breiman | Random Forests[END_REF] is an ensemble of decision tree classifiers. Each tree is formed independently of the other using a randomly selected subset of a training set. The forest corresponds to a collection of trees where the classification result is decided whether by weighted voting or majority voting. The RF is widely used in solving classification problems [START_REF] Zhang | Comparing the Performance of Random Forest, SVM and Their Variants for ECG Quality Assessment Combined with Nonlinear Features[END_REF][START_REF] Abdulhay | Classification of Normal, Ictal and Inter-ictal EEG via Direct Quadrature and Random Forest Tree[END_REF][START_REF] Lin | Early Detection and Assessment of Liver Fibrosis by using Ultrasound RF Time Series[END_REF][START_REF] Ayata | Emotion Recognition from Multimodal Physiological Signals for Emotion Aware Healthcare Systems[END_REF], particularly for classifying DR retinal images [65, 66, X, X].

The RF has four main parameters [START_REF] Scornet | Tuning parameters in random forests[END_REF] which are the number of trees in the forest, the maximum depth of the tree, the number of features considered for splitting a node and the size of the training set. The model variance of a RF classifier decreases with respect to the rise of tree number, while maintaining the same bias [START_REF] Buczak | A Survey of Data Mining and Machine Learning Methods for Cyber Security Intrusion Detection[END_REF]. The RF is characterized by a low number of control where the complexity of the prediction phase is 𝑶(𝒔𝒆𝒕 × 𝒕𝒓𝒆𝒆) where 𝒔𝒆𝒕 is the feature set size and 𝒕𝒓𝒆𝒆 is the number of trees [START_REF] Hassine | Important Complexity Reduction of Random Forest in Multi-Classification Problem[END_REF].

Implementation of the MAS-PDR

Android is an open source operating system for mobile devices, published by Google under the Apache license [START_REF] Do | Automatic license plate recognition using mobile device[END_REF]. The implementation was made for Android smartphones using the Android software development kit. We use the JAVA language to write a program in Android Studio. The processing related to image processing and classification is coded using The "Open Source Computer Vision (OpenCV)" multiplatform library, developed by Intel. It focuses mainly on image processing and computer vision [START_REF] Elloumi | A mobile computer aided system for optic nerve head detection[END_REF][START_REF] Kumari | Automatic License Plate Recognition Using OpenCV and Neural Network[END_REF] and provides rapid and efficient data structures and algorithms that can be used for complex real-time applications [START_REF] Amiraj | Implementation of Hand Detection based Techniques fo Human Computer Interaction[END_REF]. It offers more than 2500 optimized image processing functions written in C / C ++ language [START_REF] Elloumi | A mobile computer aided system for optic nerve head detection[END_REF]. To compile and incorporate the functions written in C / C ++ language, the Android native development kit is installed and configured in our project.

The PDR screening method is implemented using Android Studio 3.5 with a PC powered by Intel Core i3, CPU 2 GHz and 4GO RAM. A graphical user interface is developed to allow using the method as an Android app, as shown in Fig. 9. When the application is launched, the "Fundus Image Selection" button allows opening the smartphone gallery in order to select the fundus image. Thereafter, the processing proposed in [START_REF] Elloumi | A mobile computer aided system for optic nerve head detection[END_REF] is processed to locate and display the OD in the graphical interface. The "Neovascularization Detection" button leads to run the suggested method and post a message to the user indicating the screening result.

Experimental Results

In this section, we aim to evaluate the proposed method for NVD detection, in terms of detection performance and execution time. For this purpose, the experiment consists in identifying the dataset and the detection metrics used for evaluation, as depicted in the first sub-section. In the second sub-section, the NVD detection performances of the suggested method are extracted and compared with the different existing techniques. Then, the evaluation of the robustness of the method with images captured by a smartphone is presented in the third sub-section. Moreover, the execution time of our method is evaluated and compared to some related work in the last sub-section.

Fundus image dataset

Based on the state of the art study presented in section 2, the NV detection methods are always evaluated using dataset where fundus images are collected from different databases since no one contains sufficient NVD fundus images. For this purpose, we construct a database of 306 images captured by retinograph, which contains 106 NVD images and 200 healthy images. To ensure a reliable evaluation, 30% of fundus images are assigned as NVD. The image resources used in this document are collected from eight publically accessible databases, where the number of images is detailed in Table 2. The collected fundus images have different resolution, such as the DRIVE, STARE and MESSIDOR datasets where the sizes are respectively 768×584, 700×605 and exceed 1440×960. This divergence leads to different OD size where the radius ranges from 80 to 200 pixels. In order to unify the processing, the images are resized to have an OD radius of 100 pixels.

Evaluation approach

To evaluate the performance of our method, we use three parameters for the evaluation purpose which are sensitivity (Sens), specificity (Spec) and accuracy (ACC) given in equations ( 7) -( 9), respectively. Sensitivity = (7)

Specificity = (8)
Accuracy = (9)
where TP, TN, FP and FN are respectively the True Positive, the True Negative, the False Positive and the False Negative detected images.

To ensure credibility whether for chosen classifiers or for deduced performances, we apply a 10-cross validation. The process consists in splitting the dataset where 70% of the data are used for training and 30% for testing. The repartition is randomly done ten times to provide different sets whether dedicated for training or testing.

Feature evaluation

Our main contribution consists at adequately choosing features in order to reflect the NV properties. For this purpose, we proceed to evaluate the features ability to distinguish between healthy and neovascularized OD. For each feature, we model graphically all extracted values as points in a 2D Cartesian space, where the vertical axis expands the value gap, as shown in Fig. 10. The feature values that correspond to healthy and neovascularized images are modeled respectively with blue and orange colors.

We deduce that values of each class are apparently clustered, despite the important size of the dataset. This evaluation attests the meaningful of the chosen features. However, the clusters are not linearly separable, where their value gaps are overlapped. The value crossover is obvious where reflected properties are already outlined in a healthy OD. Therefore, a screening cannot be performed using any feature separately.

Classification evaluation

In this section, we choose the adequate classifier and its configuration that allows achieving a higher detection performance. Within this objective, we extract the features of all fundus image datasets. Thereafter, the SVM and random forest classifiers are trained with different configuration, using the same feature set.

