A Unique Discrete Wavelet & Deterministic Walk-Based Glaucoma Classification Approach Using Image-Specific Enhanced Retinal Images

1  Introduction

Glaucoma is an incurable retinal distortion caused by an increase in intraocular pressure (IOP) due to uneven generation and flowing “aqueous humor” [1]. A thorough examination of the retinal structures such as the optic disc (OD) and the cup (OC) can prevent glaucoma. Expert ophthalmologists clinically examine the human eye for glaucoma using several practices, such as fundus (retinal) image structural analysis [2]. However, these are tedious and error-prone due to their non-mechanical nature. As technology advances, CAD has become a standard medical practice for ophthalmologists in making quick and accurate glaucoma diagnoses. The CAD follows a fixed approach that contains major phases such as retinal image pre-processing, region-of-interest (ROI) segmentation, feature extraction, and classification using artificial intelligence (AI) approaches. The initial CAD phase is pre-processing, which usually eliminates noise existing in the image and applies various approaches to enhance the retinal image for a clear structural view. The feature extraction phases identify significant texture patterns in enhanced images for auto-screening by AI approaches.

In contrast to ordinary images, the structural analysis of fundus images is highly sophisticated due to the complex retinal tissue textures. In most cases, the textures of both the glaucomatous and healthy eyes are usually similar, and their discrimination requires a high level of cognitive processing. In the proposed CAD approach, complex texture analysis has been carried out on qualitatively improved retinal images using the combination of DTW and DWT for proper identification of the glaucomatous eye. It extracts the significant retinal texture patterns for the accurate designation of glaucomatous images. The rest of the paper is presented in different sections: Section 2 gives existing CAD-based glaucoma detection approaches that are motivated for the proposed approach; Section 3 demonstrates the proposed retinal image enhancement and the new feature extraction approach for glaucoma image classification; Section 4 investigates the classification results for scientific findings, and; Section 5 concludes the paper with the future work.

2  Existing Glaucoma Practices and Motivation

There are currently several existing works in the field of CAD-based glaucoma classification. This section presents a detailed investigation of them in terms of CAD’s major phases: image pre-processing, feature extraction, and classification. Muthmainah et al. [3] extracted first-order statistical (FoS) features from contrast-limited adaptive histogram equalization (CLAHE)-based enhanced retinal images. Then these features are ranked and fed to support vector machines (SVM) and k-nearest neighbor (k-NN) approaches for glaucoma screening. Afterward, Belgacem et al. [4] extracted the cup/disc ratio (CDR) of retinal images for glaucoma identification. Later, principal component analysis (PCA) features are extracted by Christopher et al. [5] to diagnose the glaucoma progression. Next, both texture and structural features are extracted by An et al. [6] using Visual Geometry Group (VGG)-19-based transfer learning (TL) approaches, and the classification is done with a random forest (RF) classifier. Subsequently, Rehman et al. [7] extracted statistical and fractal features from denoised and edge-enhanced images for glaucoma identification using SVM, RF, Ada, and RusBoost ML approaches. Later, an anisotropic diffusion filter is utilized by Mohamed et al. [8] for retinal image denoising before correcting image illumination. Then, the enhanced images’ super-pixel-based features were classified using the SVM classifier. Afterward, Oh et al. [9] collected retinal features using a convolutional neural network (CNN) along with the visual field (VF) test characteristics and then selected using a chi-square test. SVM, RF, and XGBoost classifiers were used in their study. Thomas et al. [10] then applied artificial neural networks (ANN) to human eye visual fields for glaucoma screening. Later, Thakur et al. [11] extracted both structural features such as CDR from vessel-free retinal images and non-structural features of different orders from grayscale images. These features are ranked and classified using Naive Bayes (NB), SVM, k-NN, and RF classifiers. Next, histogram-based (HE) enhanced retinal images are segmented by Shanmugam et al. [12] using an adaptive network (Au-Net) for OD and OC proportions. Nawaldgi et al. [13] extracted the co-occurrence matrix of gray-level (GLCM) characteristics. Then, DWT features were extracted from electro-retinography signals by Gajendran et al. [14]. ML classifiers used these DWT features for early-stage glaucoma detection. Patel et al. [15] then split the color channels of retinal images into bit-planes to generate local-binary patterns (LBP) for classification. Later, the retinal image color channels’ LBP features were extracted and classified using SVM by Rebinth et al. [16]. Next, Arsyan et al. [17] extracted invariant moment features from the HE-enhanced retinal OC and blood vessels. Then k-NN is applied by considering the five nearest neighbors. Table 1 summarizes the literature survey done for the proposed method.

