An exclusive-disjunction-based detection of neovascularisation using multi-scale CNN

In this article, an exclusive-disjunction-based detection of neovascularisation (NV), which is the formation of new blood vessels on the retinal surfaces, is presented. These vessels, being thin and fragile, get ruptured easily leading to permanent blindness. The proposed algorithm consists of two stages. In the ﬁrst stage, the retinal images are classiﬁed into non-NV and NV using multi-scale convolutional neural network, while in the second stage, 13 relevant features are extracted from the vascular map of NV images to achieve the pixel locations of new blood vessels using a directional matched ﬁlter along with the Difference of Laplacian of Gaussian operator followed by an exclusive disjunction function with adaptive thresholding of the vascular map. At the same time, the pixel locations of optic disc (OD) are detected using intensity distribution and variations on the retinal images. Finally, the pixel locations of both new blood vessels and OD are compared for classiﬁcation. If the pixel locations of new blood vessels fall inside the OD, they are labelled as NV on OD, else they are labelled as NV elsewhere. The proposed algorithm has achieved an accuracy of 99.5%, speciﬁcity of 97.5%, sensitivity of 98.9%, and area under the curve of 94.2% when tested on 155 non-NV and 115 NV images.


INTRODUCTION
Diabetic retinopathy (DR) is one of the leading eye-related diseases that cause visual impairment and even leading to permanent vision loss among the working-age people in the United States [1]. It is affected by diabetes mellitus due to abnormal glucose levels in the body. DR has become an economic problem in most of the developed countries like the United States as the cost of ophthalmic chronic complications caused by diabetes exceeded 1 billion dollars in 2007 [2].
The retina of the eye is affected by different types of lesions due to DR. Microaneurysms are the most common lesion that appears as red dots on the fundus photographs. These microaneurysms are the first sign of DR and progress to form exudates due to excessive leakage of lipids as bright yellow spots on the fundus image. At this stage, larger and dark red blot haemorrhages are also observed. The severe stage of DR is proliferative DR, in which retinal ischemia can trigger abnormal blood vessel changes such as venous beading, intra-retinal microvascular abnormalities, and new vessel growth.
The formation of new blood vessels on the retinal surface is called neovascularisation (NV). Conventionally, NV is identified by fluorescein angiography (FA) [3]. FA is a medical diagnostic tool used to study the vascular map of the retinal structures. The drawback of this method is that injection fluorescein in the veins of blood leads to various side effects such as severe headache, hypotension, vomiting etc. Hence, a timely and predicable computer-aided diagnosis will significantly overcome the above-mentioned side effects along with the detection of NV in the retinal area.
New blood vessels get easily ruptured and cause blood leakage due to their fragile nature, and the leakage of blood forms a layer on the surface of the retina, which poses a high risk of visual impairment. This condition for many people with DR goes unrecognised until blood leakage occurs in the eye [4]. Depending on the new blood vessel pixel locations on the screening photographs, NV is categorised into two types: if the locations of NV are within or up to one optic diameter of the optic disc (OD), they are termed as neovascularisation on optic disc (NVD), else they are known as neovascularisation  Figure 1 illustrates the normal retinal image, the retinal image with NVD, and the retinal image with NVE.
A computer-aided robust algorithm is essential for the identification of DR in its early stage before it goes into the worst condition. The detection of NV in retinal images is a challenging task as it is difficult to detect the thin vessels over the entire image. To alleviate this problem, a novel algorithm is developed to analyse the fundus images for the detection of NV. If NV is not present in the image, there is no specific requirement for blood vessel segmentation and OD detection for those images. In the earlier works, the images with NV and without NV were subjected to blood vessel segmentation or OD detection as their prior step. In our proposed methodology with the advent of deep learning methods, initially, a classifier is developed to identify the presence of NV on the image. If NV is detected, the second stage of the proposed algorithm is implemented, else the algorithm ends in the first stage itself. The other novel step implemented in this proposed work is to incorporate the exclusive disjunction function for the detection of pixel locations of new blood vessels with high precision.
The rest of this paper is organised as follows. In Section 2, the existing work relevant to this research work is explained. In Section 3, the proposed methodology is briefly described. Section 4 presents the experimental results of the proposed algorithm. Discussion and conclusions are explained in Section 5.

