Mobile Aided System of Deep-Learning based Cataract Grading from Fundus Images

Keywords: Cataract, Deep learning, MobileNet-V2, Random forest, M-health. 1

The cataract is an ocular disease which requires early detection to avoid reaching a higher severity level. However, a worldwide deficiency of ophthalmologists and medical imaging devices is registered, which prevents early cataract detection. Our main objective is to propose a high performance method of cataract grading with a lower computational processing to be suitable for mobile devices. The main contribution consists in extracting features through a transfer-learned and fine-tuned MobileNet-V2 model, and deducing the cataract grade using a random forest classifier. The evaluation is conducted using a dataset of 590 fundus images, where 91.43% sensitivity, 89.58% specificity, 90.68% accuracy and 92.75% precision are achieved. In addition, the method implemented into a smartphone requires an average execution time of 1.41 second. The method implementation as an app into a smartphone associated to an optical lens for retina capturing, presents a mobile-aided-grading system that facilitates diagnosing the cataract disease.

Introduction

The cataract is an ocular disease where the eye lens, initially transparent, becomes cloudy due to protein accumulation [START_REF] Zhou | Automatic Cataract Classification Using Deep Neural Network With Discrete State Transition[END_REF][START_REF] Cao | Hierarchical method for cataract grading based on retinal images using improved Haar wavelet[END_REF]. This pathology is the main cause for half of the blind worldwide, where their number may achieve 40 million in 2025. It is always diagnosed using the ophthalmoscopy technique where the blurriness of the retina components is similar to the protein accumulation and hence to the cataract severity, where the mild, moderate and severe grade are respectively shown in Fig. 1. A higher difficulty has been noticed in recognizing cataract, despite that significantly affects the life quality by imposing activity limits. Therefore, it is highly recommended a periodical diagnosis to avoid achieving advanced stages [START_REF] Zhou | Automatic Cataract Classification Using Deep Neural Network With Discrete State Transition[END_REF][START_REF] Cao | Hierarchical method for cataract grading based on retinal images using improved Haar wavelet[END_REF][START_REF] Song | An Improved Semi-Supervised Learning Method on Cataract Fundus Image Classification[END_REF]. However, worldwide deficiencies of ophthalmologists and medical imaging devices are observed. Elsewhere, the cataract affects a population that exceeds 50 years old, having a limited mobility. Consequently, a delay of early cataract diagnosis is registered.

Actually, several lenses have been recently proposed which can be snapped onto mobile devices to ensure capturing fundus images [START_REF] Akil | Detection of retinal abnormalities using smartphone-captured fundus images: a survey[END_REF]. The provided fundus images are easily readable and have an acceptable quality with respect to the ones captured by classical ophthalmoscopy. For this purpose, our main idea is to suggest a novel method for cataract grading. The challenge is to perform reliable grading from fundus images using lower complexity processing to be suitable for mobile devices. For such need, we perform cataract grading through the MobileNet-V2 deep learning architecture associated to the random forest classifier. The implementation of the method into a smartphone as an app leads to a Mobile-Aided-Grading (MAG) system for the cataract disease. The paper is organized as follows. Section 2 describes the propounded method for cataract grading. The method evaluation is presented in section 3. The implementation of the MAG system is detailed in section 4, followed by a conclusion in section 5.

2

Novel method for cataract grading

2.1

Preprocessing & data augmentation

The fundus images are resized to (224×224×3) as required for MobileNet-V2. In addition, a cataract-affected fundus image appears with a blurred region with a different contrast than the retina background. Furthermore, handheld capturing with a smartphone leads to a light leakage, and so to a randomly increased contrast in image sections. To resolve this problem, we apply the Contrast Limited Adaptive Histogram Equalization (CLAHE) approach to enhance the fundus image contrast. Thereafter, a mask is applied to encompass the retina from its background. Elsewhere, we put forward data augmentation where the fundus images are rotated, zoomed, shifted and flipped in both vertical and horizontal direction [START_REF] Blaiech | Impact of Enhancement for Coronary Artery Segmentation Based on Deep Learning Neural Network[END_REF]. Both preprocessing and data augmentation are depicted in the black dotted squares of Fig. 2.

Fine tuning and transfer learning

The preprocessed image is provided to a MobileNet-V2 architecture to generate feature map. This architecture is a convolutional neural network, which is composed of 17 bottleneck residual blocks followed by a global average pooling layer. The limited size of images, as the case of cataract-affected fundus images, avoids converging the model weight, thus not achieving higher performance grading. For this purpose, we adopt the transfer learning method where a MobileNet-V2 model, trained with the "ImageNet" dataset containing 1000 categories, is used in our method [START_REF] Boudegga | Fast and efficient retinal blood vessel segmentation method based on deep learning network[END_REF]. The initial classification layer is replaced by a set of three layers. The first one consists in a fully connected dense layer with the ReLU function where the feature map size is reduced to 256. The second layer applies a dropout function to initiate the classification. The last one is a dense layer with the Softmax function which provides a vector of probability features, where the size is identified experimentally as mentioned in section 3.2. To enhance the weight convergence, we proceed to fine-tune the model, which allows updating its weights during training with a learning rate of 0.0001. In addition, the optimal weight with respect to accuracy is saved after each epoch, in order to accelerate the model convergence while avoiding overfitting [START_REF] Boudegga | Fast and efficient retinal blood vessel segmentation method based on deep learning network[END_REF]. Training is done into 150 epochs using the "Adam" optimizer and the "categorical-cross entropy" loss function. Classification for cataract grading with Random Forest

Our goal is to achieve a higher performant classification even with a reduced dataset size while having a lower complexity to be suitable for a mobile implementation. The classifier retrieves a feature vector from the deep learning model, which is composed of four probability values with respect to the four cataract grades. It is noticed that some grades have a higher dependency with specific features, while other grades correspond to a significant variation in a whole feature sub-set. To handle the feature correlation, the Random Forest (RF) is used to ensure the classification into cataract grading. It is considered as a set of decision trees where each one is formed by a feature subset, randomly selected [19]. The RF has two main parameters, which are the number of trees in the forest and the maximum depth of the trees. We perform an experimental study, as detailed in section 3.2, where the RF is employed with a varied depth to identify the one achieving better detection performances.

3

Experimental results

Dataset and evaluation metrics

Two public databases have recently uploaded in Kaggle which are the "Cataract Dataset" and "Ocular Disease Recognition (ODiR)" respectively containing 100 and 293 fundus images affected by different cataract stages. To guarantee a reliable evaluation, a dataset of 590 fundus images is build which are split into 220 non-cataract, 65 mild stage, 145 moderate stage and 160 severe stage fundus images. The images of each grade are randomly divided into five subsets where the three first ones are used for training, the fourth is dedicated for validation, while the last is used for testing. The experimental evaluation is conducted by referring to four metrics which are sensibility (Sens), the specificity (Spec), the accuracy (Acc) and the precision (Prec), respectively computed as indicated in equations (1-4).

Sens =

(1) ; Spec = (2) ; Acc = (3) ; Prec = (4)

where TP, TN, FP and FN are respectively True Positive, True Negative, False Positive and False Negative cataract-detected images.

3.2

Cataract grading performance A first experimentation is performed where the size of feature vector is varied. It was deduced that a vector of four feature allows achieving a better classification performance. In a second experimentation, we conduct an experimentation of four different evaluations, where the tree depth is varied from 1 to 4, which corresponds to the number of probability features taken into account. The maximal number of trees is fixed to 300 in order to guarantee achieving better feature combinations. The metrics for the four evaluations are illustrated in Table .1, where it is deduced that using a depth of 4 allows achieving the highest performances. Then, we evaluate our methods with respect to the existing ones by comparing the whole accuracy and sensitivity and specificity of each grade, where the values are shown in Table 2. We notice that our method achieves the highest accuracy and realizes better sensitivity performances in the first, third and fourth grades. Mobile-Aided-Grading System for Cataract Disease

The whole method is coded using the python language where MobileNet-V2 is implemented using the "Keras" API. The cloud service "google Colab" is employed for training and testing the deep learning model which contains 2,257,984 parameters, where 2,223,872 are updated through fine tuning. To run the MobileNet-V2 model into a smartphone, the "TFLiteConverter" class of the public "tf.lite" API is utilized to convert the trained "TensorFlow" model into a "TensorFlowLite" model. The whole method is coded with the JAVA language and implemented as an android app. To employ the model, the "TensorFlow Lite Task" library is implemented, which contains easy-to-use methods to create apps using "TensorFlowLite" model. Then, the "Tensor-Flow Lite Android Support" library is used, which allows managing input data and interpreting the provided output. Image processing and the RF classifier grading is performed using The "Open Source Computer Vision (OpenCV)" library which is compiled through Android Native Development Kit (NDK) [START_REF] Boukadida | Mobile-aided screening system for proliferative diabetic retinopathy[END_REF].