2.1 The Proposed Approach’s Contributions

The in-depth literature survey has identified some CAD phase-wise research limitations such as Image pre-processing: (i) Most of the pre-processing approaches were designed for gray-scale medical images, (ii) The parameter values for enhancement were manually assigned, (iii) Texture intensity and structure improvement did not address jointly; Feature extraction & classification: (i) Image features have extracted without or with minimal usage of time- or frequency-domains, (ii) Most of the feature extraction approaches are limited by constraints such as threshold values, image dimensions, and directions, (iii) Inter-pixel relations are extracted with simple mathematical operations, and (iv) Texture patterns are extracted by considering only immediately adjacent pixels.

The proposed CAD approach has been motivated and designed to address the identified limitations with the following contributions:

Image pre-processing:

•   Color retinal images’ brightness and texture improvement are jointly considered.

•   Image-specific parameters are scientifically calculated and employed in the enhancement.

Feature extraction and classification:

•   Retinal image textures are analyzed using orthogonal (e.g., Daubechies (Db)) and biorthogonal (e.g., Bior Nr. Nd or Bi Nr. Nd) wavelets.

•   Texture patterns have been extracted using graph theory and traveler’s walks for various memory constraints.

•   Texture pattern extraction considers both immediate and non-immediate neighboring pixels.

•   All significant graph-based features are extracted to build powerful feature vectors.

3  The Proposed CAD Glaucoma Approach

In this study, retinal images were considered from various public datasets: ACRIMA [18] (396: glaucomatous, 309: normal), ORIGA [19] (168: glaucomatous, 482: normal), RIM-ONE [19] (325: glaucomatous, 458: normal), Drishti [16] (70: glaucomatous, 31: normal), and HRF [16] (15: glaucomatous, 15: normal). Furthermore, patients’ retinal images (110: glaucomatous, 110: normal) are collected from the Goutami Eye Institute [20] (HOSPITAL) to test the proposed approach’s performance. This approach has balanced retinal image illumination and structure improvement, and extracted pixel intensity relationships using DTW on graphs generated from DWT of images. DWT is a time-frequency localization approach. It explores the frequency and spatial information concurrently from the given 2D input image using a decimation operation with wavelet filter banks. High-pass and low-pass filters in filter banks extract details and approximate information from fundus images in the form of wavelet coefficients. The DTW operation can be interpreted as a tourist planning to visit randomly located locations on a multi-dimensional graph (map). The traveler begins his journey at a given point and proceeds to the next-nearest place in a deterministic manner, i.e., move to the next-nearest place that has not been visited in the most recent steps. This travel can explore neighboring relationship patterns that characterize the given map. The overall procedure is shown in Fig. 1 and explained in the following sub-sections.

Figure 1: The procedural flow of the DWT-DTW-based glaucoma classification approach

3.1 Retinal Image Pre-Processing

The proposed pre-processing has been divided into two stages: Image visual quality improvement and details enhancement. The entire approach is given in Algorithm 1 (A1) and explained w.r.t step numbers (A1: Sn). In this study, image edges are preserved by the Regional Laplacian-Filtering (RLF) approach that constructs Gaussian-pyramid (GP) for each image (IRGB) resolution. It extracts image lower-resolutions level by level (GPlevel) (A1: S1) by successive down-sampling. The discriminating details of each successive GPlevel are used to generate Laplacian-pyramid levels (LPlevel). The RLF is applied image-level-wise as well as coefficient-wise. These are designated by the position (pr, pc) and pyramid levels (pl) (A1: S2), using three stages:

•   Stage 1: Remapping computation: Each sub-region (SRl) is processed with a remapping computation C(.) using Csd and Cse, operations and τ. The value τ represents pl-level GP coefficient at the position (pr,pc). The Csd modifies finer scale details by using sf(v), which is generated by intensity variation (σiv), noise level (nl), mean (Mu), and standard deviation (Sd) of the image. Using the image average entropy (Entavg), the Csechanges edge amplitudes. Then image sub-region remapping (C(SRl)) is defined using a simple point-wise operation.