RELATED WORK
With the advent of computer-aided diagnosis, many algorithms have been implemented to identify DR and its symptoms using fundus images. There are two types of detection: supervised [5][6][7][8][9] and unsupervised [10][11][12][13][14][15][16]. However, in recent years, significant approaches have been developed to detect DR. Goat-man et al. [8] proposed the first research work in detecting the new blood vessels using watershed lines and a Canny edge detector. The extracted vessel candidate segments are classified into healthy or abnormal vessels using a support vector machine (SVM) classifier with 15 features. All these 15 features are, however, not vital in classifying all the time, and sometimes, some features even degrade the classification. Therefore, feature selection criteria are required along with k-fold cross-validation to validate the classifier performance. Although this method provides more accuracy, it is difficult to sustain with a low false error rate. Yu et al. [7] proposed an automatic image processing procedure for NVD detection by segregating the blood vessels using multi-level Gabor filtering. In this, the retinal images are classified with an SVM considering the features observed from morphological and texture analysis. The retinal feature elimination method is implemented to detect the finest feature subsets for the optimal performance of the classifier. This method is limited with a feature selection as it leads to generating more parameters, which may degrade the performance rate. Agurto et al. [17] use multi-scale amplitude modulation and frequency modulation methods for differentiating healthy and abnormal screening images. Textural features such as instantaneous frequency along with its related angles and instantaneous are measured using different scales of retinal images. Using the distance metrics of obtained feature vectors, inter-structural similarity is identified, and the effects of these similarities on different pathological lesions of fundus photographs are identified. The major drawback of this is computational time as it involves more operations to state the final result. Tsai et al. [18] developed a supervised classifier to spot the choroidal NV changes in the retinal images. The learning strategy of the classifier is Adaboost, which is merely a combination of small weak classifiers into one classifier to get better performance in the classification of the retinal images, but a small change in one of the small classifiers may largely affect the entire classifier. Qummar et al. [19] have considered five different pre-trained convolutional neural networks (CNNs) to classify different stages in DR using a large Kaggle dataset. The result of this method is mainly based on the performance of the system where it is being developed. Chaudhuri et al. [10] used a 2-D matched filter for blood vessel segmentation. A Gaussian-shaped curve is used for the detection of piecewise linear segments of blood vessels in the retinal images by considering a grey-level cross section of blood vessels. They constructed 12 different templates that are used to search for vessel segments in all possible directions. Although this method developed a novel algorithm to extract blood vessels, the performance of this method is very low. Roychowdhury et al. [20] segmented OD using the MaxVeSS algorithm. A region-based classifier identifies the bright regions, which are near to the major blood vessels. OD is the brightest probable region that is segregated by creating a best-fit ellipse. Lalonde et al. [21] combined the Canny edge detector and the Hausdorffbased template matching algorithm to detect the circular-shaped OD boundary. Even though model-based algorithms [20,21] achieve good results, they involve more time in segmentation. Hence, feature-based algorithms depend on the characteristics of the OD such as size, brightness, and shape. Gupta et al. [22] proposed a new concept of the neovascularity score with the features extracted from the texture and vessels of local patches. Each labelled patch consists of 525 features that are used to train the random forest (RF) classifier. Guo et al. [23] used fractionalorder Darwinian particle swarm optimisation algorithm based on the intensity variations to segment the OD. However, the occurrence of uneven illumination, hard exudates, and retinal pathologies limits this method. Fan et al. [24] extracted features from the patches (sub-images) of the fundus images, and the resultant feature vectors are applied to the RF classifier. RF develops a pattern from the patches. Each tree of the RF acts as the local segmentation masks. Although the methods [22][23][24] achieve meaningful results but becomes stagnant if the number of sub-images is more than 10 6 . Al-Rawi et al. [14] enhanced the performance of the matched filter using filter parameters to capture the blood vessels of images. In this method, vessel length and standard deviation of intensity profile are optimised for better vessel detection. Hassan et al. [25] implemented an algorithm in which blood vessel segmentation is carried out by mathematical morphology, which involves two methods. To enhance the blood vessels and suppress the background information, smoothing is performed on the screening images using mathematical morphology. Finally, the enhanced image is segmented using the k-means clustering algorithm. Marín et al. [26] use a neural network (NN) scheme for pixel classification and compute a 7-D vector composed of grey-level-and moment-invariant-based features for pixel representation. In this method, grey-level-invariant-based features and momentinvariant-based features are calculated for each pixel and represented in a 7-D feature vector for further classification of vessel and non-vessel. Despite the sophistication, the methods [25,26] are not able to reduce the effect of false edges in the retinal images.
From the above literature survey, it can be seen that most of the prior work is done in the detection of NVD, but very little work has been carried out on the detection of NVE, in which, the detection of NVE is carried out considering the patches of the screening photographs. The computational time and the percentage of accuracy in terms of precision were less as the patches considered may not have NV, but the same may be present in the rest of the image. To circumvent this problem, a novel algorithm is proposed, which involves two stages. In the first stage, the multi-scale CNN detects the presence of NV on retinal images by masking each sub-image with filters. Later, the images with NV are subjected to blood vessel segmentation and OD detection. The pixel locations of the new blood vessels are obtained by applying adaptive thresholding followed by an exclusive disjunction function. Finally, on comparing the pixel locations of new blood vessels and OD boundary locations, the type of NV (NVD/NVE) present on the neovascularised image is identified.