The whole method is run as an app into a "Samsung Galaxy A31" smartphone having an octa-core processor (2 x 2GHz & 6 x 1.95GHz) and 4 Go RAM. To evaluate the execution time, three fundus images are randomly selected from each grade, where the average execution time of the whole method is about 1.41 second.

Conclusion

We have suggested a novel method for cataract grading, where the MobileNet-V2 architecture has been used for feature extraction, while the RF classifier has been performed for grading. The experimental evaluation has proved that our proposed method can achieve higher performance grading with respect to recent related work. In addition, the lower complexity has allowed performing grading under two seconds when run on a smartphone. Those grading and computational performances have resulted a MAG system for the cataract disease, where its mobility and lower cost boost the early cataract diagnosis. In our future work, we aim to enhance the grading performance by extracting other features that reflect the cataract disease. Subsequently, an ensemble learning principle can be put forward to perform accurate grading. In addition, we will be interested in extending the mobile system to detect other ocular pathologies such as the diabetic retinopathy and the glaucoma.

Fig. 1 .

 1 Fig. 1. Retinal images of cataract grades. (a) Non-cataract. (b) Mild. (c) Moderate. (d) Severe This work was supported by the PHC-UTIQUE 19G1408 Research program.

Fig. 2 .

 2 Fig. 2. Processing flowchart of the proposed cataract grading method 2.3Classification for cataract grading with Random Forest

Table . 1

 . . Performance of cataract grading

	Arch.	MobileNet-V2		MobileNet-V2 & Random Forest
	Training pa-	Size of Feature vector		Tree depth
	rameters	4	8	12	1	2	3	4
	Sens (%)	87.50	85.94	83.08	93.22	92.19	91.18	91.43
	Spec (%)	77.78	74.07	75.47	78.57	79.63	86.00	89.58
	Acc (%)	83.05	80.51	79.66	86.09	86.44	88.98	90.68
	Prec (%)	82.35	79.71	80.60	82.09	84.29	89.86	92.75

Table . 2

 . . Cataract grading performance of related methods

	Methods of cataract grading	Non-cataract Sen Spec	Sen	Mild Spec	Moderate Sen Spec	Severe Sen Spec	Acc
	Yang et al. [4] (2016)	89.3	90.4	79.5	87.9	74.6	96.7	75.0	98.9	84.5
	Cao et al. [2] (2020)	93.53 95.44 82.17 93.83 73.27 94.55 89.66 97.37 85.98
	Song et al.[3] (2019)	--	--	--	--	--	--	--	--	88.6
	Zhou et al. [1] (2019)	--	--	--	--	--	--	--	--	89.23
	Our method	97.73 93.48 61.54 80.00 89.66 86.67 93.75 93.75 90.68
	4


Yaroub Elloumi

Nesrine Abroug

Mohamed Hedi Bedoui

End-to-End Mobile System for Diabetic Retinopathy Screening Based on Lightweight Deep Neural Network

Keywords: Diabetic retinopathy, Deep learning, Transfer Learning, Mobilehealth

Diabetic Retinopathy (DR) is the leading cause of visual impairment among working-aged adults. Screening and early diagnosis of DR is essential to avoid visual acuity reduction and blindness. However, a worldwide limited access to ophthalmologists may prevent an early diagnosis of this blinding condition. In this paper, we propose a novel method for screening DR from smartphone-captured fundus images. The main challenges are to perform higher accurate detection even with reduced quality of handheld captured fundus images and to provide the result into the smartphone used for acquisition. For such a need, we apply transfer learning to the lightweight deep neural network "NasnetMobile" which is used as a feature descriptor, while configuring a multilayer perceptron classifier to deduce the DR disease, in order to take benefit from their lower complexity. A dataset composed of 440 fundus images is structured, where the acquisition and statement are performed by expert ophthalmologists. A cross-validation process is conducted where 95.91% accuracy, 94.44% sensitivity, 96.92% specificity and 95.71% precision in average are achieved. In addition, the whole processing flowchart is implemented into a mobile device, where the execution time is under one second whatever the fundus image is. Those performances allow deploying the proposed system in a clinical context.

Introduction

Diabetic Retinopathy (DR) is an ocular disease registered for 30% of diabetes-affected patients [START_REF] Sabanayagam | Incidence and progression of diabetic retinopathy: a systematic review[END_REF]. Based on the world health organization report, 146 million suffer from DR [START_REF] Pan | Characteristics of Neovascularization in Early Stages of Proliferative Diabetic Retinopathy by Optical Coherence Tomography Angiography[END_REF]. Advanced stages of DR may lead to severe visual acuity impairment 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], with 37 million blind persons worldwide. Therefore, DR screening is mandatory for the early diagnosis and initiation of appropriate treatment to improve the visual outcome and to prevent blindness. Fundus examination is the main clinical approach to screen DR. Actually, a heavy workload is requested from ophthalmologists, where a ratio of 50 per million persons worldwide is required to ensure early screening and timely management of DR. However, only 21 countries have verified the targeted ratio, where the actual global ratio is about 29 ophthalmologists per million persons [START_REF] Resnikoff | Estimated number of ophthalmologists worldwide (International Council of Ophthalmology update): will we meet the needs[END_REF][START_REF] Singh | Innovative Diagnostic Tools for Ophthalmology in Low-Income Countries[END_REF]. Consequently, in many countries, there is a lack of periodical DR screening, hence an important delay of DR diagnosis.

Recently, several optical lens-based devices have been proposed, which can be snapped into smartphones to capture fundus images. Those devices are distinguished by their low-cost and mobility, which are associated to the smartphone availability in terms of connectivity, data storage and processing [START_REF] Panwar | Fundus Photography in the 21st Century--A Review of Recent Technological Advances and Their Implications for Worldwide Healthcare[END_REF][START_REF] Bolster | How the smartphone is driving the eye-health imaging revolution[END_REF][START_REF] Russo | Comparison of Smartphone Ophthalmoscopy with Slit-Lamp Biomicroscopy for Grading Vertical Cup-to-Disc Ratio[END_REF]. The mobile devices ensure capturing fundus images with sufficient quality compared to those captured by conventional fundus cameras. However, blurs and noise are always deduced caused by the handheld aspect of the mobile capturing. Several clinical studies have been performed and have shown similar DR detection accuracy from smartphone-captured fundus images and conventional fundus cameras-captured images [START_REF] Akil | Detection of retinal abnormalities using smartphone-captured fundus images: a survey[END_REF]Prassana, 2013;Monjur, 2019).

Previous studies have aimed to automatically screen DR from smartphone-captured fundus images (Hacisoftaoglu, 2020;[START_REF] Kashyap | Mobile phone based diabetic retinopathy detection system using ANN-DWT[END_REF][START_REF] Kalpiyapan | An Automatic System to Detect Exudates in Mobile-Phone Fundus Images for DR Pre-screening[END_REF]. Some work has addressed the problem of limited quality of fundus images, where the different limitations were highlighted in (Hacisoftaoglu, 2020). To outperform those problems, the methods have been based on intensive computational processing. In [START_REF] Mueller | Automated Detection of Diabetic Retinopathy from Smartphone Fundus Videos. Ophthalmic Medical Image Analysis[END_REF], DR detection was provided though a multiple instance for the AlexNet Deep Convolutional Neural Network (DCNN) architecture, while the method suggested in (Hacisoftaoglu, 2020) used the ResNet50 neural network as a feature descriptor. Such processing could not be run into embedded or smartphone devices, due to the limited material resources.

Other methods have aimed to run DR screening into smartphones where the main contribution was based on suggesting low complexity processing. In [START_REF] Boukadida | Mobile-aided screening system for proliferative diabetic retinopathy[END_REF]Elloumi, 2020), features were extracted though linear computational complexity, where the DR stages were detected using the SVM classifier. Elsewhere, lightweight DCNNs were employed such as mobilenet-V2 and inception-V3, respectively used in [START_REF] Suriyal | Mobile assisted diabetic retinopathy detection using deep neural network[END_REF][START_REF] Hagos | Transfer Learning based Detection of Diabetic Retinopathy from Small Dataset[END_REF][START_REF] Majumder | A deep learningbased smartphone app for real-time detection of five stages of Diabetic Retinopathy[END_REF]. However, these methods did not consider the decreased quality of smartphone-captured fundus images, where they were validated using database images acquired by classical conventional fundus cameras. Little work has addressed both challenges, hence failing to achieve higher performance, such as the one described in [START_REF] Kashyap | Mobile phone based diabetic retinopathy detection system using ANN-DWT[END_REF] where 62% precision was registered.