•   Stage 2: SR-pyramid generation: Generates a Laplacian pyramid LP[C(SRl)] for C(SRl).

•   Stage 3: Updating the output pyramid: The generated level-wise LP coefficients, i.e., LPl[C(SRl)](pr,pc) are assigned to the output (TI), i.e., LPl[TI](pr,pc).

It is followed by a series of image-specific luminance and gradient modulations on TIRGB(A1: S3). The luminance transaction (LT) is carried out by mapped luminance levels (GR_Yd) using a luminance-level ordered set, GYd={ld1,ld2,…,ldn−1}. The GYd is defined as the pair-wise differences of YsortIRGB={l1,l2,…,ln} and a mapped luminance-level set GRYd={rd1,rd2,…rdn−1}. Image luminance enhancement is followed by structural (OD, OC, and blood vessels) improvement using gradient transition (GT) on LT outcome i.e., LMEIMG. In GT, image gradients SI∂fx and SI∂fy are employed using a new gradient inflation function (Ifun) that operates on pixel values (pv) at each (pr, pc) location. Finally, SI∂fx and SI∂fy are integrated (by collapsing) to form complete enhanced retinal images (RIFE) (A1: S4).

3.2 The Proposed Retinal Image Feature Extraction

The objective is to extract retinal image (i.e., RIFE) texture patterns using various Db and Bior Nr. Nd wavelets and tourists’ walks. As per the existing literature, our proposed approach is the first one that extracts DWT and DTW-based retinal image features for glaucoma classification. In this approach, an undirected graph constructed with DTW trajectories formed using the image’s DWT coefficients of Wr×Wc size. According to graph theory, a retinal image-mapped graph (IG) is formed by a vertex-set (Vs) and an edge-set (Es), i.e., IG = (Vs, Es). The mapping is carried out in two phases: Vs generation and Es construction. Initially, each RIFE’s DWT coefficient is mapped to a vector Vs. In the next stage, a tourist walks among the vertices (Vs) using the partially self-avoiding property that forms trajectory paths based on various reminisces (i.e., memory) (RM) values. Since the objective of feature extraction is to retrieve significant image texture relationship patterns, it uses distance and similarity measures to identify neighboring vertices as shown in Fig. 2. The distance is measured using a weighted Euclidean distance (EDc) approach. Weights were generated using cosine similarity between coefficients. For each source vertex (Sv), the neighborhood (Nh) co-vertex count has been determined using the radius (R), i.e., Nc=∑r=1R8∗r as shown in Fig. 2e.

Figure 2: The neighborhood test for various ‘R’ values along with sample DTW whirlpool trajectories

As shown in Eq. (1), the distance covered by R between the source (center) and participating (Ps) vertices is calculated by a metric EDpusing vertex positions.

EDp=(Ws((xs−xp)2+(ys−yp)2))12,p=1toNc(1)

where (xs, ys) is the Sv vertex position, and (xp, yp) is the Ps vertex position. The weight function, Ws is measured using cosine similarity between positional DWT coefficients using Eq. (2),

Ws=SBs∗SBp/∑SBs2∗∑SBp2,SB∈{LL,LH,HL,HH}(2)

where LLs, LHs, HLs, and HHs are DWT coefficients of Sv and LLp, LHp, HLp, and HHp are DWT coefficients of Ps. The EDpvalues are generated for each pair of Sv and Ps. In this approach, the first eight closest neighbors (NVs) are considered for each Vs from the neighborhood participation set Nps based on EDpvalues.

NVs={Vp1,…,Vp8},EDp1<…<EDp8<EDother,EDother∉NVs,EDother∈NPs(3)

Tourists’ walks start by considering each vertex v∈Vs to generate corresponding DTW trajectories. These were controlled by a dual-rule moving protocol (MP) as given in Eq. (4). The first rule is that each movement should consider the nearest neighbor according to the distance measured using Eq. (1). The other is that, while considering a vertex as the nearest neighbor for the movement, it should not have been visited in the previous RMnumber of steps.