MATERIALS AND METHOD
A careful analysis of the prior work revealed the limiting factors in each method. Hence, a novel algorithm has been proposed to detect the presence of NV and also to classify them depending on their pixel locations. The pixel locations of the OD and new blood vessels are used to classify the images into either NVD or NVE by considering the intersection of two abnormal vessel locations and OD region locations.

Data
The proposed algorithm is tested on different publicly available datasets such as DRIVE, STARE, MESSIDOR, HRF, and Kaggle DR using MATLAB software. A total of 270 images were collected and labelled with the help of experts from the collaborating hospital. Finally, 18 retinal images were captured by a non-mydriatic fundus camera with 45 • FOV from the rural areas of Andhra Pradesh for different age groups. Furthermore, the images were collected locally, and the images from the publicly available dataset were labelled by the doctors of the Department of Ophthalmology, Gayatri Vidya Parishad Institute of Health Care and Medical Technology.

Pre-processing
In the proposed method, there are two stages, and separate processing techniques will be implemented for each stage. Figure 2 describes stage 1 of the proposed method. The fundus images are taken from different publicly available datasets, and the labelling of the dataset is done by an ophthalmologist from the collaborating hospital. The retinal images collected are divided into training and testing datasets in the ratio 7:3. The dataset collected is up-sampled and down-sampled to avoid unbalanced distribution and overfitting. In up-sampling, flipping and rotation of the images are performed to enrich the dataset for getting a better performance rate. In down-sampling, the extra images from the major class are discarded to balance the dataset. Table 1 illustrates the number of retinal images considered in up-sampling and down-sampling, respectively. The major pre-processing step in stage 1 is augmenting the input retinal images into different kernel sizes like 532 × 532, 256 × 256, and 128 × 128 either by bicubic  The output of stage 1 decides the further pre-processing of the image to the next stage. If the image is non-NV, no preprocessing is required as no new blood vessels are present in non-NV images. Figure 3 indicates the second stage of the proposed method, where the image is to be enhanced to segment the blood vessels and OD.
If NV is detected in stage 1, the image I rs is subjected to erosion by a disc-shaped structuring element se d , which reduces the impact of bright lesions, exudates located near to the blood vessels followed by image reconstruction.