For the SVM, we experimentally test the classifier with three different kernels that are respectively the sigmoid, the RBF and the polynomial, where the achieved accuracy, sensitivity and specificity are indicated in the three first 3. We note that the C, γ and d parameters are selected using the grid search method, which is widely used and considered by the most accurate optimization technique [START_REF] Kavzoglu | A kernel functions analysis for support vector machines for land cover classification[END_REF]. For the random forest, the feature number is fixed to the maximal value, as we have only four ones. In addition, the tree number is fixed to 500. The tree depth is varied following the above values {6, 8, 10} where their results are illustrated in the three last columns of Table 3. We deduce that using the RF classifier allows achieving 98.69% accuracy, 97.73% sensitivity and a 99.12% specificity, for any depth suggested. That is why, the RF classifier with tree depth equal to 6 is chosen for our proposed method. We use the box plots to present the performance of these experiments, as shown in Fig. 11(a). These box plots demonstrate high performances in terms of accuracy, sensitivity and specificity. Moreover, those higher performances are guaranteed whatever the dataset used for training testing. This aspect proves the performance of our method or when using new captured fundus images, which corresponds to clinical utilization.

Evaluation with respect to existing methods

We evaluate our method with respect to the existing ones in terms of detection performances and number of extracted features, as illustrated in Table 4. Our proposed method registers the highest accuracy and specificity compared to all NV and NVD detection methods. Moreover, our method achieves better sensitivity compared to the NVD method presented by [START_REF] Agurto | Detection of neovascularization in the optic disc using an AM-FM representation, granulometry, and vessel segmentation[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF], even we proceeded with a 10-cross validation. This performance is caused by the targeted NV properties which present adequate and complementary set for the NV modeling. We note that our dataset has greater or similar size than the ones used in [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF][START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF]. While the accuracy of the method described in [START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF] is not provided, the detection performance of our method outperforms the methods proposed in [START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF] and [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF]. Moreover, the achieved sensitivity and specificity obviously exceed the ones registered the three methods. This result is due to the meaningful processing features that we put forward.

Evaluation of the method robustness with respect to smartphone captured images

In this section, we evaluate the suggested method with respect to the degraded quality of fundus images captured by smartphones. We notice that no public database of The merged plot sizes reflect the sustainability of the method whatever the degraded images used for training or for testing. We deduce that the detection performances remain higher even with a degraded image quality. Accordingly, the result proves the robustness of our method and confirms its ability to be employed on a mobile MAS system for PDR.

Computational performance of MAS-PDR

Complexity analysis

The point spread function, the CLAHE algorithm and the black-hat filter proceed to browse all pixels of the OD sub-image in order to provide the new pixel values. therefore, each processing requires (𝑛 × 𝑛) to be done [START_REF] Chen | Gray-level grouping (GLG): an automatic method for optimized image contrast Enhancement-part I: the basic method[END_REF], where (𝑛 × 𝑛) is the size of OD sub-image. The Otsu thresholding consists in comparing and generating a pixel value, which is repeated (𝑛 × 𝑛) times [START_REF] Chen | A survey on Otsu image segmentation methods[END_REF]. Similarly, the extraction of each vessel requires (𝑛 × 𝑛) instructions [START_REF] Suzuki | Topological structural analysis of digitized binary images by border following[END_REF].

The complexities of the RIKs method, the Erosion morphological operator and the convex hull algorithm are equal to (𝑛 × 𝑛). Those processing are performed 𝑣 times, where 𝑣 is the number of vessels. Moreover, the vessel density requires scanning all pixels and hence performed in (𝑛 × 𝑛). Finally, the RF classifier leads to browse 500 trees composed by 4 features and hence requiring constant complexity to be processed. Consequently, the whole method complexity is equal to 𝑂(𝑛 × 𝑛 × 𝑣), where (𝑛 × 𝑛) is the size of OD sub-image ad 𝑣 is the number of vessels.

. Execution time evaluation

In this section, we proceed to evaluate the execution time performance of our proposed method. For this purpose, the MAS-PDR app is implemented in the SAMSUNG S5 smartphone, which can be combined with the optical lens D-EYE. Thereafter, we choose randomly 20 fundus images which are partitioned into 10 healthy and 10 NVD, where execution times are respectively shown in Fig. 13(a), Fig. 13(b). We deduce that the average execution time of healthy images is about 0.9 seconds, while it is equal to 2.63 seconds for the NVD images. In fact, our method is based on extracting retinal vessels and then exploring each segmented vessel where NVD leads to increasing the vessel number. As an example, the average number of vessels in healthy OD is about 40, while it is equal to 100 in the case of NVD images. This difference explains the gap of execution times among healthy and NVD fundus images.

Thereafter, we compare the execution times of our method to the existing NVD detection methods, where values are shown in Table 5. We indicate that only methods providing the execution times are considered. We deduce that our method achieves better execution time than all reported methods, despite that our method is executed on smartphone device while others were implemented in desktops. For instance, the detection requires more than 2 minutes when using the methods proposed in [START_REF] Hassan | Detection of Neovascularization in Diabetic Retinopathy[END_REF][START_REF] Usman Akram | Detection of neovascularization in retinal images using Table 5. Execution times for NV detection methods Method Execution time Goatman et al[END_REF][START_REF] Silkar | Detection of neovascularization in retinal images using mutual information maximization[END_REF][START_REF] Goatman | Detection of New Vessels on the Optic Disc Using Retinal Photographs[END_REF]. Particularly, our method provides a faster result than the one suggested in [START_REF] Yu | Machine Learning Based Automatic Neovascularization Detection on Optic Disc Region[END_REF]. This result is caused by the optimal feature set that we suggested which is limited on four features with a low computational complexity. Accordingly, the computational performance is perfectly adequate to the clinical employment of MAS-PDR.

Conclusion

In this paper, an automated method for NV detection has been proposed to provide the early detection of NV. This method was implemented into smartphones to provide a MAS system for PDR. This processing consists in detecting and enhancing the OD. Thereafter, the vessel tree is segmented where each vessel is extracted separately. Our main contribution consists in providing four adequate features that are exactly related to the morphologies of the neovascularized vessels. The provided features are given to a RF classifier to ensure higher performance detection with 98.69% accuracy. We have also evaluated the robustness of the method by applying the motion blur to the fundus image datasets, where a higher performance is maintained with 98.91% accuracy.

In our future work, we aim to propose a MAS system for DR severity while guaranteeing the same accuracy and robustness. In addition, we will provide real-time detection which can be performed into a retinal capture video stream. Furthermore, other work must be focused into generating a new database dedicated for smartphone-captured fundus images.

Fig. 1

 1 Fundus images: (a) Healthy image, (b) PDR image

Fig. 2

 2 Fig.2 Diagram of our proposed method for NV detection

  ) has a healthy tortuosity where T =1.1. The neovascularized vessel shown in Fig.4(b) has high tortuosity where T = 2.