The originality of our work is to describe an automated method that (1) ensures higher performant DR screening from smartphone-based fundus photography and which (2) has a low complexity to be implemented into a smartphone associated with a mobile device. The whole hardware and software tool presents an end-to-end mobile system from fundus image acquisition to DR screening. For such a need, a preprocessing is performed to enhance the image quality. Then, the DCNN "Nasnet-Mobile" is used as a feature descriptor, which is characterized by its higher performance, lightweight processing and fast convergence even with a reduced database size. Then, the extracted features are provided to a Multi-Layer Perceptron (MLP) classifier with a single hidden layer, to deduce the DR disease. This work is a part of project leading to mobile computer-screening system for DR which we already developed in [START_REF] Akil | Detection of retinal abnormalities using smartphone-captured fundus images: a survey[END_REF], Elloumi, 2020;[START_REF] Boukadida | Mobile-aided screening system for proliferative diabetic retinopathy[END_REF].

The suggested method is introduced in the rest of the paper. Section 2 describes the automated method for DR screening. The experimental evaluation of the detection performance and the execution time is presented in section 3. The conclusion and some future work are detailed in section 4.

2.

Novel Method for DR Screening Thereafter, a data augmentation is applied in order to increase the dataset size and enhance the DL model robustness. For this purpose, all images are flipped and shifted horizontally and vertically, rotated with angle 30°, zoomed and contrast-adjusted with respect to the varied contrast of the smartphone-captured fundus images [START_REF] Blaiech | Impact of Enhancement for Coronary Artery Segmentation Based on Deep Learning Neural Network[END_REF][START_REF] Elloumi | Mobile Aided System of Deep-Learning Based Cataract Grading from Fundus Images[END_REF]. The Nas Network (NasNet) is a CNN architecture provided by the neural architecture search (Nas) framework [START_REF] Gupta | InstaCovNet-19: A deep learning classification model for the detection of COVID-19 patients using Chest X-ray[END_REF][START_REF] Cogan | MAPGI: Accurate identification of anatomical landmarks and diseased tissue in gastrointestinal tract using deep learning[END_REF]). It a research algorithm that designs an optimal convolutional architecture is for a given dataset, through a scalable method. The framework is based on a controller recurrent neural network (RNN) where networks are iteratively generated and trained using the provided dataset. Then , their accuracies are returned to the controller to enhance the next versions of architectures [START_REF] Cogan | MAPGI: Accurate identification of anatomical landmarks and diseased tissue in gastrointestinal tract using deep learning[END_REF][START_REF] Bahri | Remote Sensing Image Classification via Improved Cross-Entropy Loss and Transfer Learning Strategy Based on Deep Convolutional Neural Networks[END_REF]. The research leads to compose the network by convolutional layers called "normal cell" and "reduction cell" having identical structure with different weights. The first cell type generates a feature map preserving the same resolution than the input. the second one reduces the feature map size through a stride =2.

Using the "ImageNet" dataset that contains 1,000 categories [START_REF] Li | Automatic Detection of Diabetic Retinopathy in Retinal Fundus Photographs Based on Deep Learning Algorithm[END_REF], the Nas framework was provided an architecture where the selected cells are as modelled in Fig. 2. We note that Nas framework may provide a lightweight architecture called "NasNet-Mobile" made up of only four million parameters [START_REF] Bahri | Remote Sensing Image Classification via Improved Cross-Entropy Loss and Transfer Learning Strategy Based on Deep Convolutional Neural Networks[END_REF], which is able to perform an accurate classification [START_REF] Winoto | Small and Slim Deep Convolutional Neural Network for Mobile Device[END_REF].

Transfer Learning of Nasnet-Mobile Architecture

The available dataset is composed of few hundreds of smartphone-captured fundus images. To ensure reliable performance, the transfer learning method is endorsed [START_REF] Bouden | A Novel Deep Learning Model for COVID-19 Detection from Combined Heterogeneous X-ray and CT Chest Images[END_REF], where the NasNet-Mobile model, initially trained with the "ImageNet" dataset that contains 1,000 categories [START_REF] Li | Automatic Detection of Diabetic Retinopathy in Retinal Fundus Photographs Based on Deep Learning Algorithm[END_REF], is retrieved. The classification layer is interchanged by the four ones, as described in fig. 2. The first layer consists of an Average Pooling where the input feature map is spatially partitioned into a grid of square blocks with side 2, and average over each blocks are stored in the output feature map. Then, a flatten is performed to align all features into a single row. The third layer applies a dropout function to prevent overfitting, with a threshold equal to 0.7. The last one is a dense layer with a ReLU function where the feature vector size is reduced to 32, while decreasing the error through back-propagation.

The model is finetuned in order to update the weights of neurons during training, where the chosen learning rate is 0.000005 [START_REF] Li | Automatic Detection of Diabetic Retinopathy in Retinal Fundus Photographs Based on Deep Learning Algorithm[END_REF][START_REF] Mateen | Exudate Detection for Diabetic Retinopathy Using Pretrained Convolutional Neural Networks[END_REF]. The optimal weight is stored after each epoch, to guarantee converging the model. Training is performed into 150 epochs, and the weights are updated following the "Adam" optimizer [START_REF] Boudegga | Fast and efficient retinal blood vessel segmentation method based on deep learning network[END_REF]. The "categorical-cross entropy" loss function is adopted, where the loss is based on the sum of all computed ratios. The main hyper parameters used for training are summarized in Table 1.

MLP Configuration

The classifier must retrieve a feature map from the NasNet-Mobile deep learning model in order to ensure a performant classification, through low-complexity processing. Based on those constraints, the MLP classifier is chosen to ensure the classification of DR-affected fundus images. It is considered as a neural network where the weights are randomly predefined. Indeed, it is widely employed in medical classification problems. The MLP can be configured in terms of number of hidden layers and number of neurons inside. We choose a single hidden layer to reduce the computational complexity. After that, we perform an experimental study where the neuron number is varied. Then, training and testing processes are iteratively performed to evaluate the current MLP, as detailed in Table 2. Based on the experiment results, we deduce that a hidden layer with 10 neurons will allow achieving the best classification result.

Experimental Results

dataset

Patients' data were collected in the department of ophthalmology belonging to Fattouma Bourguiba University Hospital (Tunisia), between 2019-2020. Image acquisition was performed after preliminary eye examination and dilating pupil of patient eyes using mydriatic substance. Fundus images were captured using a Volk-InView dispositive, as shown in Fig. 3, allowing a field of view of 50°. Several clinical studies have attested the higher quality of fundus images captured by Volk-InView, compared to other optical lenses such as D-Eye, Retina Peek and Welch Allyn (Karakaya, 2020). All anonymized captured images were evaluated by two independent masked retina specialists (NA and IK). Screening the DR lesions of retinal photographs using the "International Clinical Diabetic Retinopathy Classification Severity Score" was performed, where images were graded as non DR and DR.

The dispositive was snapped into an "Ipod Touch" device where the camera resolution was about 8 Mp. The dataset was composed of 440 images, where 260 were classified as healthy and 180 contained DR lesions. The image resolution was 892*892 pixels with 96 dpi, where some healthy and DR affected captured retina are shown in Table 3. It is easy to distinguish retinal components, such as the optic disk, the macula and DR lesions, even those having small sizes. The evaluation is performed through a five-fold cross validation approach to guarantee a reliable evaluation, where the dataset is partitioned into 5 subsets. To overcome the problem of the reduced dataset size, four subsets representing 80% of fundus images are dedicated for training. The fifth subset is partitioned equitably between validation and testing sub-sets, as illustrated in Fig. 3.

ML Implementation

The method is coded using the Python language. Preprocessing is performed using the OpenCV library, while NasNet-Mobile and MLP are implemented using the "Keras" API. The training and testing steps are executed on the cloud service "google Colab". The curve slopes of accuracy and loss for both training and validation are retrieved as depicted in Fig. 4. It is deduced that both accuracy (resp. loss) curves increase (resp. decrease) progressively to become almost constant.

Evaluation Metrics

The performance of our method is evaluated through the Accuracy (Acc), Sensitivity (Sens), Specificity (Spec) and Precision (Prec) metrics, which are computed as indicated in equations 3, 4, 5 and 6.