Classification using a multi-scale CNN
The multi-scale CNN is an ensemble of three CSNets (coloured and size-based NN) each consisting of 16 layers. In Figure 4, the network architecture of each CSNet is illustrated. Each layer has its prominence in the classification of a dataset. The input layer of the NN considers the input data, which is coloured and specific in the size of the retinal image to be trained. The finetuned resized and RGB-coloured dataset is provided as input to the CNN to develop trained CSNet (h). Three CSNets each with different input kernel sizes are developed and ensemble to attain a multi-scale CNN model Ɱ. Each CSNet is trained with a dataset (S , L) of different kernel sizes (532 × 532, 256 × 256, The training set (S train , L train ) is divided into mini-batches with size n = 8, such that (S i , L i ) ∈ (S train , L train ) ∀ i ∈ N (< K ∕n). These are optimised to reduce the loss function iteratively in the multi-scale CNN model (h ∈ Ɱ). Each CSNet is trained with specific resized retinal datasets to obtain the optimised loss function value. The convolution layer in the feed-forward NN is used for pixel feature extraction. Using the translation invariance method, features are extracted from input images for classification. It contains filters each of size 5 × 5, which are convolved with the input image to obtain the feature response map (kernel map). The filters are also referred to as sliding filters or kernels. One of the main advantages of this layer is that it evaluates the learning rate of each CSNet. Figure 5 describes the evaluation of the convoluted response from the input image by translating kernel with a one-pixel width over the complete input image. In the proposed work, 20 filters are considered to convolute and generate the effective feature response map (ℤ) for the precise classification of retinal images The learning rule is given by The learning rule is updated as where is the index set, in which all neurons are considered to convolute the kernel with every location on the input image. The cross-entropy loss function (E ) is used to optimise the hyper-parameters to reduce the error that occurs in the stochastic gradient descent method used for weight adjustment where h(s, w) is the multi-scale CNN model used to predict the class 'l ' with respect to input 's' at weight 'w' and E (.) is the cross-entropy cost function. The stochastic gradient descent algorithm (SGDM) [27] is implemented to update the weights as it requires only first-order partial gradients with limited memory requirement and provides high computational efficiency. The parameters updated in this method are invariant to the rescal-ing of the gradient. It works with sparse gradients, and it naturally performs a form of step size annealing. Individual adaptive learning rates are computed by considering the estimates of the first and second moments of the gradients. The expected value of the objective function E[S i ( )] is minimised to optimise the objective function. In this method, exponential moving averages of the gradient 'a t ' and squared gradient 'a st ' are updated and controlling the exponential decay rate by hyper-parameters q 1 , q 2 ∈ (0, 1) where g t is the partial differential gradient of S t evaluated at each time step 't'. Hence, it is also called the mini-batch gradient descent algorithm where f i ( ) is the objective function and is the initial learning rate. The momentums of this method are updated by using (7) and (8).
The feature response obtained is the linear combination of all filter responses. The weights are updated to reduce the error and biasing effect. To attain this with a high-performance rate, the non-linearity activation function is applied to NNs [28].
The rectified linear unit activation function is used for the introduction of non-linearity to the network as follows: i.e.
In the CNN, pooling layers are important layers, which involve inflating the receptive fields and deducing the overfitting effect. In the CSNet, two types of pooling layers are considered.
Initially, the max-pooling layer is considered for the pooling of best feature maps to elevate the efficiency of the classifier. To achieve this, the max filter and the average filter are considered to measure the average of best feature maps to provide excellent features to a fully connected (FC) layer in the CSNet. In the CSNet, each 2 × 2 patch of the feature maps with a stride 2 × 2 is down-sampled to obtain max and mean value in the square matrix for max-pooling and average pooling layers, respectively.
The resultant best feature maps from the average pooling layer are transformed into a single column vector termed as FC layer. A special activation function known as softmax is followed by the FC layer to categorise the retinal images into NV and non-NV datasets with high probable efficiency. The output of each convolutional layer in the CSNet is illustrated in Figure 6. The obtained result is labelled as the retinal image with NV or without NV for outputs 0 and 1, respectively. The images with no new thin blood vessels (non-NV) are not processed further in the second stage.