Fig. 4

 4 Fig.4 Vessels with different tortuosity: (a) low tortuous vessel, (b) high tortuous vessel

Fig. 3

 3 Pre-processing and Vessel segmentation: (a1) and (a2) healthy and NV OD image; (b1) and (b2) green channels of OD images; (c1) and (c2) pre-processed OD images ; (d1) and (d2) black-hat results of OD images ; (e1) and (e2) segmented vessel trees

Fig. 5

 5 Fig.5 Vessel distribution in terms of tortuosity: (a) healthy images, (b) neovascularized images

Algorithm 1 :

 1 vessel width computing Input : a vessel Output :𝐿 = h -1 Begin h1 Repeat apply Erosion (h*h) hh+1 Until (achieve black image) End

Fig. 7

 7 Fig.7 Vessel distribution in terms of width: (a) healthy images, (b) neovascularized images

  (a1) is equal to NB = 135, while it is equal to NB = 227 for the neovascularized OD illustrated in Fig.3(a2).

Fig. 8

 8 Fig.8 Number of branches computing

Fig. 9

 9 Smartphone graphical interface: (a) Healthy image detection, (b) NV detection

  Fig.10 distribution of feature values: (a) tortuosity, (b) width; (c) density: (d) number of branches columns of Table

Fig. 11

 11 Fig.11 Performance visualization using box plots: (a) initial fundus images dataset, (b) motion blurred fundus image dataset

Fig . 13 Fig. 12

 1312 Fig.12 original and blurred fundus images: (a) and (c) fundus images, (b) and (d) fundus images after applying motion blur filter

Table 1 .

 1 Targeted NV Properties in terms of NV detection methods

			NV properties	Vessel	Vessel	Vessel	Number of	Number of	Vessel	Retina
				tortusoity	density	width	Vessels	Branches	length	texture
	Neovascularization	screening	Hassan et al. (2012) [5]				X		X

Table 2 .

 2 Fundus images selected from publically Databases

	Database	Number of	Number of NVD
		healthy images	images
	DRIVE	15	0
	DIARETDB1	20	3
	HRF	15	3
	DIARETDB0	20	7
	Messidor	40	17
	Kaggle	0	10
	STARE	17	3
	EyePACS	73	63

Table 3 .

 3 Performance comparison between SVM and RF classifiers

	Classifier		SVM			Random forest
		Sigmoid	RBF	Poly	depth = 6	8	10
	Acc (%)	94.02	97.39	98.47	98.69	98.69	98.69
	Sens (%)	91.30	95.70	97.88	97.73	97.73	97.73
	Spec (%)	95.50	98.25	98.75	99.12	99.12	99.12

Table 4 .

 4 Comparison of NV detection methods

			Method	Dataset	Number of	Acc	Sens	Spec
					Feature
	Neovascularization	screening	Hassan et al. (2012) [5] Agurto et al. (2012) [7] Agurto et al. (2015)[12] Gupta et al. (2017) [14] Yu et al. (2018)[15] Huang et al. (2018)[9]	11 NV + 302 Neg 27 NVD + 30 Neg 100 NVD + 200 Neg 100 NV + 679 Neg 134 NVD + 290 Neg 42 images	2 41 1248 525 42 5	_ 88% _ 95.23 % 89.20%	93.90% 96% 78% 92 .2% 92.9% _	89.40% 83% 94% 83% 96.30 % _
	vessel	segmentation	Goatman et al. (2011) [13] Akram et al. (2013) [10] Welikala et al. (2014) [8] SilKar et al. (2017) [11]	38 NVD + 71 Neg 63 NV + 451 Neg 20 NV + 40 Neg 26 NV + 1368 Neg	15 10 4 2	_ 95% _ 97.49%	84.2% 96.5% 100% 97.45%	85.90% 93% 90% 96.03%
			Proposed method	106 NVD + 200 Neg	4	98.69 %	97.73%	99.12 %

Agurto et al. (2012) [7] X X Agurto et al. (2015)[12] X X X Gupta et al. (2017) [14] X X X X Yu et al. (2018)[15] X X X X X X Huang et al. (2018)[9] X X vessel segmentation Goatman et al. (2011) [13] X X X X X X Akram et al. (2013) [10] X X X X X Welikala et al. (2014) [8] X X X X SilKar et al. (2017) [11] X X

This work was supported by the PHC-UTIQUE 19G1408 Research program.


Alexandre Nominé

Julien Martin

Cédric Noel

Gérard Henrion

Thierry Belmonte

Ilya V Bardin

Petr Lukeš

Cédric Noël

Toward Optimization of Electrolyte Composition for Treatment of Aluminum and Magnesium by Plasma Electrolytic Oxidation

Keywords: plasma electrolytic oxidation, PEO, aluminum, magnesium, cathodic discharge, isoeletric point (IEP)

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Introduction

Plasma Electrolytic Oxidation (PEO) is of increasing industrial interest due to the perspectives this process offers in structure lightening and eco-friendly production. It allows fast growth (some μm.min -1 ) of crystalline oxide coatings (1-2) on the surface of light alloys (Al, Mg, Ti). Moreover, unlike anodizing, it is, a one-step process that does not require any hazardous compounds [START_REF] Yerokhin | Plasma electrolysis for surface engineering[END_REF]. The process consists in applying a sufficiently high current or voltage between a working-electrode and a counter-electrode to ensure the breakdown of the growing oxide layer in a conductive electrolyte. The as-produced micro-discharges (MDs) are essential to give access to the core material and feed the PEO-layer growth. They are responsible for the development of the porosity and roughness of the layers [START_REF] Arrabal | 3-Dimensional structures of open-pores in PEO films on AZ31 Mg alloy[END_REF][START_REF] Curran | Porosity in plasma electrolytic oxide coatings[END_REF][START_REF] Tillous | Microstructure and 3D microtomographic characterization of porosity of MAO surface layers formed on aluminium and 2214-T6 alloy[END_REF]. It has been shown that the development of detrimental large MDs, can be limited by the use of a bipolar rather than a unipolar current [START_REF] Hussein | The effect of current mode and discharge type on the corrosion resistance of plasma electrolytic oxidation (PEO) coated magnesium alloy AJ62[END_REF][START_REF] Yerokhin | Spatial characteristics of discharge phenomena in plasma electrolytic oxidation of aluminium alloy[END_REF] or by hybrid mode (unipolar then bipolar) (9-10) leading to significant increase in coating thickness and density and consequently an improved corrosion and wear resistance. By varying the positive (anodic) to negative (cathodic) charge quantity ratio Q p /Q n , Jaspard-Mécuson et al. [START_REF] Jaspard-Mécuson | Tailored aluminium oxide layers by bipolar current adjustment in the Plasma Electrolytic Oxidation (PEO) process[END_REF] showed that a ratio Q p /Q n of 0.89 led to a soft sparking regime with particularly interesting results in terms of coating thickness and homogeneity. While the importance of the cathodic half-period has been clearly established, it is interesting to note that MDs were only detected during the anodic period (i.e. when the working electrode is the anode). Considering exclusively the electrochemical processes, oxidation must take place only under anodic polarization.