Sensitivity

Performance Evaluation of Proposed Method

This method is evaluated using all cross-datasets, where the performance metrics of each one are shown in Table 4. We deduce that our method carries out higher accuracy, which achieves 97.73%. Even with an equitable partition between healthy and DR-affected images, sensitivity and specificity have higher values whatever the cross dataset is. The performances of cross-validation sets are illustrated through the box plots represented in Fig. 5. The reduced plot sizes justify the sustainability of the DR screening whatever the image set, either used for testing or for training. Consequently, it reflects the method robustness and confirms its capacity to be used as a mobile aided screening system for DR. The trained Nasnet-Mobile model associated to the MLP classifier must be updated to be suitable for smartphone uses. Therefore, the method is implemented as an android app through an Android Studio 4.2 and JAVA Development Kit (JDK) 15.0.2. Therefore, the "TFLiteConverter" class of the public "tf.lite" API is used to convert the trained "TensorFlow" model into a "TensorFlowLite" model. The NasNet-Mobile is converted into a FlatBuffer file (.tflite) and stored into a "TensorFlowLite" model to be called through the "TensorFlow Lite Android Support" library. The MLP classifier and the image enhancement processing are implemented using the predefined function of the "Open Source Computer Vision (OpenCV)" multiplatform library which is compiled by an Android Native Development Kit (NDK). Thereafter, we evaluate the computational performance of DR screening when run in a mobile device as an app. For such a need, 10 images (partitioned equitably on healthy and DR-affected fundus images) are randomly selected from the dataset and tested through the app executed into a "Samsung Galaxy A31" smartphone having an octacore processor (2 x 2GHz & 6 x 1.95GHz) and 4 Go RAM. We deduce that all execution time is above one second, as depicted in Fig. 6. In addition, close values are registered where the average value is equal to 0.894 second. Accordingly, we deduce that the computational performance is adequate to promote using our system in clinical contexts.

Conclusion

DR is a major cause of blindness worldwide. Our challenge consists in screening DR using a mobile CAD system, while ensuring all tasks from the fundus image acquisition to the decision generation. For such a requirement, we have proposed a preprocessing to enhance the image quality. Then, we have employed a lightweight DL architecture and a low complexity classifier to carry out higher performant DR screening. The experimentation has been proved respecting the clinical constraints in terms of screening performance and execution time.

In our future work, we aim to extend the dataset size by continuous collaboration with the expert ophthalmologist team. Afterwards, the provided system will be extended to ensure fundus image grading into DR severity. Otherwise, the system will be oriented to other ocular pathologies such as glaucoma, aged macular degeneration or hypertensive retinopathy. Furthermore, the lightweight processing principle can be carried out into other mobile-health domains [START_REF] Khessiba | Innovative deep learning models for EEG-based vigilance detection[END_REF].

  2.1. Pre-processing and Data processingBasically, the dataset images must be resized to (224×224×3) to be provided to the NasNet-Mobile. Preprocessing aims to enhance the fundus image quality in order to promote DR screening. In fact, the handheld capture of fundus images leads to a blurred illustration of retinal components, especially the DR lesions characterized by a small size such as micro-aneurysms or hard exudates. Thus, the point spread function is applied to clearly model the retina[START_REF] Boukadida | Mobile-aided screening system for proliferative diabetic retinopathy[END_REF], as shown in fig.1(b). The variability on the light source causes a non-balanced contrast of the smartphone-captured fundus images. To resolve this problem, the Contrast Limited Adaptive Histogram Equalization (CLAHE) approach[START_REF] Chalakkal | Automatic segmentation of retinal vasculature[END_REF] is applied, as illustrated in fig.1(c).

Figure 1 :

 1 Figure 1: Fundus images: (a) captured with Volk-inView, (b) after deblurring, (c) after contrast enhancement

Figure 2 :

 2 Figure 2: Processing flowchart of the proposed DR screening method

Figure 3 :

 3 Figure 3: Dispatching of subsets for 5-fold cross validation

Figure 4 :

 4 Figure 4: Evaluation of training performance in terms of epochs: (a) Training and validation accuracy values; (b) Training and validation loss values

  Positive) is the number of images classified correctly as DR-affected, TN (True Negative) is the number of images classified correctly as healthy, FP (False Positive) is the number of healthy images identified as DR, and FN (False Negative) is the number of DR-affected images classified as healthy.

Figure 5 :

 5 Figure 5: Performance visualization using box plots

Figure. 6 :

 6 Figure. 6: Execution time of DR screening application in terms of fundus images

Table 1 :

 1 Hyper parameters of training NasNet-Mobile model

	Parameter	Value
	Optimizer	Adam optimizer
	Learning rate	0.000005
	Regularization	Dropout (0.7)
	Mini-batch size	2
	Epoch	200
	Loss function	Binary cross-entropy

Table 2 :

 2 performance classification in terms of neuron number of hidden layer

	neuron number of hidden layer	8	10	12
	Sens	88.57	94.44	94.29
	Spec	91.67	96.15	85.42
	Acc	89.83	95.4.45	90.68
	Prec	93.94	94.44	90.41

Table 4 :

 4 DR screening performances in terms of cross-datasets

		Acc (%) Sens (%) Spec (%) Prec (%)
	First cross-database	97.73	94.44	100.00	100.00
	Second cross-database	93.18	88.89	96.15	94.12
	Third cross-database	95.45	94.44	96.15	94.44
	Fourth cross-database	97.73	94.44	100.00	100.00
	Fifth cross-database	95.45	100.00	92.31	90.00


Yasmine Mrad

Yaroub Elloumi

Mohamed Akil

Mohamed Hédi Bedoui

A Fast and Accurate Method for Glaucoma Screening from Smartphone-Captured Fundus Images

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A fast and accurate method for glaucoma screening from smartphonecaptured fundus images Yasmine Mrad a , Yaroub Elloumi a,b,c , Mohamed Akil b , Mohamed Hedi Bedoui a a Medical Technology and Image Processing Laboratory, Faculty of medicine, University of Monastir, Tunisia. The glaucoma is an eye disease that causes blindness when it progresses in an advanced stage. Early glaucoma diagnosis is essential to prevent the vision loss. However, early detection is not covered due to the lack of ophthalmologists and the limited accessibility to retinal image capture devices.

In this paper, we present an automated method for glaucoma screening dedicated for Smartphone Captured Fundus Images (SCFIs). The implementation of the method into a smartphone associated to an optical lens for retina capturing leads to a mobile aided screening system for glaucoma. The challenge consists in insuring higher performance detection despite the moderate quality of SCFIs, with a reduced execution time to be adequate for the clinical use.

The main idea consists in deducing glaucoma based on the vessel displacement inside the Optic Disk (OD), where the vessel tree remains sufficiently modeled on SCFIs. Within this objective, our major contribution consists in: [START_REF] Maheshwari | Automated Diagnosis of Glaucoma Using Empirical Wavelet Transform and Correntropy Features Extracted From Fundus Images[END_REF] segmenting retinal vessels inside the OD, (2) locating centroid points that adequately model the vessel distribution, (3) identifying features that relevantly reflect the vessel displacement, and (4) providing the feature set to a classifier in order to deduce the glaucoma disease. Furthermore, all processing steps are carefully chosen based on lower complexity, to be suitable for fast clinical screening.

A first evaluation of our method is performed using the two public DRISHTI-DB and DRIONS-DB databases, where 99% and 95% accuracy, 96.77% and 95.12% sensitivity and 100% and 94.73% specificity are respectively achieved. Thereafter, the method is evaluated using two fundus image databases respectively captured through a smartphone and retinograph for the same persons. We achieve 100% accuracy using both databases which assesses the robustness of our method. In addition, the detection is performed on 0.155±0.035 second when executed on a smartphone device. Our proposed smartphone app provides a cost-effective and widely accessible mobile platform for early screening of glaucoma in remote clinics or areas with limited access to fundus cameras and ophthalmologists.

Introduction

Glaucoma damages the Optic Nerve Head (ONH) due to elevated or inappropriate intraocular pressure in the eye. It is estimated that patients suffering from glaucoma will have reached 76 million by the end of 2020 and 111.8 million by 2040 [START_REF] Maheshwari | Automated Diagnosis of Glaucoma Using Empirical Wavelet Transform and Correntropy Features Extracted From Fundus Images[END_REF]. Glaucoma gradually and asymptomatically causes the loss of the visual field [START_REF] Hagiwara | Computer-aided diagnosis of glaucoma using fundus images: A review[END_REF]. It is often referred as a "silent thief of sight" which is noticed only when the disease progresses to a significant loss of peripheral vision. Therefore, the early diagnosis of glaucoma is essential to stop or slow the progression of the disease and to prevent blindness. Indeed, a delay is recorded in the glaucoma diagnosis due to several causes which are: (1) the lower ratio of ophthalmologists per population; (2) the high cost of glaucoma therapies which achieve 2,511$ and 803 € for advanced disease, respectively in United States and Europe [START_REF] Poemen | US Ophthalmic Review[END_REF]; and (3) the higher cost of the available clinical devices for retinal image capturing.

