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In this study, we propose a Second Order Shearlets (SOS) based system for Oral Cancer Classification (OCC) that leverages histopathological images. The fundamental premise of the system is the observable variations in texture patterns between normal and abnormal cells within these images, which can be exploited for differentiation. The images undergo a transformation from the RedGreenBlue (RGB) color space to the HueSaturationValue (HSV) color space, followed by the extraction of cooccurrence texture features via the SOS system. Further enhancement of feature extraction is achieved by applying a median filter for denoising the histopathological images. The proposed SOSOCC system, equipped with a probabilistic classifier at the final stage, was presented with an assortment of 1224 images for evaluation. The results indicated a noteworthy classification accuracy of 98.6% when employing stratified kfold crossvalidation, thereby underlining the system's efficacy in identifying oral cancerrelated abnormalities. Moreover, a comparative analysis was conducted with Wavelet, Curvelet, and Contourletbased representation systems to underscore the superior performance of the SOSOCC system. This study provides valuable insights into the application of the SOS approach to oral cancer classification and sets a promising precedent for future research.
oral cancer, multiscale analysis, multidirectional analysis, Second Order Shearlets, colour spaces
Oral cancer, a result of cellular mutations within the oral cavity, manifests a higher incidence in males compared to females. Risk factors include smoking, excessive alcohol consumption, a suboptimal diet, and a familial history of cancer. Early diagnosis enhances survival rates, thus necessitating the development of effective classification systems [1].
Prior studies have focused on various aspects of Oral Cancer Classification (OCC) systems. For instance, one utilized temporal features, energy, and entropy components from each color channel of median filtered histopathological images, employing knearest neighbors and support vector machine classifiers for OCC [1]. Another study implemented a Convolutional Neural Network (CNN) based OCC system with optimally adjusted layers and filters for high performance extraction of deep features [2]. Efforts to reduce computational complexity led to the development of a lightweight CNN model with fewer parameters [3], while an attentionbased CNN system was designed to offer two paths for efficient classification: compression and learning [4].
In addition to these, the literature also presents OCC systems that employ a fuzzy Support Vector Machine (SVM) [5], a multiple instance learningbased approach [6], and asymmetric residual hashbased histopathological image retrieval [7]. Other studies have focused on the development of a matrix form classifier [8], dictionary learning for histological image classification [9], an autoencoder based system [10], and a feature blending approach [11]. Spatial and morphological methods have also been explored [12], as have adaptive fuzzy systems [13], trust countingbased systems [14], and the use of a golden eagle optimization algorithm for feature selection [15]. Furthermore, the influence of dimensionality within CNN has been examined [16].
In light of the aforementioned studies, the present work aims to explore the extraction of textures from histopathological images using Second Order Shearlets (SOS) for OCC. The proposed approach involves the use of cooccurrence features of SOS subbands for the discrimination between normal and abnormal images.
The remainder of the paper is structured as follows: Section 2 elaborates on the design of the SOSbased OCC system, while Section 3 presents a comparative analysis of the SOSOCC system's results with those of Wavelet [17], Curvelet [18], Contourlet [19], and First Order Shearlets (FOS) based systems. Finally, Section 4 provides a conclusion, drawing upon the experimental results.
The structures within the histopathological images may give rise to either lowlevel or highlevel textures. In many cases, such textures are influenced by disease processes. The proposed SOS for the OCC system is considered a binary pattern recognition system with three stages; preprocessing, feature extraction, and probabilistic classification. Figure 1 shows the block diagram of the SOS based OCC system.
Figure 1. Proposed SOSOCC system using histopathological images
2.1 Preprocessing
This is the first stage of the SOSOCC system where noise removal and colour space conversion occur. A median filter, which is a nonlinear filter, is employed to remove noise and preserve edges [1]. This study uses a small window of 3×3 and finds the median value inside the window. The center pixel is replaced by the median value to restore the noisefree pixel. This process is repeated until the last pixel is restored. It is an order statistic filter that operates on the data inside a window of size (2m+1, 2m+1). It is defined by
$\begin{array}{r}M F_{i j}=\operatorname{median}\left\{I_{i+k, j+l}: k, l=m, \ldots m\right\} \\ \text { for } i, j=(m+1) \ldots . .(nm)\end{array}$ (1)
where, the noisy image is represented as I and the pixel’s location are (i,j). Figure 2(a) shows the histopathological images and Figure 2(b) shows its corresponding noise free images.