However, as PEO is a plasma-assisted process, it is still unclear why breakdown should occur only during the anodic half-period and not under cathodic polarization.

Previous works have shown that cathodic micro-discharges can develop not only under specific processing conditions -e.g. Mg alloys in NH 4 F based electrolyte (12 -13) -but also with conditions that are widely used in PEO (Mg alloys in alkaline-silicate electrolytes) [START_REF] Nomine | Effect of cathodic micro-discharges on oxide growth during plasma electrolytic oxidation (PEO)[END_REF]. It has also been highlighted that cathodic MDs are detrimental to the coating growth on magnesium substrates and that they do not contribute to oxidation. It is also worth noting that cathodic MDs present different physical properties than the conventional anodic MDs; the Hα line profiles can be fitted with a single Voigt function (i.e., only one electron density) [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF] unlike results observed by Jovović et al. in the case of anodic discharges [START_REF] Jovovic | Spectroscopic study of plasma during electrolytic oxidation of magnesium-and aluminium-alloy[END_REF] and the emission intensities of different species stay relatively constant within the processing time [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF] which is not what is observed in the case of anodic discharges [START_REF] Hussein | Spectroscopic study of electrolytic plasma and discharging behaviour during the plasma electrolytic oxidation (PEO) process[END_REF]. This suggests that unlike anodic discharge (16 -17) there is likely only one type of cathodic discharge.

On the other hand, Sah et al. [START_REF] Sah | Cathodic pulse breakdown of anodic films on aluminium in alkaline silicate electrolyte -Understanding the role of cathodic half-cycle in AC plasma electrolytic oxidation[END_REF] have shown that within ranges of very high cathodic current densities (some 1000s A.dm -2 ) cathodic MDs can be observed. Under those conditions, cathodic MDs promote the randomisation of the anodic discharge sites, thus preventing the development of excessively large anodic discharges that are known to be detrimental to the coating homogeneity. Therefore, predicting under which conditions cathodic MDs would occur could help to improve the process by avoiding detrimental discharges. It appears that the electrolyte composition and pH, and therefore the available charges in the electrolytic bath are the key parameters to address this issue. Hence, the present communication investigates the influence of (i) the surface charge on the grown oxide and (ii) the electrolyte composition on the breakdown regime, either anodic or cathodic or both.

Experimental Procedure

The process is run in an electrolytic cell equipped with glass windows. Samples are commercial Al 2024 (Cu 3.9 -5 wt%, Mg 0.5 -1.2 wt%, Mn 0.4 -1.2 wt%, Fe 0.3 wt%, Si 0.5 -1.2 wt%, Zr 0.25 wt%, Ti 0.15 wt%, Cr 0.1 wt%, Al as balance) and Mg EV31 (Nd -2.86 wt%, Gd -1.38 wt%, Zn -0.25 wt%, Zr -0.66 wt%, Mg as balance) alloys. Prior to processing, the samples are ground with water-cooled P1200 SiC paper (15.3 μm median SiC powder diameter) and rinsed successively in distilled water and ethanol. pH and composition of the electrolytes used in this study are listed in Table 1.

Table 1. Electrolyte compositions and pH

Coatings are grown using a bipolar pulse current supply (Ceratronic ® ), which was set to deliver a symmetrical 100 Hz quasi-square current waveform. Cathodic and anodic amplitudes are set at 8 A, (current density of 20 A.dm -2 delivered to the sample) leading to a ratio Q p /Q n = 1.

Rise and fall times are set at 300µs, off times between anodic and cathodic pulses at 100µs and hold time at +/-8A at 4.3 ms. Optical detection of MDs is performed with a photomultiplier (Hamamatsu R928) whose spectral detection covers the 185 -900 nm range. The output signal was amplified through a 300 MHz bandwidth current amplifier (Stanford Research Systems SR445).

Electrolyte

Composition pH

BASE [NH 4 F] = 10 g.L -1 (0.27 M) 6.8 KOH-2 BASE + [KOH] = 2 g.L -1 (0.036 M) 8.7 KOH-5 BASE + [KOH] = 5 g.L -1 (0.089 M) 9.2 KOH-15 BASE + [KOH] = 15 g.L -1 (0.268 M) 9.7 KOH-20 BASE + [KOH] = 20 g.L -1 (0.357 M) 12.6 SILICATE BASE + [Na 2 SiO 3 ] = 2 g.L -1 (0.016 M) 8.8 PHOSPHATE BASE + [Na 6 P 6 O 18 ] = 5 g.L -1 (0.008 M) 8.8

Results

Influence of surface pre-treatment

Cathodic MDs were first observed on magnesium substrates processed in BASE electrolyte [START_REF] Hussein | The effect of current mode and discharge type on the corrosion resistance of plasma electrolytic oxidation (PEO) coated magnesium alloy AJ62[END_REF]. In this case, it was not possible to observe any cathodic MD on aluminum substrates, even though these substrates were strongly corroded. To limit corrosion and investigate the discharge 1b) irrespective of the coating thickness. The voltage then decreases (in absolute value) at a rate which is thickness-dependent (the thinner the pre-coating, the higher the decay rate), until it reaches an asymptotic value which is proportional to the coating thickness. Interestingly, the asymptotic value is reached concomitantly with the extinction of cathodic MDs.

Influence of pH

The influence of the pH was investigated by progressively adding KOH to the BASE electrolyte according to table 1. Aluminum and magnesium samples were processed within these electrolytes. Figure 2a represents the variation of the emitted light intensity over one period of current for different substrates and electrolytes. For magnesium substrates treated in an electrolyte with a low pH (KOH-2, KOH-5, KOH-15), no light emission is observed during the anodic half-period while an emission peak due to micro-discharges appears at the beginning of the cathodic polarization (fig. 2a). In the case of high pH values (KOH-20), cathodic MDs appear at the beginning of the treatment (typically after 2 minutes) and then disappear in favor of anodic micro-discharges (fig. 2a). Treatments of aluminum in KOH-20 electrolyte give rise to anodic discharges exclusively (fig. 2a). Neither discharge nor coating growth has been observed while treating in an electrolyte with a lower KOH concentration.

Influence of electrolyte composition

Silicate-and phosphate-containing electrolytes were used to investigate the influence of the electrolyte composition. It is worth noting that both electrolytes have the same pH value (table 1). In the case of aluminum treated in SILICATE electrolyte, no discharge appeared for a bulk sample for the same reason as discussed previously. However after a pre-treatment in an alkaline-silicate electrolyte both anodic and cathodic discharges appear during one period (fig. 3a). In PHOSPHATE, only anodic discharges are observed (fig. 3a). On the other hand, in the case of a magnesium substrate, only cathodic discharges are observed in SILICATE but both anodic and cathodic discharges occur in PHOSPHATE electrolyte (fig. 3b).