To facilitate access to early diagnosis, several studies have proposed automatic methods for glaucoma screening, which differ with respect to the glaucoma properties addressed for detection. Several methods such as the ones suggested in [START_REF] Soorya | An automated and robust image processing algorithm for glaucoma diagnosis from fundus images using novel blood vessel tracking and bend point detection[END_REF][START_REF] Cheng | Sparse Dissimilarity-Constrained Coding for Glaucoma Screening[END_REF][START_REF] Cheng | Superpixel Classification Based Optic Disc and Optic Cup Segmentation for Glaucoma Screening[END_REF][START_REF] Yin | Automated Segmentation of Optic Disc and Optic Cup in Fundus Images for Glaucoma Diagnosis[END_REF][START_REF] Khalil | Improved automated detection of glaucoma from fundus image using hybrid structural and textural features[END_REF][START_REF] Bock | Glaucoma risk index:Automated glaucoma detection from color fundus images[END_REF][START_REF] Krishnan | Automated glaucoma detection using hybrid feature extraction in retinal fundus images[END_REF][START_REF] Zilly | Glaucoma detection using entropy sampling and ensemble learning for automatic optic cup and disc segmentation[END_REF][START_REF] Joshi | Optic Disk and Cup Segmentation From Monocular Color Retinal Images for Glaucoma Assessment[END_REF][START_REF] Abdullah | Localization and segmentation of optic disc in retinal images using circular Hough transform and grow-cut algorithm[END_REF][START_REF] Al-Bander | Dense Fully Convolutional Segmentation of the Optic Disc and Cup in Colour Fundus for Glaucoma Diagnosis[END_REF][START_REF] Balakrishnan | An automatic segmentation of optic disc and cup region from medical images for glaucoma detection[END_REF] segmented the Optic Disk (OD) and the Optic Cup (OC) in order to deduce the Cup-to-Disc Ratio (CDR). Moreover, the segmented OD and OC were allowed to extract the Neuro-Retinal Rim (NRR) shape where glaucoma could be identified based on the ISNT rule [START_REF] Sarhan | Glaucoma detection using image processing techniques: A literature review[END_REF]. Other methods have extracted the parapapillary atrophy which had an elliptical shape with the OD boundary having an intermediate intensity between the retina and the OD [START_REF] Muramatsu | Automated segmentation of optic disc region on retinal fundus photographs: Comparison ofcontour modeling and pixel classification methods[END_REF][START_REF] Tan | Automatic detection of pathological myopia using variational level set[END_REF]. The related work of ONH location and OD/OC extraction were explicitly detailed in the review proposed by [START_REF] Haleem | Automatic extraction of retinal features from colour retinal images for glaucoma diagnosis: a review[END_REF]. The blood vessels have been addressed in some work to screen glaucoma [START_REF] Fuente-Arriaga | Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images[END_REF][START_REF] Nayak | Automated diagnosis of glaucoma using digital fundus images[END_REF]. A strong correlation has been deduced between shape, location and density of vessels and the deterioration of the glaucomatous ONH, as studied in the survey put forward by Serhan et al. [START_REF] Sarhan | Glaucoma detection using image processing techniques: A literature review[END_REF]. Indeed, some other methods have been based on detecting the Retinal Nerve Fiber Layer (RNFL) deterioration [START_REF] Lamani | Early detection of glaucoma through retinal nerve fiber layer analysis using fractal dimension and texture feature[END_REF][START_REF] Panda | Automated retinal nerve fiber layer defect detection using fundus imaging in glaucoma[END_REF] which has been always deduced through vessel tree displacement outside the OD.

Those methods were dedicated for conventional retinography fundus images, which were characterized by a sharpness quality, as shown Fig. 1(a). Accordingly, a high accurate segmentation of retinal components was ensured, and hence achieving efficient glaucoma screening. However, the capturing process required the presence of an ophthalmologist and the use of expensive conventional retinography devices.

Furthermore, these detection methods used standard equipment that required the mobility of patients. As a result, these proposed methods did not address the problems leading to the delayed diagnosis of glaucoma. Moreover, few methods were addressed to reduce the execution time [START_REF] Elloumi | Ocular diseases diagnosis in fundus images using a deep learning: approaches, tools and performance evaluation[END_REF][START_REF] Sarhan | Glaucoma detection using image processing techniques: A literature review[END_REF], which presented a clinical constraint for employing the proposed methods.

Actually, several mobile devices for fundus image capturing have been suggested such as D-eye and iExaminer, which allow using smartphones in eye disease screening, taking advantage from their mobility, low-cost and high capabilities in terms of processing and storage [START_REF] Mercado | Clinical Application of a Smartphone-Based Ophthalmic Camera Adapter in Under-Resourced Settings in Nepal[END_REF][START_REF] Sharma | Emerging Simplified Retinal Imaging[END_REF][START_REF] Akil | Detection of retinal abnormalities using smartphonecaptured fundus images: a survey[END_REF]. It has been deduced that Smartphone Captured Fundus Images (SCFIs) have an acceptable quality compared to the images captured by ophthalmoscopes, where both fundus images, in Fig. 1, are captured from the same eye using respectively a retinograph and an optical lens-associated smartphone. In [START_REF] Dickson | Comparison Study of Funduscopic Exam of Pediatric Patients Using the D-EYE Method and Conventional Indirect Ophthalmoscopic Methods[END_REF], the D-eye showed considerable accuracy of CDR measurements compared to direct ophthalmoscopy. In addition, the D-eye gadget offered high performance for manually detecting fundus abnormalities compared to indirect ophthalmoscopy, with specificity of 0.97 and 0.98 for detecting the eye abnormalities and measuring the optic nerve size. Therefore, our main objective is to provide a Mobile Aided Screening (MAS) system for glaucoma. The challenges consist in ensuring higher accuracy detection and robustness with respect to the moderate quality of SCFIs, through a reduced execution time.

Indeed, the moderate quality of SCFIs involves a blurred and noised illustration of retinal components, as illustrated in Fig. 1(b). Thus, the existing methods have fail to achieve accurate retinal component segmentation, and so an efficient glaucoma detection. Moreover, limited processing capacities of smartphones bring to expand the screening execution time, which is inadequate with respect to the clinical context. To avoid those problems, some work has been interested into proposing a mobile MAS system for glaucoma to achieve higher performance detection with lower processing complexity. The work proposed by [START_REF] Thomas | The effectiveness of teleglaucoma versus in-patient examination for glaucoma screening: a systematic review and meta-analysis[END_REF] was indicated that the tele-glaucoma technology demonstrated moderate agreement on its ability to diagnose glaucoma and achieved 79% of specificity and 83% of sensitivity. The work described in [START_REF] Guo | A Mobile App Using the Measurement of Clinical Parameters for Glaucoma Screening[END_REF] suggested a mobile application for glaucoma screening. The glaucoma detection was based on the CDR and the NRR thinning. Detection was ensured with accuracy of 0.7625 in 9.16 seconds, which was surpassed by several existing methods whether for efficiency or execution time. Recently, Martins and al [START_REF] Martins | Offline computer-aided diagnosis for Glaucoma detection using fundus images targeted at mobile devices[END_REF] has propounded a method for diagnosing glaucoma dedicated for smartphone devices. Accuracy of 0.87, sensitivity of 0.85 and AUC of 0.93 were achieved under two seconds for retinograph-captured fundus images. However, the detection principle of all methods put forward in [START_REF] Thomas | The effectiveness of teleglaucoma versus in-patient examination for glaucoma screening: a systematic review and meta-analysis[END_REF][START_REF] Guo | A Mobile App Using the Measurement of Clinical Parameters for Glaucoma Screening[END_REF][START_REF] Martins | Offline computer-aided diagnosis for Glaucoma detection using fundus images targeted at mobile devices[END_REF] was fully based on extracting the OD and the OC, where the segmentation performance might degrade in case of SCFIs. Indeed, no evaluation was performed using SCFIs or even with classical fundus images after data augmentation.

