3.1 Image Acquisition

This study uses CT and MR images to sort a dataset of liver cancer cases into six groups. Two types of liver cancer were gathered in the image dataset: (i) benign, such as hepatocellular adenoma, hemangioma, and cyst; (ii) malignant, such as hepatocellular carcinoma, metastasis, and hepatoblastoma. Siemens Somatom definition-AS 64 and Siemens Essenza 1.5T machines with resolutions of 0.5-0.625 mm and 1-2 mm are used in the radiology department of Bahawal Victoria Hospital in Bahawalpur, Pakistan, to collect the MRI and CT datasets. The dataset containing 1200 $(100\times 6\times 2)$fused imageries was obtained. Among these, 100 patients were chosen for the examination utilizing CT scan, and 100 patients utilizing MR images with $(512\times 512)$ resolution.

3.2 Image Preprocessing using Color Wiener Filtering (CWF)

The input CT and MRI images were preprocessed using CWF. The input images have more noise illumination and noise effect. The preprocessing technique CWF was used to avoid the influence of these factors on the input image.CWF was used to restore the image after low-pass filtering rendered it blurry, stripped it of its structural information, preserved important structures, and eliminated undesirable, tiny image wrinkles or isolated edges. Restored color space, including additive noise in RGB original color space, is expressed as Eq. (1).

where $v_{i}$indicates the value of the preprocessing image;$k_{i}$denotes the pixel vector of the input image;$\eta _{i}$is the noise in the image. $i$ specifies the pixel of an image as $i(a,b)$, where $a$ and $b$are directions of the pixel axis;$v_{i}$is the mean vector of the recovered imagery$r_{i}$; $\hat{k}$ implies pixel vector of the proper image;$\overline{k}$specifies the mean vector of the proper image. The parameters with CWF filtering,$V$, is labelled in Eq. (2),

where $V$needs to be computed to identify MSE between the input and preprocessing pictures, MSE is expressed in Eq. (3),

When there is no correlation with noise, the considered image $V$ in the original image is scaled using Eq. (4):

where$C_{nn}$is the noise, and $C_{\mathrm{cov}}$is the covariance matrix. Therefore, the input image noises are eliminated, The preprocessing output is supplied to the feature extraction process.

3.3 Feature Extraction Utilizing Improved Non-sub Aampled Shearlet Transforms (INSST)

In the feature extraction stage, preprocessed images are extracted using INSST. A description of feature extraction through the INSST is described in detail. In this stage, with the aid of INSST, four different kinds of features are extracted from MR and CT image data sets, including "Co-Occurrence Matrix," "Wavelet," "Run-Length Matrix," and "Histogram."

3.4 Liver Cancer Classification based on Binarized Spiking Neural Networks

The features extracted using the INSST approach were given to a BSNN for classification. BSNN was used to classify liver cancer from the extracted features of the CT and MR images. where$c$ refers $c=s\left(x\right)$, $s$refers sign. To classify liver cancer, the intensity range (IR) is$\left[0,IR\left(Max\right)\right]$, and the firing time of the $b^{th}$ input features is specified as $input_{b}$under $b^{th}$ intensities, $IR_{b}$ is articulated in Eq. (13):

Here $FT$implies firing time. The input neuron’s latency is decreased, then the classification time is lower. Subsequently, the spike neuron of $b^{th}$ intensity equation is expressed in Eq. (14):

The fire neuron of the $l^{th}$layer agrees the input features of ${-}$1 or +1to determine the synaptic weights. Subsequently, liver cancer is predicted as normal using$X_{a}^{l}\left(ft\right)_{FA}$, as expressed in (15):

where$c_{ab}^{l}$and $SP_{b}^{l-1}$ denotes input spike patterns and binary synaptic weight linked to $b^{th}$and$l^{th}$ neurons;$\beta $ implies scaling factor for raising accuracy and linked to each neuron. It is given in Eq. (16):

where $SP_{b}^{l}\left(<ft\right)\neq 1$; hence, the neurons are not fired with the prior time step. The threshold factor for achieving the result takes the role of this scaling and function. The weight parameters are $CP$and$\chi $, where $CP$ is accuracy and$\chi $ diminish the error rate. The proposed BSNN proficiently classified lung cancer as normal and abnormal. The weight parameters $CP$and$\chi $of BSNN were optimized under the CHA to derive more exact categorization.