Discussion

Figure 4a shows the effect of cathodic discharges obtained on a sample previously treated in an alkaline-silicate solution (see fig 1 and § 3.1). Figure 4b shows the aspect of a sample after a 40 min treatment in the BASE electrolyte. In Figure 4a one sees that cathodic MDs strongly affect the coating which peels off at some places (see arrows) while figure 4b shows that a strong corrosion is observed in BASE electrolyte. These observations confirm that cathodic MDs are detrimental to the coating, and support the breakdown mechanism proposed in [START_REF] Hussein | A study of the interactive effects of hybrid current modes on the tribological properties of a PEO (plasma electrolytic oxidation) coated AM60B Mg-alloy[END_REF]. It also strengthens the motivation of investigating ways to predict and prevent cathodic breakdown. porous ceramic layer [START_REF] Lukes | The Role of Surface Chemistry at Ceramic/Electrolyte Interfaces in the Generation of Pulsed Corona Discharges in Water Using Porous Ceramic-Coated Rod Electrodes[END_REF]. According to these authors, surface charge on the oxide layer strongly affects the electric field distribution on the ceramic-coated electrode and initiation of the discharge in water. The build-up of surface charge on the oxide layer arises from acid-base dissociation of the hydrated oxide surface and accumulation of ions at the oxide/electrolyte interface. The surface charge is determined by the oxide properties and the pH of the solution.

Working with a pH higher (resp. lower) than the isoelectric point (IEP) of the oxide layer promotes anodic (resp. cathodic) discharges. The IEP, also called the point of zero charge, represents the pH at which the surface charge (or zeta potential) equals zero (19 -21). Oxide coatings, in aqueous media, become hydrated at their topmost surface and amphoteric hydroxyl groups form at the surface. These groups can catch or release a proton depending on the difference between the IEP of the material and the pH of the electrolyte. This results in either a negatively or positively charged surface. When the metallic sample is negatively biased (i.e. is cathodic) and the electrolyte pH is higher than the IEP value (negative surface charge), a large positive electric double layer (EDL) forms at the coating/electrolyte interface. The potential difference within the EDL can be estimated with the Nernst equation while the thickness of the EDL is comparable with the Debye length (see Eq. 5 and 6 in reference [START_REF] Lukes | The Role of Surface Chemistry at Ceramic/Electrolyte Interfaces in the Generation of Pulsed Corona Discharges in Water Using Porous Ceramic-Coated Rod Electrodes[END_REF]). Typically, a pH difference of +1.5 between electrolyte pH and ceramic IEP will lead to a voltage of +100 mV within the EDL while the Debye length is between 5 and 10 nm. This leads to a local electric field as high as 100 to 200 kV.cm -1 , much greater than the one applied by sample biasing (some 10s of V/cm -1 ). This prevents cathodic breakdown (see e.g. [START_REF] Lukes | The Role of Surface Chemistry at Ceramic/Electrolyte Interfaces in the Generation of Pulsed Corona Discharges in Water Using Porous Ceramic-Coated Rod Electrodes[END_REF]). Conversely, under positive bias of the electrode in an electrolyte with a pH lower than the IEP, a negative EDL forms which prevents anodic discharges. Furthermore, the surface charge of the oxide is also affected by the specific adsorption of anions or cations present in the solution other than H + /OH -ions, which can induce a substantial shift in the IEP such as e.g., phosphates anions in the case of Al 2 O 3 (ΔIEP = -4) [START_REF] Kosmulski | pH-dependent surface charging and points of zero charge. IV. Update and new approach[END_REF]. This approach is valid whatever the breakdown mechanism considered (breakdown of the liquid electrolyte, of the ceramic coating, of gas bubble in pores…) since the presence or absence of an EDL will influence the charge accumulation that is necessary for breakdown of any kind.

Table 2 sums up the results obtained in this work and from other works, in terms of electrolyte pH and the resulting breakdown regime. Isoelectric points have been taken from Parks [START_REF] Parks | Isoelectric Points of Solid Oxides Solid Hydroxides and Aqueous Hydroxo Complex Systems[END_REF] and Kosmulski (20) data bases. The IEP of MgO was determined by the classical electrokinetic method while in the case of Al 2 O 3 a broad spectra of value was found depending on the crystallographic phase, the measurement method and the salt used. Since PEO coatings are composed of α-and γ-Al 2 O 3 we could establish that the IEP is between 8 and 9.5. The majority of the IEP measurement were done by classical electrokinetics though some results were obtained by CIP (common intersection point) or using the electroacoustic method (further details can be found elsewhere (20)).

It clearly appears that the breakdown regime depends on whether the electrolyte pH is above or below the material IEP. In other words, working at a pH higher than the IEP promotes anodic breakdown and prevents the cathodic one. In conditions 7, 8 and 10, the two discharge regimes occur concomitantly. In conditions 8 and 10, the electrolyte pH is very close to the oxide IEP.

Consequently, the pH-dependant surface potential is very small, decreasing the shielding efficiency. Therefore, breakdown can occur with either polarity. In conditions 7 and 11, the issue is that the value of the IEP of MgO in phosphate is unknown. However if we assume that phosphate induces a similar IEP shift on MgO as on Al 2 O 3 , the IEP of MgO in phosphate should be around pH 8.5. Assuming so, it is not surprising that only anodic discharges appear in condition 11 while the coexistence of cathodic and anodic discharges (condition 7) could be explained just as for conditions 8 and 10. One should point out the beneficial effect of phosphate that shifts the IEP to lower values and thus extends the range of pH for which cathodic MDs are inhibited. The same reasoning holds for condition 3. In that case however, it is likely that the morphology and structure of the growing layer slightly modify the IEP towards higher values, which would explain that cathodic discharges appear first and anodic ones after a few minutes of treatment. In condition 12, the presence of cathodic discharge is likely due to the very high current imposed (some 1000s of A.dm -2 while 20 -65 A.dm -2 were used in other conditions).

Hence, the surface charge is likely to be insufficient to shield from such a high current and discharges can form within both anodic and cathodic bias voltages.

Conclusion

To conclude, synchronized measurements of micro-discharges during PEO processing of various samples within different electrolyte allow the following conclusions to be drawn:

  behavior on aluminum substrates in BASE electrolyte, Al samples were pre-treated within the electrical conditions mentioned in Section 2. (20 A.dm -2 , 100 Hz) but in an alkaline-silicate electrolyte ([KOH] = 0.018 M; [Na 2 SiO 3 ] = 0.0135 M) in order to grow oxide coatings with a thickness of 15, 30 and 45 μm. After pre-treatment, samples were PEO processed in BASE electrolyte. The evolution of light emission during one period of current is plotted in figure1a. It clearly indicates that under the aforementioned conditions, an intense light emission due to MDs is detected during the cathodic half-period. Cathodic light emission is however detected only during the first tens of seconds of treatment (vertical dashed lines in fig.1b); the emission occurs after longer times as the pre-coating thickness rises (20 s for 15 μm, 100 s for 45 μm). Variation of the cathodic voltage amplitude during the first two minutes of treatment shows that for cathodic discharges, a voltage peak of ~ -180 V is observed at the beginning of the process (fig.