For this purpose, the objective of this work is to propose a novel method for glaucoma detection dedicated for SCFIs. The rest of the paper is expended to present the suggested method. The second section describes the automated method for glaucoma detection. The experimental evaluation of the

Fast and accurate method for glaucoma screening 2.1. Principle

Our challenges consist in proposing an accurate and robust method even with a moderate image quality. Furthermore, all processing steps are carefully chosen based on lower complexity, to be suitable for mobile implementation. At first, glaucoma damages the optic nerve where the main morphological changes occur inside the ONH. Indeed, glaucoma screening from the ONH brings to higher performance detection and low complexity processing [START_REF] Soorya | An automated and robust image processing algorithm for glaucoma diagnosis from fundus images using novel blood vessel tracking and bend point detection[END_REF][START_REF] Cheng | Sparse Dissimilarity-Constrained Coding for Glaucoma Screening[END_REF][START_REF] Cheng | Superpixel Classification Based Optic Disc and Optic Cup Segmentation for Glaucoma Screening[END_REF][START_REF] Yin | Automated Segmentation of Optic Disc and Optic Cup in Fundus Images for Glaucoma Diagnosis[END_REF] in contrast to the methods exploring the whole retina, as synthetized in the comparative study performed in [START_REF] Sarhan | Glaucoma detection using image processing techniques: A literature review[END_REF]. Moreover, SCFIs are characterized by a reduced filed of view against the classical fundus images, hence avoiding presenting the papillary atrophy located outside the ONH. Therefore, the first step of our method consists in locating the OD, as detailed in section 2.2.

Thereafter, we study the impact of glaucoma on the retinal components in order to identify the adequate ones for screening, taking into account the moderate quality of SCFIs. A healthy optic nerve corresponds to a tiny excavation. However, glaucoma damages the optic nerve fibers, thus expanding the excavation, as it can be deduced when comparing Fig. 2(a) and Fig. 2(c). Similarly, the OC appears with a reduced size in a healthy fundus image. For a glaucoma-affected one, the excavation growth leads to increase the OC size, while the OD size remains stationary, as respectively distinguished from the fundus images in Fig. 2(b) and Fig. 2(d). Elsewhere, the excavation growth does not occur similarly in all directions where the glaucoma leads to destroy the ISNT rule. With respect to this indication, several methods have segmented the OD and the OC to deduce whether the CDR or shape of the NRR to detect glaucoma.

In a healthy retina, vessels spread from the middle of the excavation, as shown in Fig. 2(a). The vessels propagate beyond the large NRR, which appear with an equitable distribution in the OD, as modeled in Fig. 2(b). Otherwise, the rise in the optic nerve fiber damage leads to join the vessel to the internal border of the excavation, as we can see in Fig. 2(c). The perpendicular visual field to the retina leads to model vessels as shifted to the OD border, as depicted in Fig. 2(d). Accordingly, the optic nerve fiber damage similarly affects the OC size and the vessel distribution, where both are able to reflect glaucoma severity. In the same vein, several methods have identified the glaucoma through segmenting and locating retinal vessels.

SCFIs are always blurred and noised due to the handheld aspect, which have a moderate quality with respect to classical images. Degradation principally affects the contrast of retinal components with respect to their neighborhood. However, the OD and the OC have close intensity and blurred borders, which leads to alter at once the OD and OC segmentation. By applying their ratio, such drop in performance considerably fakes glaucoma screening. In contrast, the vessel tree remains sufficiently represented in the OD. The vessel distribution is obviously distinguishable, despite the moderate quality.

For this purpose, the main idea of our method consists in screening glaucoma from SCFIs based on blood vessels. To guarantee the method robustness, our approach will be based on evaluating the distribution of the whole vessel tree rather than based on each vessel separately. Therefore, the vessel tree is segmented and partitioned into quadrants with respect to the ISNT notion, as described respectively in sections 2.3 and 2.4. Then, a position marker of vessel distribution on each quadrant is located, which called centroid. After that, a feature set is extracted and provided to a classifier to deduce glaucoma, as summarized in the method flowchart in Fig. 3.

OD extraction and enhancement

The method proposed in [START_REF] Pourreza-Shahri | Computationally efficient optic nerve head detection in retinal fundus images[END_REF] ensured locating the ONH based on circularity and intensity through applying the radon transform. The method achieved higher accurate performance among the existing methods [START_REF] Haleem | Automatic extraction of retinal features from colour retinal images for glaucoma diagnosis: a review[END_REF][START_REF] Akil | Computational efficiency of optic disk detection on fundus image: a survey[END_REF], where 100% accuracy was performed to locate the ONH in the public DRIVE database. We note that this method can be configured to locate a sub-image having the same OD size. Afterwards, this method was extended to provide a mobile computer aided system for ONH detection [START_REF] Elloumi | Mobile computer aided system for optic nerve head detection[END_REF]. Processing was optimized to reduce complexity, where the same detection accuracy was performed a in reduced time when executed in a smartphone device. Therefore, the method suggested in [START_REF] Elloumi | Mobile computer aided system for optic nerve head detection[END_REF] would be implemented, which extracted the OD sub-images.

In addition, glaucoma screening requires detecting overlapped retinal components. However, SCFIs are characterized by a non-balanced contrast, which result in failed detection. Consequently, the second step leads to enhance the sub-image contrast with respect to the blood vessels. We proceed to extract the green channel which reveals a better contrast between the retinal structures. Next, the CLAHE algorithm is applied to ensure a better contrast equalization into the ONH region, where the results of each step are illustrated in Fig. 4.

2.3.

Vessel segmentation and splitting we proceed to segment the vessel tree into the located OD. The first step consists in inversing the OD brightness in order to model the blood vessel with higher intensity. Within this objective, the "black-hat" morphological operator is applied where the result is depicted in Fig. 5(b). Then, the Otsu technique is applied to distinguish vessel from the OD background [START_REF] Muramatsu | Automated segmentation of optic disc region on retinal fundus photographs[END_REF]. Finally, the "Medianblur" filter is used to reduce noise, which can be caused by small blood lesions [START_REF] Zhu | An Improved Median Filtering Algorithm for Image Noise Reduction[END_REF], as shown in Fig. 5(c).

The vessel tree displacement caused by glaucoma is developed mainly in superior, inferior and nasal quadrants, where the temporal quadrant contains less vessels than the other ones [START_REF] Fuente-Arriaga | Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images[END_REF][START_REF] Issac | An Adaptive Threshold Based Image Processing Technique for Improved Glaucoma Detection & Classification[END_REF]. Thereby, vessels should be partitioned on their quadrants to deduce the glaucoma displacement. Within this objective, we proceed to split the segmented vessels into four quadrants through superimposing four different masks, illustrated in Fig. 6(a)-Fig. 6(d), to the OD where the results are respectively depicted in Fig. 6(e)-Fig. 6(h).

Centroid location

It is essential to define a parameter that can reflect vessel displacement into quadrants. Our main idea consists in computing a centroid reference point for vessels belonging to the same quadrant. Then, glaucoma is deduced based on the centroid remoteness. We note that the vessel centroid is figured out in terms of all positions of vessel pixels. Hence, a blurred vessel tree has a marginal impact when extracting centroid position.

The method put forward by [START_REF] Fuente-Arriaga | Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images[END_REF] first identified elementary centroid of each pixel cluster. Then, clusters are fused and their centroids are updated until grouping all clusters having a single centroid. In order to reduce processing complexity, we propose a novel approach to locate the centroids. First, for the vessel pixels of each quadrant, the sum of their horizontal coordinate 𝑄 and vertical coordinate 𝑄 are computed, as indicated respectively in equations 2 and 3. The centroid horizontal coordinate 𝐶 (resp. vertical coordinate 𝐶 ) corresponds to the ratio between 𝑄 (resp. 𝑄 ) and the number of vessel pixels 𝑁 , as indicated in equations 4 (resp. in equation 5).

Feature extraction

Neuro-retinal rim thinning

In a healthy fundus image, the rim has a large board through the OD. The glaucoma involves increasing the OC and hence reducing the NRR. This criterion remains very helpful for clinical staff to diagnose glaucoma [START_REF] Haleem | Automatic extraction of retinal features from colour retinal images for glaucoma diagnosis: a review[END_REF]. Within this context, the method described in [START_REF] Akram | Glaucoma detection using novel optic disc localization, hybrid feature set and classification techniques[END_REF] computed the rim-to-disc ratio in order to deduce glaucoma. In [START_REF] Issac | An Adaptive Threshold Based Image Processing Technique for Improved Glaucoma Detection & Classification[END_REF], the rim area of each quadrant is figured out in order to compute a ratio that reflects glaucoma.

In fact, a significant correlation is distinguished between the blood vessel distribution into quadrants and the NRR lost [START_REF] Radcliffe | Retinal Blood Vessel Positional Shifts and Glaucoma Progression[END_REF]. In a healthy fundus image, the reduced size of excavation leads to merging blood vessels to the OD center. Consequently, centroids appear as clustered in the OD middle region. The excavation growth caused by glaucoma shifts blood vessels away from the OD center until getting closer to the OD borders [START_REF] Fuente-Arriaga | Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images[END_REF][START_REF] Nayak | Automated diagnosis of glaucoma using digital fundus images[END_REF], such as the difference between fundus images in Fig. 2(b) and Fig. 2(d). With respect to the excavation growth, the centroid positions become spaced.