3.4.1 Step by Step Procedure of Color Harmony Algorithm for Optimizing the Weight Parameter of BSNN

The CHA maximizes the BSNN performance by increasing the liver cancer classification. Therefore, the proposed BSNN method provides appropriate liver cancer classification and also reduces the error probability. The step-by-step procedure of the CHA is expressed as follows:

Step 1: Initialization

Initially, every solution candidate is viewed as a color holding various decision variables. Colors are initially dispersed at random throughout the search area and are expressed as Eq. (17)

(17)

$ Y^{0}\left(a,b\right)=Y^{L}\left(a\right)+rand\cdot \left(Y^{U}\left(a\right)-Y^{L}\left(a\right)\right) $

where$a=1,2,\ldots ,T_{V}$, $b=1,2,\ldots ,T_{C}$, and $Y^{0}\left(a,b\right)$ indicates initial value of $b^{th}$ color, $Y^{L}\left(a\right)$, and $Y^{U}\left(a\right)$ indicates lower and upper bound of $a^{th}$ variable, $rand$denotes the uniformly distributed count at $\left[0,1\right]$interval, $T_{V}$, and $T_{C}$ indicates the entire count of variable and colors.

Step 2: Random Generation

The first chroma zone color distribution was carried out after producing the initial population. Initially, colors are arranged in ascending sequence by their fitness value.

Step 3: Fitness Function

By comparing the values of each potential solution to those of the objective function variables, the fitness function of the issue may be calculated. As a result, Eq. (18) was used to express the values acquired for the objective function:

(18)

$ Fitness\,Function=Optimization\left[CP\,and\,\chi \right] $

Step 4: Concentration Phase

This stage focuses on the search for space exploration and exploitation and employs a selection scheme to balance local and global searches.. The goal is to increase the$CP$and decrease$\chi $.

Step 5: Updating the hue circle at the dispersion phase for optimizing$\chi $of the BSNN

The hue circle is updated after this phase by adding new colors that include helpful fitness-related data through which the parameter $\chi $is optimized. This process was calculated using Eq. (19),

(19)

$ S_{Y}^{new}\left(a,b\right)=d_{cm}S_{CM}\left(a,b\right)+\left(1-d_{cm}\right)S_{Y}\left(a,b\right) $

where$a=1,2,\ldots ,T_{V}$;$b=1,2,\ldots ,T_{S}$;$S_{CM}$ and $S_{Y}$indicates the optimized parameter of BSNN;$T_{S}$is the replaced colors;$d_{cm}$ indicates the uniformly distributed random number.

Step 6: Termination

Finally, the proposed BSNN with the CHA categorizes liver cancer as normal and abnormal with greater accuracy. If the optimal solution is achieved, the iteration is stopped; if not, steps 1 to 3 are repeated until the halting criteria,$y=y+1$, are fulfilled Fig. 2 shows that the Flowchart of the Color Harmony Algorithm.

Fig. 2. Flowchart of the Color Harmony Algorithm.

4.1 Performance Measures

This was used to examine the robustness of the proposed BSNN-CHA-LCC technique. The given confusion matrix was used to measure the metrics.

· True Positive ($A_{Q}$): normal accurately classified as normal.

· True Negative ($A_{M}$): abnormal accurately classified as abnormal.

· False Positive ($B_{Q}$): abnormal inaccurately classified as normal.

· False Negative ($A_{Q}$): normal inaccurately classified as abnormal.

4.2 Performance Analysis

Figs. 4-10 present the evaluation results of the proposed BSNN-CHA-LCC method. The acquired outcomes of the proposed BSNN-CHA-LCC are analyzed with the existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC models. Fig. 3 shows the output image for liver cancer classification.

Fig. 3. Liver cancer classification output.

Fig. 4 presents the accuracy analysis. The proposed method achieved31.88%, 29.75%, and 21.16% higher accuracy for normal liver cancer; 28.86%, 36.79%, and 34.33% better accuracy for abnormal liver cancer compared to the existing methods, such as MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC, respectively.

Fig. 4. Accuracy analysis.