Figure 1 .

 1 Figure 1. Variation of (a) the light emission over one current period of a pre-coated sample

Figure 2 .

 2 Figure 2. Chronogram of (a) the light emission and (b) the applied current over one current

Figure 3 .

 3 Figure 3. Evolution of light emission over one period of current for (a) aluminum and (b)

Figure 4 .

 4 Figure 4. Photograph of (a) an aluminum sample pre-treated in an alkaline-silicate solution up to

Table 2 .

 2 Dependence of the breakdown regime on the type of substrate and on the electrolyte pH and composition. (C and A types of MD stand for cathodic and anodic respectively)

	N° Substrate Electrolyte	pH	IEP	MD type	Ref.
	1	Mg	BASE	6.8	12.4 ± 0.3 C	(12)
	2	Al	BASE	6.8	8 -9.5	C	Fig. 1
	3	Mg	KOH-20	12.6	12.4 ± 0.3 C then A	Fig. 2
	4	Al	KOH-20	12.6	8 -9.5	A	Fig. 2
	5	Mg	KOH-5	9.15	12.4 ± 0.3 C	Fig. 2
	6	Mg	SILICATE	8.8	12.4 ± 0.3 C	Fig. 3
	7	Mg	PHOSPHATE	8.8	?	C & A	Fig. 3
	8	Al	SILICATE	8.8	8 -9.5	C & A	Fig. 3
	9	Al	PHOSPHATE	8.8	5.0	A	Fig. 3
	10 Mg	KOH+Na 2 SiO 3	12.6	12.4 ± 0.3 C & A	(14)
	11 Mg	Na 2 SiO 3 + Na 4 P 2 O 7 .10H 2 O	12.5	?	A	(22)
	12 Al	KOH + Na 2 SiO 3	12.5	8 -9.5	C & A	(18)
	13 Al	KOH + Na 2 SiO 3 + Na 4 P 2 O 7	12	5	A

ACKNOWLEDGMENT The authors are grateful to Prof. T.W Clyne and Prof. N.StJ. Braithwaite for useful discussion and Pr. E. McRae for careful proof reading and supervising English writting ABBREVIATIONS PEO plasma electrolytic oxidation; IEP isoelectric point; MD micro-discharge; EDL electric double layer

 Detrimental cathodic breakdown can be avoided by adjusting the electrolyte pH to values higher than the isoelectric point of the growing oxide in the same electrolyte. This is due to the double layer that forms at the surface and which lowers the electric field across the oxide layer  Adding phosphate compounds in the electrolyte shifts the IEP to lower values. Besides avoiding the cathodic discharging, this allows a wider range of pH values to be used for which only anodic breakdown occurs.

AUTHOR INFORMATION

Corresponding Authors

* Dr. Alexandre Nominé, mail: alexandre.nomine@open.ac.uk * Dr. Gérard Henrion, mail: gerard.henrion@univ-lorraine.fr

Funding Sources

We greatly acknowledge the Conseil Régional de Lorraine for granting A. Nominé's PhD work under decision 11CP-769. This work was carried out within the framework of the COST TD1208 network.


domain: spi chim phys

text:
Alexandre Nominé

" J Martin

Gérard Henrion

Thierry Belmonte

J Martin

Effect of cathodic micro-discharges on oxide growth during plasma electrolytic oxidation (PEO)

Keywords: plasma electrolytic oxidation (PEO), magnesium, breakdown, micro-discharges, bipolar current pulse

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Plasma electrolytic oxidation is a promising surface treatment that might replace conventional anodizing to grow thick protective oxide coatings on light alloys (e.g. Al, Mg, Ti...). Although, both processes consist in immersing a work electrode and one or several counter electrodes in a conductive electrolyte, the physical mechanisms of oxide growth are basically different. In anodizing, oxide growth is driven by redox reactions and follows the Faraday law. The coating thickness is limited to some tens of micrometres with growth rates of hundreds of nanometres per minute. On the other hand, due to the high current density (1-100 A.dm -2 ) and voltage (400 -1000V) applied during the PEO process, micro-discharges (MDs for short) are repeatedly ignited at the surface of the substrate [START_REF] Yerokhin | Plasma electrolysis for surface engineering[END_REF]. Therefore, PEO allows fast synthesis of coatings with thicknesses reaching hundreds of micrometres in a few tens of minutes [START_REF] Shchedrina | Non-destructive methods to control the properties of MAO coatings on the surface of 2024 aluminium alloy[END_REF][START_REF] Krishna | A comparative study of tribological behavior of microarc oxidation and hard-anodized coatings[END_REF][START_REF] Bala Srinivasan | Effect of pulse frequency on the microstructure, phase composition and corrosion performance of a phosphate-based plasma electrolytic oxidation coated AM50 magnesium alloy[END_REF][START_REF] Wang | Effects of the ratio of anodic and cathodic currents on the characteristics of micro-arc oxidation ceramic coatings on Al alloys[END_REF]. The breakdown of oxides layers by MDs is considered as the principal mechanism that contributes to the oxide growth. The influence of the discharge features on the properties of the PEO layers has been already reported [START_REF] Martin | Effects of electrical parameters on plasma electrolytic oxidation of aluminium[END_REF][START_REF] Stojadinović | Spectroscopic and realtime imaging investigation of tantalum plasma electrolytic oxidation (PEO)[END_REF]. For instance, Mécuson et al [START_REF] Jaspard-Mécuson | Tailored aluminium oxide layers by bipolar current adjustment in the Plasma Electrolytic Oxidation (PEO) process[END_REF][START_REF] Mécuson | Diagnostics of an electrolytic microarc process for aluminium alloy oxidation[END_REF] showed that a judicious setting of the cathodic current half-period parameters (amplitude, duration) with respect to the anodic ones induces a voltage drop associated with the quasi disappearance of MDs. This regime, called the "soft regime", improves the compactness, growth rate and corrosion resistance of the layers.

Nevertheless, though the role of the cathodic half-period was clarified, no MDs were observed under cathodic biasing. However, we recently showed that within specific conditions, cathodic MDs could be observed [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF]. Surprisingly, no anodic MDs were detected, and the light emission corresponding to cathodic MDs has a pseudo periodic behaviour [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF]. The following sections will show the influence of cathodic MDs on the oxide growth. The influence of one current halfperiod (either anodic or cathodic) on the one coming immediately after (cathodic or anodic, resp.) will be pointed out.