Subsequently, we aim to provide features that reflect the centroid remoteness. Since the four zones are affected on both extremities of the perpendicular axis, we quantify the centroid remoteness through Euclidian distances between each neighbor centroid. The temporal centroid escapes to a similar shifting since it contains less vessels. Therefore, we choose to overpass the temporal quadrant in order to guarantee higher accuracy detection. Accordingly, we consider two features which correspond to the distances between superior-nasal and inferiornasal centroids, as illustrated with red arrows in Fig. 7, where the distances in the healthy OD in Fig. 7(a) appear clearly smaller than the ones in the glaucoma-affected OD in Fig. 7(b).

Vessel displacement in relation to the ISNT rule

In a healthy OD, the inferior quadrant contains the thickest rim, followed by the superior, nasal and temporal quadrants, as known as the ISNT rule [START_REF] Jonas | Pattern of Glaucomatous Neuroretinal Rim Loss[END_REF]. Similarly, inferior and superior quadrants include the wide portion of the vessel tree [START_REF] Issac | An Adaptive Threshold Based Image Processing Technique for Improved Glaucoma Detection & Classification[END_REF]. For a glaucoma-affected fundus image, the optic nerve excavation growth leads to expand the OC. The rim thinning does not occur similarly in all directions where rim thicknesses into quadrants changes differently. The glaucoma involves violating the ISNT rule where the excavation expands principally in the inferior and superior quadrants. As a result, the thinning leads to shift the blood vessels from inferior and superior regions towards the nasal region [START_REF] Issac | An Adaptive Threshold Based Image Processing Technique for Improved Glaucoma Detection & Classification[END_REF]. Consequently, the centroids of inferior and superior quadrants remain closed to the OD border.

In contrast, the added vessels to the nasal quadrant arise from inferior, superior and temporal neighborhood quadrants. The shifted vessels significantly affect the distribution of vessel density, and so the nasal centroid location. Hence, even with a thinned rim, the nasal centroid is not always relocated to be near of OD border. Similarly, the reduced vessel density in a temporal quadrant and the vessel displacement in the direction of the OD center do not allow modeling the temporal centroid displacement in terms of glaucoma. Accordingly, we extract two features that reflect the ISNT, which correspond to two Euclidian distances between inferior and superior centroids and their corresponding borders, as indicated with blue arrows in both images of Fig. 7.

Classifier

The Support Vector Machine (SVM) classifier is a supervised learning method, used in classification and regression problems. It attempts to fit a hyperplane through the feature space in order to discriminate between classes provided as growntruth data on the training process. The SVM classifier is frequently employed for the pathology detection method, especially for binary classification, which achieves higher performance detection. This higher accuracy is ensured even with a reduced training dataset. Moreover, the SVM classifier is characterized by lower complexity whatever the dataset size is. For this purpose, we choose the SVM as a classifier on our proposed method.

The kernel function is used to map the feature points to a higher dimension [START_REF] Acharya | Decision support system for the glaucoma using Gabor transformation[END_REF]. Since features are not linearly separable, the RBF kernel is employed, which is chosen based on the accuracy and the execution time. Elsewhere, the SVM is used with a gamma value equal to 0.1 and a C value equal to 1, where the values are experimentally chosen based on detection performance.

Experimental results

Evaluation of glaucoma screening method

Dataset and evaluation metrics

To test and evaluate the proposed method, two publically available datasets are selected which are frequently used in serval methods for glaucoma assessment. The first one is the DRISHTI-DB dataset which contains a total of 101 images provided by the Medical Image Processing (MIP) group, IIIT Hyderabad. All images were taken with dilated eyes, centered on the OD with a field of view of 30 degrees and a dimension of 2896×1944 pixels. The second dataset is the DRIONS-DB [START_REF] Al-Bander | Dense Fully Convolutional Segmentation of the Optic Disc and Cup in Colour Fundus for Glaucoma Diagnosis[END_REF][START_REF] Haleem | Automatic extraction of retinal features from colour retinal images for glaucoma diagnosis: a review[END_REF][START_REF] Abbas | Glaucoma-Deep: Detection of Glaucoma Eye Disease on Retinal Fundus Images using Deep Learning[END_REF] which contains 110 digital retinal images including 50 normal images and 60 glaucoma images with a dimension of 600 × 400 pixels. The fundus images were acquired from patients approximately 53 years of age, approximately centered on the ONH [START_REF] Haleem | Automatic extraction of retinal features from colour retinal images for glaucoma diagnosis: a review[END_REF]. We note that DRIONS-DB contains suspect fundus images which are avoided in our experimentation. The overall healthy and glaucoma-affected images are mentioned in Table1. The performance of our method is evaluated through the accuracy, sensitivity and specificity metrics [START_REF] Thakur | Survey on segmentation and classification approaches of optic cup and optic disc for diagnosis of glaucoma[END_REF][START_REF] Mvoulana | Fully automated method for glaucoma screening using robust optic nerve head detection and unsupervised segmentation based cup-to-disc ratio computation in retinal fundus images[END_REF], which are computed as indicated in equations 6, 7 and 8.

Sensitivity = TP TP + FN (6) 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 = 𝑇𝑁 𝑇𝑁 + 𝐹𝑃 (7)
Accuracy = TP + TN TP + FP + TN + FN [START_REF] Khalil | Improved automated detection of glaucoma from fundus image using hybrid structural and textural features[END_REF] where TP (True Positive) is the number of images classified correctly as glaucoma-affected, TN (True Negative) is the number of images classified correctly as healthy, FP (False Positive) is the number of healthy images identified as glaucomatous and FN (False Negative) is the number of glaucoma-affected images classified as healthy. To correctly evaluate our contribution, those metrics are computed after locating the OD using the method detailed in [START_REF] Elloumi | Mobile computer aided system for optic nerve head detection[END_REF].

Performance evaluation of glaucoma screening method

This method is evaluated using each dataset separately, where all fundus images are used for training and testing steps. The experimentation shows that our method achieves 98.01% accuracy, 93.54% sensitivity and 100% specificity when the evaluation is performed using the DRISHTI-DB database. Furthermore, when the evaluation is performed using DRIONS-DB database, our proposed method provides 95% of accuracy, 95.12 % of sensitivity and 94.73% of specificity, as shown in Table 2. Accordingly, the higher detection performance on both datasets confirms the accuracy of our suggested method for glaucoma screening. As the DRISHTI-DB is widely used for evaluating several automated methods of glaucoma screening, we compare our method with recent ones where accuracy, sensitivity and specificity are depicted in Table 3. It is obviously distinguished that our method outperforms several existing state-of-the-art glaucoma detection methods, and is tabled among the most highly performant ones. 3.2. Performance evaluation with respect to SCFIs

Dataset

The second experimentation consists in evaluating the suggested method using SCFIs. Within this objective, we evaluate our method using the RIAMP dataset proposed in [START_REF] Besenczi | Automatic optic disc and optic cup detection in retinal images acquired by mobile phone[END_REF], which contains healthy and glaucoma-affected fundus images acquired from 16 people. For each person, a first fundus image was captured with Topcon retinal camera and three others with the optical lens "iExaminer" snapped to a smartphone iPhone 4S. For instance, fundus images captured form healthy and The classical fundus images are provided to an ophthalmologist to generate the groundtruth. Some retinas are considered as suspect, whether for classical or smartphone captured fundus images, which requires additional diagnosis to deduce if the patient is glaucoma-affected. Therefore, suspect images are avoided to keep only healthy and glaucoma-affected ones, which correspond respectively to two and nine people, for both classical and SCFI databases.

We notice that three smartphone captured fundus images are acquired for each person. Therefore, to have a stability between classes and achieve a sufficient dataset size for training, two images for each glaucoma-affected person are identified and added, based on their better quality. The structure of both datasets are detailed in Table 4.

Performance evaluation

To evaluate the robustness of our method, the experimentation consists in evaluating our method using each dataset separately and then comparing the achieved detection performance. For each dataset, the training and testing processes are performed using the same image set. Thereafter, the metrics of accuracy, sensitivity and specificity are computed to evaluate the method for each dataset, which are depicted in Table 5. Based on the experimental results, we distinguish that our proposed method correctly detects all fundus images. Furthermore, the same detection performance is ensured even with smartphone captured fundus images. Accordingly, this experiment proves the robustness of the suggested method with respect to the moderate quality caused by the mobile device capturing. Hence, we can deduce that our method is adequate to be implemented it on a MAS system for glaucoma.