After noise removal, RGB to HSV (Hue, Saturation, and Value) colour space conversion takes place. The HSV colour space aligns with the human vision more closely than the RGB colour space. It represents the models in such a way that how colour appears under the light. The conversion formulae [20] are as follows:
$\begin{array}{r}H=\cos ^{1} \frac{0.5[(RG)+(RB)]}{\sqrt{(RG)^2+(RB)(GB)}} \\ H \in[0, \pi] \text { for } B \leq G\end{array}$ (2)
$\begin{array}{r}H=2 \pi\cos ^{1} \frac{0.5[(RG)+(RB)]}{\sqrt{(RG)^2+(RB)(GB)}} \\ H \in[\pi, 2 \pi] \text { for } B \succ G\end{array}$ (3)
$S=1\frac{3}{R+G+B} \min (R, G, B)$ (4)
$I=\frac{R+G+B}{3}$ (5)
where, H, S, and V represent the Hue, Saturation and Value components in the HSV colour space corresponding to R (Red), G (Green), and B (Blue) components in the RGB colour space. Figure 3(a) shows the HSV images of RGB images in Figure 2(b) and the components of HSV colour spaces are shown in Figure 3(b) to Figure 3(d).
Figure 2. (a) Input histopathological images (b) Noise free images by median filter
Figure 3. (a) HSV images of RGB images in Figure 2(b); (b) H channel; (c) S channel; (d) V channel
2.2 Feature extraction
In this stage, a perceptionbased statistical method is employed to extract histopathological images' features. The 1^{st} order stochastic features are based on the Probability Density Function (PDF) distribution of intensities. In contrast, the 2^{nd} order features are obtained from the PDF of pairs of intensity levels. The cooccurrence features are based on the estimation of the 2^{nd} order joint PDF f(i,jΔx,Δy) where the spacing between the pair of pixel (i,j) in the x and y directions are represented by Δx and Δy respectively. It is defined for an input image I of size NxN.
$C_{\Delta(i, j)}=\frac{\#(((x, y),(x+\Delta x, y+\Delta y)): I(x, y)=i, I(x+\Delta x, y+\Delta y)=j)}{\#(((x, y),(x+\Delta x, y+\Delta y)): 1 \leq x, y, x+\Delta x, y+\Delta y) \leq N}$ (6)
The application of Eq. (6) produces a cooccurrence matrix from which a number of stochastic texture features can be computed. To compute the cooccurrence matrix, the frequency of occurrence of a pixel with intensity i adjacent to a pixel with intensity j is generated for all elements (i,j) of the given square matrix. Then the normalized cooccurrence matrix is obtained by dividing all elements in the cooccurrence matrix by the total number of frequency of occurrences. Due to the normalization, the sum of all elements in the cooccurrence matrix equals 1. There are 14 features [21] that can be extracted and are undoubtedly the most wellknown features used in many texture analysis methods in the medical domain. Table 1 shows the extracted texture features.
Table 1. SOSOCC system's performance measures
No 
Features 
No 
Features 
1 
Contrast 
8 
Angular second Moment 
2 
Sum of Squares (Variance) 
9 
Correlation 
3 
Sum Average 
10 
Inverse different moment 
4 
Entropy 
11 
Sum Variance 
5 
Difference Variance 
12 
Difference Entropy 
6 
Sum Entropy 
13 
Maximal Correlation Coefficient 
7 
Information Measures of Correlation1 
14 
Information Measures of Correlation2 
Before feature extraction, each component of HSV image is represented by SOS [22, 23]. From the obtained SOS subbands, the stochastic texture features are extracted. The SOS is defined by
$\psi_{c s t}(x)=\frac{1}{\left\operatorname{det} P_{s d}\right} \Psi\left(P_{s d}^{1}(xt)\right)$ (7)
where, P_{sd} is the product of SOS operator and dilation matrices. They are defined in Eq. (8) and Eq. (9) respectively.