Experimental procedure

The process is carried out on commercial EV31 magnesium alloy substrates (table 1) in alcalinosilicate ([KOH] = 0.036 mol.L -1 + [Na2SiO3] = 0.016 mol.L -1 ) and ammonium fluoride ([NH4F] = 0.27 mol.L -1 ) electrolytes. The current is supplied by a pulsed generator (Ceratronic ® ) that can deliver several types of waveforms as shown in table 2. The light emitted by the MDs was recorded with a Hamamatsu R928 photomultiplier (PM) whose output signal was amplified by a 300 MHz bandwidth current amplifier (Standford Research Systems SR445). The PM signal as well as current and voltage waveforms were collected and recorded using a 1 GHz bandwidth oscilloscope (Agilent 54832B). Space and time properties of MDs like their size, overall number and mean lifetime were determined from the analysis of images recorded using a Photron Fastcam SA1.1 ultra-high speed video camera (UHSC) whose acquisition rate was set at 125 kHz. Due to the important volume of data, images were processed using the TRACE software [START_REF] Bardin | Investigating Transport of Dust Particles in Plasmas[END_REF][START_REF] Endstrasser | Video tracking and post-mortem analysis of dust particles from all tungsten ASDEX Upgrade[END_REF].

Oxide layer composition and morphology were characterized with a Philips XL30 scanning emission microscope equipped with a field-emission gun (FEG) and an EDX detector. Samples were cut, mounted in resin at low temperature and low pressures in order to let the resin penetrate the oxide layer. Then, samples were polished through successive grades of SiC abrasive papers and finely polished to 1 µm with diamond paste. In order to avoid charge accumulation during SEM investigations, samples were covered with a thin layer of gold, deposited by sputtering.

Phase composition was investigated by X-ray diffraction (XRD), using a INEL diffractometer equipped with a Co Kα anticathode (λ = 1.78897 Å).

Results and discussion

Characterisation of coatings

The surface of the samples oxidized in conditions that promote the formation of cathodic MDs (current signal WAVE1, NH4F electrolyte), exhibits an extremely rough surface visible to the naked eye. The SEM top-view micrograph shown in figure 1 shows large pores spread in a foamy layer. Flakes are visible (fig. 1a) and the oxide even peels off in places (fig. 1b).

Cross section micrographs (fig. 2) show that substrate is strongly corroded. This might greatly contribute to the roughness of the sample. They also confirm the localized delamination of the coating. Unlike usual PEO layers, the oxides formed in NH4F electrolytes have a structure in strata (fig. 2c). Apparently the strata do not adhere either to the substrate or to each other.

The EDX spectrum of the synthesized coating (point 1 in fig. 2a) is presented in figure 3a. It shows intense peaks of magnesium, fluorine and oxygen due to the presence of MgO and MgF2 in the coating. This is supported by the X-Ray diffraction pattern that clearly indicates that the coating is exclusively composed of those phases (fig. 3b). A high peak of carbon is also detected.

It is attributed to the insertion of epoxy resin between strata during the encapsulation process.

Besides, EDX spectra made on magnesium substrate (point 2 in fig. 2a) show a carbon peak at least five times smaller than those measured on the coating (point 1 in fig. 2a).

Role of anodic and cathodic half-periods on coating growth and breakdown

The previous results establish that treatments in NH4F electrolyte with AC current degrade the layer properties drastically. The following study aims to determine whether those defects come from the electrolyte composition or from cathodic MDs. Thus, treatments have been made under unipolar (either cathodic or anodic) DC pulsed current (respectively WAVE2 and WAVE3).

Since under AC current, MDs appear only under cathodic biasing, it is relevant to investigate MDs under unipolar cathodic regime (WAVE2). However, and surprisingly, no MDs are observed (fig. 4). Furthermore, no oxides could be measured on the sample and no evidence of corrosion could be found. This result shows that the anodic half-period plays an important role on the generation of cathodic MDs.

Under anodic DC pulsed current (WAVE3), an oxide layer grows, though no discharges are observed (fig. 5). The oxide layer exhibits also a strata structure in these conditions (fig. 5b). The layer grows during anodic biasing and without any discharge assistance. Hence, the oxide certainly grows according to the following chemical reactions:

Mg 2+ + O 2-→ MgO Mg 2+ + 2 F -→ MgF2
The layer has a fine grain size or is even partly amorphous for the oxide growth does not need any heat transfer, unlike layers grown with MDs. XRD pattern shows very low diffraction peak intensities of layer components (MgO and MgF2) as compared to the substrate (fig. 3b). Note that the sample is only corroded under anodic biasing (fig. 5a). However, without MDs, no layer spalling occurs.

Breakdown mechanism of cathodic MDs

The physical mechanisms that lead to breakdown in liquids are complex and still under study [START_REF] Bruggeman | Characterization of a direct dc-excited discharge in water by optical emission spectroscopy[END_REF][START_REF] Bruggeman | Non-thermal plasmas in and in contact with liquids[END_REF][START_REF] Hamdan | Time-resolved imaging of nanosecond-pulsed micro-discharges in heptane[END_REF]. Nevertheless, the aforementioned results make it possible to propose a mechanism of cathodic breakdown. The sample is immersed in electrolyte (fig. 6a) and simultaneously corroded and oxidized (fig. 6b) under anodic biasing. Oxidation leads to the formation of a dielectric layer composed of magnesium oxide and fluoride (MgO and MgF2) (fig. 3b, fig. 4b). Under cathodic biasing, electric charges are accumulated on both sides of the dielectric layer (fig. 6c), which increases locally the electric field. When the electric field reaches a sufficient value, breakdown occurs (fig. 6d). Cathodic breakdown causes local spalling of the layer (fig. 1). This provokes the electrical contact between the metal electrode and the electrolyte. Consequently, a large part of the charges flows through large porosities caused by spalling and thus limits charge accumulation (fig. 6e). However, in some places, charge accumulation can be sufficient to reach the breakdown electric field and therefore to lead to breakdown, but to a lesser extent than previously (fig. 6f).

After 16 ±2 cycles of accumulation/breakdown [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF], charge accumulation is made impossible due to the increase in the number of shortcuts (fig. 6g) which quickly evacuate charges. Then, MDs eventually stop before the end of the cathodic period (fig. 1b in [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF]).