MAS system for glaucoma as smartphone app

The whole method is implemented as an app on an android operating system through the android SDK. This latter is a software development kit which provides several functions to fully use the system architecture and components. All image processing and machine learning steps are implemented using the "Open Source Computer Vision (OpenCV)" library [START_REF] Domínguez | IJ-OpenCV: Combining ImageJ and OpenCV for processing images in biomedicine[END_REF][START_REF] Dagade | Driver Alertness Monitoring using OpenCV and Android Smartphone[END_REF]. This library has more than 2,500 optimized algorithms, which includes a comprehensive set of both classic and state-of-the-art computer vision and machine learning algorithms. It is developed using C++ and can be supported by several operating systems and interfaced through many languages such as Python, JAVA and MATLAB. The OpenCV functions are implemented on an Android app using the Android Native Development Kit (NDK) [START_REF] Tedeschi | A real-time automatic pavement crack and pothole recognition system for mobile Android-based devices[END_REF], which allows compiling native application codes such as C/C ++ for Android applications to run on the Dalvik virtual machine. With this method, native codes can be used repeatedly and the execution speed can be faster. The Android NDK provides the native API compiler system and packages the native codes into APKs by integrating JAVA Native Interface (JNI) [START_REF] Juang | Proceedings of the 2nd International Conference on Intelligent Technologies and Engineering Systems (ICITES2013)[END_REF]. A graphical use interface is developed where the first step consists at uploading a fundus images from the gallery through the button entitled "Fundus image selection". Thereafter, the whole method is run through a button called "glaucoma detection". The detection result is displayed below the button indicating the provided class, as shown in Fig. 9.

Computational performance of MAS system

Computational performance analysis

The CLAHE algorithm spreads all pixels to adjust pixel values, where the processing complexity is about (𝑛 × 𝑛) [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 OD sub-image size. The Black-hat filter inverses pixel values. Therefore, each processing requires (𝑛 × 𝑛) and the Otsu thresholding tests each value is order to assign 0 or 255, where each processing requires (𝑛 × 𝑛) to be done [START_REF] Chen | A survey on Otsu image segmentation methods[END_REF][START_REF] Suzuki | Topological structural analysis of digitized binary images by border following[END_REF]. Next, the Median Blur is processed for each pixel to remove noise, which is performed in (𝑛 × 𝑛) instructions. Four masks are applied to the provided image, where each one requires (𝑛 × 𝑛). After that, the processing of locating each centroid leads to adding all pixel coordinates, and so is performed in (𝑛 × 𝑛). Finally, the classification ensured by the SVM classifier is equal to max((𝑓 × 𝑑), 𝑑²) [START_REF] Madroñal | SVM-based real-time hyperspectral image classifier on a manycore architecture[END_REF], where 𝑓 is the number of features and 𝑑 is the image number used for training, hence requiring constant computational complexity. As a consequence, the whole method requires the complexity of O(𝑛 × 𝑛) to be done.

Execution time evaluation

In this section, we evaluate the execution time of our method when implemented in the smartphone as an app. For this purpose, we quantify the execution times of glaucoma screening for SCFIs indicated in Table 7, where their values are depicted in Fig. 10. We note that the architectural characteristics mentioned in the last line of Table 8. It is deduced that the average execution time is equal to 0.155±0.035 second, where the difference is registered whether for healthy or glaucoma affected images. The achieved execution times are perfectly adequate with the clinical context for ensuring glaucoma screening.

Thereafter, we compare our method to the state-of-the art ones where the execution times and hardware and software tools are respectively mentioned in the second, third and fourth columns of Table 8. As mentioned in the introduction, several methods do not focus on computational performance with execution times above 10 seconds in several methods. Furthermore, our smartphone-based method ensures the faster glaucoma screening, jointly with the method proposed in [START_REF] Cheng | Sparse Dissimilarity-Constrained Coding for Glaucoma Screening[END_REF] which is performed in a desktop architecture having a processor with a 3Ghz of frequency. Among methods aiming for mobile glaucoma screening, our app outperforms the work proposed [START_REF] Martins | Offline computer-aided diagnosis for Glaucoma detection using fundus images targeted at mobile devices[END_REF] in terms of detection performance and execution time where glaucoma is deduced under tow seconds with 0.87 accuracy and 0.85 sensitivity.

Conclusion

In this paper, we have put forward a method for glaucoma screening dedicated to SCFIs. The method principle consists in identifying the main glaucoma proprieties that rely in the OD, reflecting proprieties through carefully selected features and providing them to a supervised classifier. Our method achieves detection with 99% accuracy, 96.77% sensitivity, and 100% specificity when evaluated using the DRISHTI-DB. The method implementation through an app leads to a mobile computeraided system for glaucoma detection. The experimentation confirms that our method ensures performant detection even when using SCFI. Besides, the glaucoma screening is performed on 0.155 second which is adequate for clinical issues.

In future work, we aim to extend our method in order to provide the severity stage of glaucoma screening. In addition, other ocular pathologies can be detected such as diabetic retinopathy and age macular degeneration. Moreover, the smartphone app can ensure uploading the fundus images to be transferred to ophthalmologists to anticipate medical care and therapy. Python & TensorFlow Lite [START_REF] Cheng | Sparse Dissimilarity-Constrained Coding for Glaucoma Screening[END_REF] from 0.12 to 0.17

b

  LIGM, Univ Gustave Eiffel, CNRS, ESIEE Paris, F-77454 Marne-la-Vallée, France. c ISITCom Hammam-Sousse, University of Sousse, Tunisia.

Fig. 1 .

 1 Fig. 1.fundus images: (a) captured with retinograph; (b) captured with optical lensassociated smartphone

Fig. 2 .Fig. 3 .

 23 Fig. 2. (a) Optic nerve head excavation of healthy retina; (b) Fundus image of healthy retina; (c) Optic nerve head excavation of glaucomatous retina; (b) Fundus image of glaucomatous retina

Fig. 5 .Fig. 6 .Fig. 4 .

 564 Fig.7(a) and Fig.7(b) illustrate the centroid locations in respectively healthy and glaucoma ODs, respectively.

Fig. 7 .

 7 Fig. 7. Centroids of blood vessels located in different zones of OD: (a) Healthy OD, (b) Glaucoma affected OD

Fig. 8 .

 8 Fig. 8. Fundus images: (a) captured with Topcon retinal camera; (b) captured with iExaminer

Fig. 9 .

 9 Fig. 9. Graphical Use Interfaces of the application

Table 1 .

 1 Databases used in proposed method

	Database	Number of fundus images
		Healthy	Glaucoma images
	DRIONS-DB	40	20
	DRISHTI-GS	31	70

Table 2 .

 2 Performance of the proposed method

	DB	Accuracy	Sensitivity	Specificity
	DRISHTI-DB	99%	96.77%	100%
	DRIONS-DB	95%	95.12%	94.73%

Table 3 .

 3 Performance comparison with state-of-the-art methods

	Method	Accuracy	Sensitivity	Specificity
	[58]	82.20%	--	--
	[59]	--	95,52%	--
	[60]	76.77%	--	--
	[61]	95%	100%	90%
	[57]	98%	100%	94.4%
	Proposed method	99%	96.77%	100%

Table 4 .

 4 Selected images from RIAMP database

		Healthy images	Glaucoma images
	Standard images	9	2
	Mobile images	9	4

Table 5 .

 5 Detection performances of our method in terms of datasets

		Accuracy	Sensitivity	Specificity
	Standard images	100%	100%	100%
	Mobile images	100%	100%	100%

Table 8 .

 8 Execution times in terms of hardware and software tools of glaucoma detection methods

	Glaucoma detection methods	Execution time (in seconds)	Hardware tools	Software tools
			core i7, 3.4	MATLAB
	[14]	25	GHz
			RAM : 4GB
	[59]	19.44	3.40 GHz Intel core i7,	MATLAB
			Intel Core i3,	Python 2.7 & OpenCV 2.4
	[64]	18	3.5 GHz
			RAM: 6GB
			Intel Xeon, 3.3	Python environment with
	[57]	11	GHz, RAM : 8	Anaconda
			GB
	[21]	9.16±0.78	Cloud platform	-	-
	[63]	8.1	GHz quad core, 2.66	MATLAB
			Processor :	Python based on Keras
	[65]	2.4	NVIDIA Tesla	with Tensorflow backend
			P40 GPU
			Samsung S8,
	[22]	< 2	Quad core, Up
			to 2.3GHz,
			GPU Mali G71

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

Acknowledgements

Funding for this study came from Campus-France through the PHC-UTIQUE Research program (grant number: 19G1408). The authors acknowledge the help of Dr. Aymen Daldoul, ophthalmologist in the hospital center of Nevers agglomeration (France), to provide the groundtruth of smartphone-captured fundus images.