$S_r^{(l)}(x):=\left(\begin{array}{cc}1 & \sum_{m=1}^l r_m x_2^{m1} \\ 0 & 1\end{array}\right)\left(x_1, x_2\right)^T$ (8)
$A_{a, \alpha}=\left(\begin{array}{cc}a & 0 \\ 0 & a^\alpha\end{array}\right)$ where $a>0$ and $\alpha \in[0,1]$ (9)
where, α is the scaling factor and $\alpha=\frac{1}{3}$ is used to analyze the SOS for OCC. This scaling helps to identify the location and the direction of discontinuity curves. For frame construction, the decomposition system employs some form of anisotropy. The orientation and location of system elements are controlled by the constructed frames. Ridgelet transform uses α=0, wavelet transforms use α=1 and the Curvelet and Shearlets use α=0.5. These values are not sufficient for separating different curvatures by the SOS that requires $0<\alpha<\frac{1}{2}$. The rates of decay vary depending on the circumstances, which in turn makes it possible to locate the boundaries. Using this scaling with $\alpha=\frac{1}{3}$, the decay rate of SOS offers more precise curvature and orientations of distinct areas in an image [23]. Figure 4 shows samples of 3^{rd} level subbands of different representation systems. Features are extracted from each channel of the HSV colour space. From each subband, a total of 42 features are extracted per sample.
Figure 4. Subbands at 3rd level decomposition (a) SOS (b) FOS (c) Contourlet (d) Curvelet (e) Wavelet
2.3 Probabilistic classification
The probabilistic classifiers compute the possibilities of samples that may fall into one or more classes. The Bayesian classifier performs better in many medical image classification systems than the probabilistic classifiers. Using the posterior probabilities, the Bayesian classifier classifies whether the sample belongs to normal or abnormal. Let us consider the test sample as s. The Bayesian classifier is defined by
$\left\{\begin{array}{l}P\left(\omega_1 \mid s\right)>P\left(\omega_2 \mid s\right), \text { normal } \\ P\left(\omega_1 \mid s\right)<P\left(\omega_2 \mid s\right), \text { abnormal }\end{array}\right.$ (10)
where, $P\left(\omega_1 \mid s\right)$ and $P\left(\omega_2 \mid s\right)$ denote the posterior probabilities of belonging to normal and abnormal respectively. These probabilities can be obtained using Bayesian theorem and are given by:
$P\left(\omega_1 \mid s\right)=\frac{P\left(\omega_1\right) P\left(\omega_1 \mid s\right)}{P(s)}$ (11)
$P\left(\omega_2 \mid s\right)=\frac{P\left(\omega_2\right) P\left(\omega_2 \mid s\right)}{P(s)}$ (12)
Suppose the prior probability P(ω_{1}) and P(ω_{2}) are equal to each other. The Bayesian classifier in Eq. (9) can be yielded as:
$\left\{\begin{array}{l}P\left(s \mid \omega_1\right)>P\left(s \mid \omega_2\right), \text { normal } \\ P\left(s \mid \omega_1\right)<P\left(s \mid \omega_2\right), \text { abnormal }\end{array}\right.$ (13)
Thus, the classification depends on the comparison between $P\left(s \mid \omega_1\right)$ and $P\left(s \mid \omega_2\right)$.
The power of texture to discriminate oral cancer patients from normal subjects is accessed from 1224 (290 normal and 934 abnormal) histopathological images [24]. Figure 5 shows the histopathological images of normal and abnormal categories. As the resolutions of images in the databases are not equal, the resolution of images is set to 256×256 pixels after median filtering. In order to represent the images in SOS, Wavelet, Curve let, and Contourlet, a squareshaped resolution (256×256) is chosen.
The commonly used model evaluation approaches are train/test split and kfold crossvalidation. Though they are very effective, they provide misleading results when used on an imbalanced database. As the database is imbalanced (290 normal and 934 abnormal), stratified kfold crossvalidation is employed. It is an extension of the standard kfold crossvalidation. The standard approach divides the dataset into kfolds, but it does not ensure that each fold has the same number of images per category. In contrast to the standard approach, the stratified approach maintains the same number of images per category in each subset. In this approach, stratified 10fold crossvalidation is employed. Thus, each fold has 29 normal and 93 abnormal samples. The remaining four abnormal samples from 934 samples are added in the last fourfolds. The SOSOCC system’s performance measures are shown in Table 2 and the confusion matrices obtained by the features are shown in Figure 6. In Figure 6, zero (0) represents the abnormal class and one (1) represents the normal class.
It is inferred from Figure 6 that the SOSOCC system performs significantly better than others, with an overall accuracy of 98.6%. The sensitivity and specificity of the SOSOCC system are 99.1% and 96.9%, respectively. The accuracies of other systems are 95.4% (Contourlet), 93% (Curvelet), and 90.4% (Wavelet). The obtained texture features from histopathological images contribute to significant performance improvement. Texture features from other transformations such as wavelet and contour let are insufficient to significantly discriminate the normal and abnormal tissues, thus their performances are less than the SOS based system. Figure 7 shows the OCC system's ROCs by different representation systems. In Figure 7, true positive rate is the positive prediction rate (sensitivity) of the system, whereas the false positive rate is the incorrect prediction of positive classes (1specificity).