Difference of Laplacian of Gaussian (DLOG) operator for blood vessel segmentation
Generally, blood vessels have small curvatures with lower reflectance and appear darker when compared to the surroundings on the retinal surface. The main novelty of the method proposed in this paper is to extract the blood vessels from NV images not only to save the memory and also to reduce the computational time. If the image tested over the multi-scale CNN is identified as NV, then inverted green channel is extracted from the input resized retinal image 'I rs '. In addition to this, while enhancing the tiny blood vessels along with it, the noise present in the retinal photographs is also increased. For image enhancement, contrast limit adaptive histogram equalisation (CLAHE) is performed to a small region called tiles. The enhanced NV images are used to extract the blood vessels by using a directional matched filter with the DLOG operator. The Laplacian of Gaussian (LOG) operator is a second-order differentiable mask used to detect edges of the image by taking out the inward and outward edges with less mathematical operations. The LOG operator is expressed as Here, i 2 + j 2 (= p 2 ) is the shortest distance from (i, j ) to the centre of the blood vessel along its length and is the intensity distribution parameter. The LOG operator is high sensitive to noise. But the DLOG operator acts as a bandpass filter and removes noise components from the image for better enhancement. The DLOG operator is represented as The blood vessels that are away from the centre are having less vessel width relative to the vessels near to the centre. The matched filter with transfer function G( ϝ) results in a value d o (t ) where s( ϝ) & ℵ( ϝ) are the Fourier transform of s(t ) and n(t ), respectively. n(t ) is the additive white Gaussian noise. The matched filter is implemented to detect the edges with optimal parameters where negative sign indicates the detection of darker objects in an image. The blood vessels are detected when the filtered response is beyond the threshold limit. For precise detection of blood vessels on the retinal surface, the filter is rotated to all probable directions. The resultant of these filtered responses will be considered, and blood vessels are extracted by assuming the background with constant intensity. The blood vessels are obtained as piecewise segments. Thus, the filter is applied to several cross-sections for matching to minimise the false edges. The matched filter kernel is represented as where V l is the length of the segment along the blood vessel with constant orientation. This method not only reduces false edges but also suppresses the negative effect of noise in the background of the retinal image [10]. The DLOG operator is slightly similar to the Canny edge detector, where the average maximum of directional derivatives at each pixel is calculated. The orientation of the rth kernel is represented by Ω r . The rotation matrix is considered as and the point in the new coordinate system is (x, y). A set of 15 such kernels are applied to the retinal image, and every pixel with the maximum response is considered. The profile of the DLOG operator is illustrated in Figure 7.
The DLOG curve is truncated to x = ±5 to reduce the infinitely double-sided trails. A neighbourhood N is expressed where 'B' is the number of the neighbourhood points and 'm r ' is the average of the kernel responses. Finally, the vascular map is extracted from the input retinal image for NV images to detect the new blood vessels from (15). Figure 8 illustrates the blood vessel extraction from the NV retinal images.

Detection of new blood vessels using an exclusive disjunction function
In the proposed method, 13 features are extracted from the vascular map of the neovascularised image by considering each vessel's contrast, length, width, density, and orientation. Initially, the number of segments and their lengths from the vascular map is calculated, as the NV images have more segments [8]. The features extracted from the vascular map are as follows: Tortuosity (T i ): It is a measure of the number of tortuous paths along each segment where 'k' is the number of segments and i is the tangential angle from the segment to the centre point of the vessel.
Vessel density (D(k)): The blood vessels are mostly formed in clusters. Hence, vessel density is a prominent feature in detecting the thin blood vessels where b ∈ S and b ≠ k.
Here, 's(k) ⊕ E' is the path of 'k th ' segment, 'E' is the circular structuring element, and 'S ' is the set of all segments.

Mean vessel width (V w ): The vascular map of the NV image is
skeletonised to measure the mean vessel width.
The feature vectors obtained are observed, and an adaptive thresholding technique is applied enabling removal of new blood vessels from the vascular map of the NV retinal images by considering optimal values of the feature vectors as thresholding limits where F R (x, y) is the resultant vascular map after applying thresholding limit to every pixel of the vascular map F (x, y) with size i × j . The resultant matrix will be having value of either 1 or 0 for every pixel location highlighting the presence or absence of major blood vessels in NV images, respectively. V l opt , T iopt, and V wopt are the optimal features of vessel length, tortuosity, and vessel width, respectively, given in (18). The two vascular maps before and after thresholding are subjected to exclusive disjunction to get the pixel locations of new blood vessels only. The output of the exclusive disjunction is defined as C N The matrix C N consists of new blood vessel locations with pixel value either 1 or 0 indicating the presence or absence of new blood vessels, respectively. The pixel locations of new blood vessels are stored in a matrix 'A' with size M × 2. The number of rows in the matrix 'A' represents the number of new blood vessels located in the retinal image, and the column number represents the pixel coordinate system.