MP=Vpn,if⟨Rule1:(Vpn∈NVs&EDp(VPn)<EDp(VPi),i=1,…,8&n≠i)Rule2:VpnnotvisitedinlastRMsteps⟩(4)

where, Vpn is the next vertex in visiting list. The DTW will continue to visit vertices one-by-one by the MP until they reach the whirlpool situation. It occurs when a tourist continually visits the same vertex series without escaping.

Detection of a whirlpool in DTW is a challenging task. During the DTW progression, a vertex can revisit. According to the second rule of MP, in the current step, recently visited vertices (from the last RM steps) cannot be considered. Sample whirlpool situations have shown in Figs. 2a−2d, and their early detection can save computing resources. A new policy has been adopted for the detection of whirlpool situations. It is based on the sequence of vertices revisited during DTW, as shown in Fig. 3. Our policy has utilized a 1D vector Mwp to keep track of visited vertices and a structure Swp for each vertex that records the number of times it has been visited. The whirlpool identification policy (Ipolicy) is designed using Eq. (5).

Ipolicy=WP,if[(Vpr>Pmax,Vpr∈Mwp)∨(Vsc>=Lmax,Vsc∈Swp)∨(||T||==Amax)](5)

Figure 3: (a) The track of DTW’s visited vertices (b) an example of a situation that can lead to a whirlpool for the DTW trajectory (c) vertex’s visited record structure

This policy covers three situations: (1) the maximum number of times (Pmax), a vertex pattern (Vpr) appears; (2) a vertex visited step count (Vsc) with a maximum limit (Lmax), and; (3) the DTW trajectory T that covers the maximum area Amax.

In the proposed approach, Pmax and Lmax values are 3 and 5 respectively. The maximum edge count (Amax) is set at 25, to avoid boundless paths. Once a whirlpool occurs, DTW progression stops, and the vertices covered in that journey form a trajectory corresponding to that Vs. This process repeats for all available vertices in Vs. Finally, an undirected graph (RIG) is constructed by considering all these DTW trajectories corresponding to each vertex. The proposed approach has generated individual RIG for different RM values. Retinal image texture patterns are then captured using graph-based features (Table 2) of RIG.

Using these graph-based features corresponding to each RIG, a feature vector is constructed for each retinal image. This study considers RM values from 1 to 6.

FVRIG={DavgRM,EjdRM,LdRM,CCavgRM,EgRM,CviRM,CeRM,PavgRM,MCRM,HavgRM,EcRM},1≤RM≤6(6)

All extracted FVRIG are supplied to ML classifiers for glaucoma screening. The following section presents the obtained results and the corresponding analysis.

4  Results and Analysis

The entire experiment was carried out on the ROI (i.e., OC and OD areas) of color retinal images. The whole procedural flow is shown in Fig. 4. Initially, the retinal images’ intensity is improved using the image-specific edge and details modifier controllers Cse and Csd of the RLF approach. Then LT and GT operations are applied for luminance enhancement and texture improvement, respectively. Image-specific parameter-based preprocessing produces better-quality retinal images than existing methods, such as LM&GM [21] and CLAHE [22]. Some sample results are shown in Fig. 5. When compared to the CLAHE and LM&GM approaches, the qualitative results show strong evidence for both luminance and structural image improvement.

Figure 4: The block diagram of the proposed glaucoma screening approach

Figure 5: (a) Original input images, (b), (c), and (d) enhanced images by CLAHE, LM&GM, and the proposed pre-processing

The quantitative assessment of the proposed enhancement approach is carried out using three quality metrics: (i) Structural Similarity Index (SS_Index): It measures the image similarity, which is a product of image structure, contrast, and luminance, (ii) Mean Square Error (MSE): It measures the difference between original and enhanced images. A lower MSE value indicates qualitative image enhancement, and (iii) Blind Image Spatial quality (BIS): It is a blind (no reference) image spatial measurement for image quality. It returns a non-negative value between [0, 100]. The lower value indicates a better qualitative image. All these measures for the same sample images from Fig. 5 are reported in Table 3.