The most striking feature of all ROCs is how they are very close to the yaxis. Based on this feature, the ROC curve is interpreted. The two ends of the curve correspond to situations in which all states are considered to be normal (specificity=0 and sensitivity=1), or all states are considered to be pathological (specificity=1 and sensitivity=0), respectively. The points in the middle represent different degrees of decision making that are intermediate in nature. The ROC curve of a perfect observer, who never makes an incorrect diagnosis, will look like a stepbystep function, with axes that are labeled x=0 and y=1, whereas the ROC curve of a chance observer, who randomly diagnoses each case as normal or abnormal, will look like a straight line with a gradient of one that passes through the origin. If the ROC is located closer to the top left corner of the graph, then one observer is superior than the other (0.1 point). So, this provides a framework by which to compare the observations of many witnesses (in this case, automated techniques). The ROC curves for each observer may be derived, and then a comparison can be made by selecting (as the best observer) the curve that is located in the area of the graph that is most directly above the top left corner.
As this curve is drawn between the sensitivity and 1specificity, the curve for the system very close to the yaxis is the best compared to others. Thus, the best system for OCC is in the order of SOS>FOS>Contourlet>Curvelet>Wavelet. All the performance measures shown in Figure 6 and Figure 7 are obtained by decomposing the histopathological images at 3level with 8directions. Figure 8 shows the performance for other levels of decomposition.
Figure 5. Sample histopathological images
Table 2. SOSOCC system's performance measures
Sensitivity (%) 
Specificity (%) 
Overall Accuracy (%) 
True Positive (TP) 
True Negative (TN) 
TP+TN 
True Positive (TP)+True Negative (FN) 
False Positive (FP)+True Negative (TN) 
TP+FP+TN+FN 
Table 3. SOSOCC system's performance for different validation approaches
Techniques 
System Accuracy (%) 

Random Split (70:30) 
kfold Cross Validation (k=10) 
stratified kfold Cross Validation (k=10) 

Wavelet 
84.5 
86.8 
90.4 
Curvelet 
88.5 
90 
93.0 
Contourlet 
90.8 
92.6 
95.4 
FOS 
93 
94.8 
96.4 
SOS 
95.7 
96.5 
98.6 
(a) Wavelet
(b) Curvelet
(c) Contourlet
(d) FOS
(e) SOS
Figure 6. Confusion matrices of the OCC system using different representation systems
It can be seen from Figure 8 that the features from the 3rd level of representation systems provide better results than the other levels. This is because lowlevel features cannot distinguish the patterns of normal and abnormal images. While increasing the level from 1 to 2 and then to 3, the system’s accuracy increases as more discriminating features are extracted. However, the system’s accuracy decreases due to the redundant data at higher levels [25]. Among the representation systems, the performance of Wavelet is poorer as it provides only three directional features such as diagonal, vertical and horizontal.
Table 3 shows the performance of stratified kfold crossvalidation approach with other validation approaches such as random split (70:30) and kfold crossvalidation in terms of accuracy using 3^{rd} level features from each representation systems. It can be seen from Table 3 that the stratified kfold crossvalidation approach gives better results than other validation approaches. This is because the stratified kfold crossvalidation is better for imbalanced dataset.
Figure 7. OCC system's ROCs by different representation systems
Figure 8. OCC system's performances for different levels
The texture changes in the histopathological images are significant in interpreting them to achieve high classification accuracy. In this work, an SOS based OCC system is designed using histopathological images. The texture differences between the abnormal and normal histopathological images are assessed using 1224 images obtained from oral cancer patients. The resulting 2^{nd} order stochastic texture feature achieved a classification accuracy of 98.6% (Sensitivity 99.1% and specificity 96.9%) using a Bayesian classifier. The results proved that the SOSOCC system might have applications in the early detection of oral cancer. The performance of the stochastic texture features is analyzed using different frequency domain representation systems such as Wavelet, Curvelet, Contourlet, FOS, and SOS. The obtained accuracies are 96.4% (FOS), 95.4% (Contourlet), 93% (Curvelet) and 90.4% (Wavelet). In the future, the specificity of the SOSOCC system can be improved by using a balanced database while training and testing the classifier.
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