OD detection and classification
Generally, in the retinal images, the most probable brightest closed region with eccentricity between 0 and 1 is OD. The proposed method has detected the pixel locations of the OD region to classify the NV into NVD or NVE. The OD is localised by detecting the maximum intensity distributed region from each of the RGB channels separately. To find the threshold value (T v ), initially, 'T v ' is considered as zero. The maximum threshold value is obtained as follows: where l is a variable, Similarly, threshold values of RGB channels (R t , G t , and B t ) are updated. The boundary of the OD is detected as the common intersected region from the extracted red, green, and blue channels of the input image. OD c represents the common intersected region where R t , G t , and B t are greyscale images after applying the respective updated thresholding limits to each channel of the input image. Due to the presence of exudates in some cases, two or more brightest common regions are extracted.
The brightest common region with large area and eccentricity within the limits 0 to 1 is considered as OD of the retinal image. The pixel locations of the OD region are identified and represented as N × 2 matrix ′ B ′ . ′ N ' is the number of pixels in OD region and each row of the matrix ′ B ′ represents the pixel coordinates of each pixel in the OD region.
The pixel locations of new blood vessels in matrix ′ A ′ are compared with each pixel location of the OD region. If the pixel coordinates of the new blood vessels lie within the OD region then the NV on the fundus image is termed as NVD, else it is classified as NVE.
The pixel locations of blood vessels are analysed with the pixel coordinates of the OD region, and the number of common rows can be represented as 'n'. The value of 'n' is calculated by (22) and (23). Initially, the value of 'n' is assumed to be zero, i.e. n = 0 The value of 'n' decides the classification of the neovascularised image as either NVD or NVE. The proposed method has achieved an accuracy of 99.5%, and pixel error of 0.45% occurred due to different types of abnormalities present in the dataset during the screening of the retinal images under different environmental conditions.

EXPERIMENTS AND RESULTS
All the experiments were performed using MATLAB software of version 2018a with a desktop having 16-GB RAM and i7 core Intel processor. The proposed algorithm is developed by considering 270 retinal images from different publicly available datasets. Each CSNet in the multi-scale CNN is trained with variable input retinal size to optimise the loss function and enhance the testing accuracy with different resolutions of the image. The images are resized to 532 × 532, 256 × 256, and 128 × 128. If the image is confirmed with NV by the multiscale CNN, then the retinal images are further pre-processed to enhance the image by CLAHE with contrast limited to 0.04, and Rayleigh distribution is applied to the retinal image. Blood vessels are extracted from the enhanced fundus image using the directional matched filter with a DLOG operator with = 2, i = 6, and Ω r = 15 • . In this proposed method, the new blood vessels are removed from the vascular map by considering optimal thresholding limits of vessel width, length, and tortuosity, respectively. The OD region is detected by considering the maximum intensity region having eccentricity lying between 0 and 1.

Performance of classifier
The effect of overfitting and the unbalanced distribution of the dataset during the training is avoided by up-sampling and downsampling the original dataset. Table 2 indicates the performance

FIGURE 9
Testing accuracy vs learning rate metrics of CSNet trained with sampled datasets and un-sampled datasets. It is observed that the network with the up-sampling dataset was more efficient than the other two networks. The SGDM is implemented to optimise the hyperparameters, which occupy less memory and minimum execution time. The proposed method has achieved 100% training and 99.6% testing accuracy with loss function value in the limits between 0.0072 and 0.01. The initial learning rate for each CSNet is 0.001. Figure 9 describes the decrease in accuracy with an increase in learning rate. The accuracy and loss function plots shown in Figure 10 depict the overall training performance of the multi-scale CNN.