Cathodic micro-discharges in alkaline-silicate electrolytes

NH4F electrolytes offer adequate conditions to observe and study cathodic MDs. However, the aforementioned results show that those conditions are not fairly suitable for any industrial application due to poor layer properties. To grow thicker and denser layers on magnesium, alkaline-silicate electrolytes are often preferred [START_REF] Arrabal | Characterization of AC PEO coatings on magnesium alloys[END_REF][START_REF] Duan | Growth process of plasma electrolytic oxidation films formed on magnesium alloy AZ91D in silicate solution[END_REF][START_REF] Duan | Effect of electrolyte additives on performance of plasma electrolytic oxidation films formed on magnesium alloy AZ91D[END_REF][START_REF] Liang | Electrochemical corrosion behaviour of plasma electrolytic oxidation coatings on AM50 magnesium alloy formed in silicate and phosphate based electrolytes[END_REF]. In these conditions, many anodic MDs are ignited and form an oxide layer at high rate. Unexpectedly, cathodic MDs can also appear in alkaline-silicate electrolyte (fig. 7). The cathodic MDs that appear in alkaline-silicate electrolyte show an oscillating pseudo-periodic behaviour as it was observed in NH4F (inset fig. 7). However MDs appear during a shorter time (300-600µs) in alkaline-silicate than in NH4F electrolyte (1.7-2.1 ms) [START_REF] Nomine | The evidence of cathodic micro-discharges during plasma electrolytic oxidation process[END_REF].

Figure 8 shows the evolution of light emission in the WAVE4 regime. Thanks to this regime, we remark that if a cathodic half-period follows an anodic half-period, then cathodic MDs can be observed. On the other hand, no MDs are observed during the cathodic half-period if it is not preceded by an anodic alternation. The presence of a prior anodic half-period is the condition for the appearance of cathodic MDs, irrespective of the electrolyte composition.

The influence of cathodic half-period on anodic MDs

In the WAVE5 regime, cathodic MDs are observed during the cathodic half-period when generated (fig. 9a). If a cathodic half-period is generated, the anodic overall light emission increases slightly (from 2 to 6 a.u.) during the next anodic half-period. On the other hand, if no prior cathodic half-period is generated, the anodic light emission is more intense at the beginning of the anodic half-period and then decreases by a factor of 2. The size of MDs follows a similar trend, increasing from 0.15 to 0.25 mm 2 after a cathodic half-period; and decreasing from 0.3 to 0.15 mm 2 without cathodic half-period (fig. 9c). Furthermore, the number of MDs is not affected by the presence of prior cathodic MDs (fig. 9d). The lifetime of anodic MDs increases very slightly (from 75 to 150 µs) after a cathodic half-period, but it decreases otherwise from 200 to 100µs.

Conclusion

Layers grown in NH4F are composed of MgO and MgF2. Although MDs only appears during the cathodic half-period, these oxide layers grow during the anodic half-period. Moreover, an anodic half-period is necessary to observe MDs during the next cathodic half-period. However, NH4F electrolyte is not suitable in order to grow protective layers because of both corrosion of the substrate during anodic half-periods, and spalling of the layer by cathodic MDs.

On the other hand, cathodic half-period also influences the properties of anodic MDs. Without cathodic half-period, the formation of large and long MDs is promoted. These conditions are considered as responsible for higher defects concentration and roughness of the coatings [START_REF] Melhem | Changes induced by process parameters in oxide layers grown by the PEO process on Al alloys[END_REF].

Furthermore, cathodic half-period promotes shorter and smaller MDs, these conditions being favourable to get thicker and more homogeneous layers [START_REF] Martin | Effects of electrical parameters on plasma electrolytic oxidation of aluminium[END_REF].

A correct setting of electric parameters is then essential to optimize coating quality. If cathodic MDs must be avoided, the presence of a cathodic half-period is mandatory to form layers with good properties.

Acknowledgment

We greatly acknowledge the Conseil Régional de Lorraine for granting A. Nominé's PhD work under decision 11CP-769.

6.

Table captions

Table 1 Composition of EV31 alloy.

Table 2 Current waveforms used in the present work.

Figure captions

Figure 1 :

 1 Figure 1: Top-view secondary electron micrographs showing the surface of the layer grown in NH4F electrolytes after a 40 min treatment in the bipolar DC pulse (WAVE1) regime.

Figure 2 :

 2 Figure 2: Backscattered electron micrographs of cross sections of layers grown in NH4F electrolytes during 40 minutes in the bipolar DC pulse (WAVE1) regime, at different magnifications.

Figure 3 :

 3 Figure 3: EDX spectra (a) and XRD pattern (b) of a coating grown in NH4F electrolytes after 40 minutes.

Figure 4 :

 4 Figure 4: Chronogram of the current waveform and light emission in the negative DC pulse (WAVE2) regime.

Figure 5 :

 5 Figure 5: Chronogram of current waveform and light emission (a) and backscattered electron micrographs (b) obtained after a 15-minute treatment in the positive DC pulse (WAVE3) regime.

Figure 6 :

 6 Figure 6: Mechanism of cathodic breakdown.

Figure 7 :

 7 Figure 7: Evolution of light emission (a), voltage (b) and current (c) in the bipolar regime in alkaline-silicate electrolyte. Note that time and current parameters are slightly different from those of WAVE1.

Figure 8 :

 8 Figure 8: Evolution of light emission and current in the negative hybrid regime (WAVE4) in alkaline-silicate electrolyte.

Figure 9 :

 9 Figure 9: Evolution of current (a) light emission (b) size (c) number (d) and lifetime (e) of micro-discharges under positive hybrid current (WAVE5) regime.

Figure 1 :

 1 Figure 1: Top-view secondary electron micrographs showing the surface of the layer grown in NH4F electrolytes after a 40 min treatment in the bipolar DC pulse (WAVE1) regime.

Figure 2 :Figure 3 :

 23 Figure 2: Backscattered electron micrographs of cross sections of layers grown in NH4F electrolytes during 40 minutes in the bipolar DC pulse (WAVE1) regime, at different magnifications.

Figure 4 :

 4 Figure 4: Chronogram of the current waveform and light emission in the negative DC pulse (WAVE2) regime.

Figure 5 :

 5 Figure 5: Chronogram of current waveform and light emission (a) and backscattered electron micrographs (b) obtained after a 15-minute treatment in the positive DC pulse (WAVE3) regime.

Figure 6 :

 6 Figure 6: Mechanism of cathodic breakdown.

Figure 7 :Figure 8 :Figure 9 :

 789 Figure 7: Evolution of light emission (a), voltage (b) and current (c) in the bipolar regime in alkaline-silicate electrolyte. Note that time and current parameters are slightly different from those of WAVE1.

Table 1 :

 1 Composition of EV31 alloy.

	Element	Mg	Nd	Gd	Zn	Zr
	wt %	Balance	2.86	1.38	0.25	0.66

Table 2 :

 2 Current waveforms used in the present work.

		JA	JC	T1	T2	T3	T4	T
	Waveform	Schematic
		A/dm 2			ms
	WAVE1
	(bipolar
	DC pulse)