Fig. 5 depicts precision analysis. Here, the proposed BSNN-CHA-LCC achieved 39.24%, 21.25%, and 22.29% higher precision for the normal liver cancer classification, and 13.67%, 23.16%, and 29.65% greater precision for the abnormal liver cancer classification compared to the existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC, respectively.

Fig. 5. Precision analysis.

Fig. 6 displays specificity analysis. The proposed BSNN-CHA-LCC method achieved 22.25%, 29.16%, and 21.33% higher specificity for a normal liver cancer classification and 33.22%, 28.19%, and 31.20% greater specificity for an abnormal liver cancer classification compared to the existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC models, respectively.

Fig. 6. Specificity analysis.

Fig. 7 shows the sensitivity results of the liver cancer classification. The proposed BSNN-CHA-LCC method attained31.21%, 29.51%, and 31.11% higher sensitivity for a normal liver cancer classification and 31.26%, 33.51%, and 31.61% greater sensitivity for an abnormal liver cancer compared to the existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC models, respectively.

Fig. 7. Sensitivity analysis.

Fig. 8 represents the F-scores results of the liver cancer classification. The proposed BSNN-CHA-LCC method achieves 29.01%, 27.74%, and 30.11% higher F-scores for benign data; 28.98%, 30.03%, and 33.44% better F-scores for malignant data for liver cancer than the existing MLP-LCC, mask-RCNN-LCC and DNN-GMM-LCC models, respectively.

Fig. 8. F-score analysis.

Fig. 9 represents the ROC curve. The overall accuracy is higher when the ROC curve was close to the upper left corner. The proposed BSNN-CHA-LCC method achieved 28.21%, 25.05%, and 22.11% higher ROCs for liver cancer than the existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC, respectively.

Fig. 9. Performance analysis of the ROC.

Fig. 10 outlines the Error Rate results of the liver cancer classification. The proposed BSNN-CHA-LCC method achieved 23.14%, 25.30%, and 21.44% less error rates for the normal liver cancer classification and 30.26%, 24.09%, and 22.78% lower error rates for the abnormal liver cancer classification compared with existing MLP-LCC, mask-RCNN-LCC, and DNN-GMM-LCC models respectively.

Fig. 10. Performance analysis of the Error Rate.

In this study, the proposed BSNN-CHA-LCC method was used to improve the accuracy of the system, and the BSNN was used to increase the classification accuracy. One of the main advantages of this approach was that it could improve the system accuracy without demanding substantial additional resources. On the other hand, it will be crucial to assess the success of this strategy in various contexts to identify any potential flaws and suggest areas for development. Table 1 lists that the BSNN-CHA-LCC model provided 4.52%, 9.45%, 11.45%, and 11.94% higher accuracy than the methods reported by Naeem et al. ^[7], Sun et al. ^[8], Das ^[9], and Khamparia et al. ^[10],. The BSNN-CHA-LCC attains 22.33%, 28.70%, 14.56%, 14.79% better precision than Naeem et al., ^[7] Sunet al. ^[8], Das et al., ^[9], and Khamparia et al. ^[10], respectively. The proposed BSNN-CHA-LCCachieved26.07%, 14.36%, 33.67%,and 14.32% higher sensitivity than the methods reported by Naeem et al. ^[7], Sun et al. ^[8], Khamparia et al. ^[10], and Alirr ^[18], respectively. The proposed BSNN-CHA-LCC attained 9.80%, 14.58%, 11.21%, and 12.31% higher specificity than the methods reported by Naeem et al. ^[7], Sun et al. ^[8], Das et al. ^[9], and Khamparia et al. ^[10]. The BSNN-CHA-LCC achieves 12.54%, 38.56%, 23.67%, and 30.22% better F-measure than existing methods, such as Naeem ^[7], Sun et al. ^[8], Khamparia et al. 10], and Alirr ^[18], respectively. The proposed BSNN-CHA-LCC model provides 11.22%, 22.22%, 45.14%,and 15.21% better ROCs than the methods reported by Naeem et al. ^[7], Sun et al. ^[8], Das et al. ^[9], Khamparia et al. ^[10]. The BSNN-CHA-LCC model provided 10.22%, 24.67%, 15.7%, and 18.11% lower error rates than the methods reported by Naeem et al. ^[7], Sun et al. ^[8], Khamparia et al. ^[10] and Alirr ^[18], respectively.