Performance rate of NV detection
A total of 270 retinal images are collected from different publicly available datasets, and the labelling of the datasets is done with the help of an expert doctor. Initially, 270 images are considered and divided in the ratio of 7:3 for creating training and testing datasets for the classification of NV and non-NV images using the multi-scale CNN. Now, the testing dataset is used for detecting NV on the retinal image. The receiver operating characteristic (ROC) curve in Figure 11 reveals that the proposed method has achieved maximum accuracy (ACC) of 99.5%, sensitivity (Se) of 98.9%, and specificity (Sp) of 97.5% than previously existing algorithms [8,29,30]. In addition to this, other performance metrics such as false discovery rate (FDR), precision (P), and success rate (SR) are calculated to show the efficacy of the proposed method. SR is the number of images detected precisely with the appropriate detection. The proposed method has achieved an SR of 100% in detecting the presence of NV on retinal images. The  [30], and Yu et al. [7]. Table 3 shows the comparison of the present work with the previous work. For comparison, the proposed algorithm is tested on images collected from different publicly available databases such as Kaggle DR, DRIMDB, and idrid databases. Although these databases provide a large number of DR images, most of them are of poor quality in terms of resolution and FOV etc. This method has achieved a low FDR value of 0.001 and a high precision rate of 0.99 in the detection of NV on retinal images. The Laplacian curve of the DLOG operator is truncated to ±5 by considering = 2 to reduce the computational time due to an infinitely double-sided curve. The performance of the matched filter with the DLOG operator is compared with the previous detection method, and the results are tabulated in Table 4.
The fine thin blood vessels from the vascular map are removed using the optimal values of V l opt , T iopt , and V wopt , which are adaptive and updated for each retinal image accordingly. Figure 8(d) represents the vascular map of the retinal image, in which the new blood vessels are removed. The new blood vessel locations are stored in matrix 'A' with size M × 2 using the exclusive disjunction function.
The pixel locations of OD in Figure 12 are detected and stored in matrix 'B' with size N × 2. The value of 'n' is evaluated by the intersection of new blood vessels and the OD pixel locations. It is observed that retinal images having 'n' value more than 2000-pixel locations are labelled as NVD images. Normally, the value of 'n' should be 0 for NVE images. But due to the presence of other pathological abnormalities such as

4.3
Overall performance of the proposed method Figure 10 illustrates the overall performance of the proposed method. Maximum accuracy is achieved with optimum values  of specificity as 97.5% and sensitivity as 98%. The multi-scale CNN consists of three different CSNets, which are used to optimise the loss function for better classification. Figure 13 indicates the advantage of the multi-scale CNN over each CSNet. Table 5 describes the execution time of each step implemented in the proposed algorithm.

DISCUSSION AND CONCLUSIONS
The proposed work mitigated the difficulty of detection of NV using the multi-scale CNN and the exclusive-disjunction-based function. This method achieved promising and better results compared to the previous work [8,17,31]. The previous work is confined to detection of NVD, and there is no significant work performed in the detection of NVE as it is difficult to detect when compared to NVD. Generally, NVE is detected by considering the patches of input retinal images. But, the overall accuracy in detection of NVE using patches is very less as NV is absent in the selected patches but may present in other regions of the retinal images. It is also cumbersome to select the number of patches if the size of the image is large. To circumvent the above problem, the conventional procedure is replaced with deep learning techniques. To reduce computational complexity, a multi-scale CNN is incorporated for the initial filtering of retinal images into NV and non-NV with the minimum loss function value. This method discards the non-NV images in its first stage. In the second stage, the problem of random patch consideration for the detection of NVE is overcome by locating new vessel pixel locations using the DLOG operator and the exclusive disjunction function. The DLOG operator reduces the noise fluctuations in retinal images. For effective segmentation, the blood vessels are enhanced using CLAHE before applying the DLOG operator. From the segmented vascular network, thin vessels are located by the exclusive disjunction function with the help of vascu- lar features such as tortuosity (T i ), vessel density D(k), mean vessel width (V w ) etc. Simultaneously, OD pixel locations are located and compared with new blood vessel locations for classification of the retinal image either into NVD or NVE. This method provides a novel approach for the detection of NV on retinal images. This method is tested on various publicly available datasets and one locally collected dataset. The results are illustrated in Table 6. In the future, the authors are planning to collect retinal images with both NVD and NVE by conducting various medical camps in rural areas of Andhra Pradesh, India. As a result, a robust automatic system can be developed in a hardware platform for the detection of NV.