The histogram plots in Fig. 6 show the performance of the proposed enhancement over other existing approaches. The proposed enhancement keeps the images’ texture similarity (Fig. 6a) much closer to the original images, and the MSE values (Fig. 6b) are significantly lower than those of the CLAHE and LM&GM-based enhanced images. The proposed methodology has achieved qualitatively enhanced retinal images in terms of spatial measurement, i.e., BIS (Fig. 6c), compared to the other approaches.

Figure 6: Image quality assessment plots by various measures: (a) SS_Index, (b) MSE, and (c) BIS

In this approach, six undirected graphs are built for each retinal image, accounting for all RM values using DTW trajectories. Sample retinal image-mapped graphs (for images in Fig. 5) are shown in Fig. 7. Each DWT and RM combination produced a distinct topological complex graph. This crucial property enables the proposed approach to retrieve significant texture patterns. The architecture of each graph depends on the images’ DWT coefficient inter-relationships. Unlike conventional graphs, the DWT-DTW-based graph’s structurality will dynamically change according to the image’s texture, which can capture all possible patterns. This characteristic of the DWT-DTW approach is essential for analyzing retinal (medical) image textures.

Figure 7: Sample graphs generated from retinal image mapping using the DWT-DTW approach

Once all the DWT-DTW graphs are generated, graph-based features are extracted to form feature vectors (FVRIG). The obtained feature vectors have been randomly split using a 70:30 proportion without replacement for training and testing by NB, SVM, and RF classifiers. Various wavelets (DWT and DTW) are used in this study to achieve optimal glaucoma screening. The glaucoma classification results from various datasets are presented in Table 4 in terms of percentages. In the case of ACRIMA, both SVM and RF classifiers have achieved 100% accuracy, while the NB classifier’s performance is moderately low for various wavelets. Despite the high true-positive prediction rates of SVM and RF classifiers, all these are vulnerable to false-negative predictions. The DWT-DTW approach has achieved a higher accuracy range, i.e., above 96%, with biorthogonal wavelets than with orthogonal wavelets. In this approach, the NB classifier achieved 98.1% accuracy with the ORIGA dataset, while the SVM and RF classifiers secured 99.3% accuracy. The SVM and RF classifiers have high true-negative prediction rates with ORIGA data, but all classifiers suffer from false-positive predictions. Especially with orthogonal wavelets, the DWT-DTW approach has a lower true-positive rate than biorthogonal wavelets. This approach has achieved the highest accuracy on RIM-ONE data since the dataset size was considerably larger than the remaining datasets. In this case, SVM classifiers suffer from minor false-negative predictions, while RF classifiers have a maximum true-negative prediction rate. Through the DWT-DTW approach, all three classifiers suffer from minor false-positive predictions. However, orthogonal and biorthogonal wavelets are well suited to this approach with RIM-ONE data. Based on patient retinal images collected from the hospital, the proposed DWT-DTW method performs admirably. The highest accuracies achieved by NB, SVM, and RF classifiers are 97.1%, 98.5%, and 100%, respectively. This proposed approach has lower false-positive prediction rates than false-negative predictions with the hospital data. With the NB classifier, this approach has achieved mixed responses with both wavelet types. However, the combination of biorthogonal wavelet DWT-DTW with the SVM and RF classifiers performs better than orthogonal wavelets on the patient data. In the case of the Drishti dataset, the maximum accuracy attained by all three classifiers is 96.6%. This approach’s performance is relatively high even with smaller datasets like HRF. Overall, the proposed DWT-DTW method has attained maximum performances with the SVM and RF classifiers for all instances. The corresponding performance graphs are shown in Fig. 8.

Figure 8: The DWT-DTW glaucoma classification (a) accuracy, (b) sensitivity, and (c) specificity graphs

Due to the moderate patient data size, the NB classifier has attained lower classification accuracy than other cases. In this DWT-DTW approach, the performance plots of all classifiers with RIM-ONE data are more consistent and reliable. More fluctuations are seen in classification accuracy plots by orthogonal wavelets than by biorthogonal wavelets. Referring to the other classification measures, the proposed approach has more stable true-negative prediction rates (i.e., specificity) than true-positive prediction rates (i.e., sensitivity). Because regularity improves with the order, all performance plots hit the minimal values only with the lower-order orthogonal wavelets rather than with the higher-order orthogonal and biorthogonal wavelets. The corresponding confusion matrix metrics, such as true and false positives and negatives, are shown in Table 5. The proposed approach has either 0 or 1 false-negative prediction, with a maximum of 9 false-positive predictions for the ACRIMA dataset. In the case of ORIGA data, the approach has both types of false predictions with the NB classifier but zero false-positive predictions with other classifiers. This approach has very few incorrect predictions with RIM-ONE data. The proposed approach has generated a considerably lower range of incorrect predictions in the patient retinal dataset case. In the case of the Drishti dataset, the approach has higher true-negative predictions by all three classifiers. This approach also achieved steady, correct predictions with the HRF dataset.

The proposed DWT-DTW glaucoma classification approach’s performance has been compared with similar state-of-the-art methods, as shown in Table 6. Irrespective of feature extraction approaches, the SVM classifier is widely used. Several approaches have attained an accuracy range above 97% with the RIM-ONE dataset. The highest classification measures reported [23] among existing methods are 97.6% accuracy, 94.33% sensitivity, and 99.09% specificity in various cases. The application of the time-frequency domain (i.e., DWT) is utilized by several approaches [24] and [25] for feature extraction. In the case of patient retinal data, the performance of the existing approaches [26] and [27] is moderately low.

These advantages are compared with the state-of-the-art approaches (from Table 6). The summarized report has been given in Table 7. It shows a strong reason for using the DWT-DTW method for glaucoma classification rather than existing approaches.

Further, the phase-wise research findings of the proposed CAD-based glaucoma screening method are as follows:

•   Retinal image pre-processing: (i) Qualitative retinal images have been generated due to enhancement of the images’ luminance and texture; (ii) The suggested approach improves the images without affecting the original texture using image-specific characteristics.

•   Retinal image feature extraction: (i) DTW trajectories corresponding to various wavelets’ coefficients and RM values enable us to extract significant image texture patterns; and (ii) Various topological graphs make the texture analysis powerful.

•   Retinal image classification: (i) Biorthogonal wavelet-based graph features are stronger for glaucoma classification than orthogonal wavelets; (ii) SVM and RF classifiers have achieved high glaucoma classification accuracy.

Overall, it has been determined that the combination of the biorthogonal wavelet family and DTW-based graph theory is optimal for glaucoma screening.

5  Conclusions and Future Work

The proposed CAD-based glaucoma classification is a unique approach that utilizes the combination of time-frequency localization and graph theory. Images’ textures are improved in a balanced way using image-dependent details. Various topological graphs have been generated for each retinal image to explore pixels’ neighborhood relationships using in-depth time-frequency analysis. It identifies significant directional texture patterns for accurate screening. Results have proven that the proposed enhancement improves the images’ quality without altering their texture patterns. The proposed DWT-DTW-based glaucoma screening has achieved an average accuracy of 99.5%, 98.9%, 99.56%, 96.6%, 88.8%, and 98.5%, sensitivity of 100%, 96.4%, 99.3%, 95%, 100%, and 99.03%, and specificity of 98.06%, 99.4%, 99.7%, 100%, 80%, and 98.06% on the ACRIMA, ORIGA, RIM-ONE, Drishti, HRF, and HOSPITAL datasets, respectively. Our approach has achieved optimal performance for biorthogonal DTW and RF or SVM classifiers combination. Moreover, the DWT-DTW method has achieved highly satisfactory classification accuracy in the case of patient data. The performance of the proposed method has been compared with state-of-the-art methods, and its performance is far better than existing methodologies. Thus, this CAD approach will become a powerful aid for ophthalmologists in providing faster and more accurate glaucoma screening. However, the proposed approach has fewer limitations, which include that the classification accuracy is slightly lower with smaller datasets and that this approach suffers from incorrect predictions for some combinations. These limitations will be addressed in our future work using multi-level graph CNNs.

Acknowledgement: The fundus images used in this study were given by the Goutami Eye Institute, Rajamahendravaram-533105, Andhra Pradesh, India. We would like to express our deep and sincere gratitude to Dr. Y. Srinivas Reddy, M.S. (Ophthal), and Dr. A. Prasanth Kumar, M.S. (Ophthal), for providing corresponding information and the fundus images.

Funding Statement: The authors received no specific funding for this study.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.

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