CT Image Segmentation Using Optimization Techniques under Neutrosophic Domain

: In this paper, we introduce a hybrid technique between optimization algorithms and neutrosophic theory. This new hybridization can deal with uncertainties in brain computed tomography (CT) images in three different memberships very effectively. To prove the real-time application of this theory, a new segmentation method for brain CT medical images is presented. The grayscale medical image suffers from uncertainties and inconsistencies in the gray levels due to their bad luminance. The proposed technique addressed this problem by performing neutrosophic operations on gray levels based on the S membership function.


Introduction
The segmentation process in medicine aims to extract the region of interest (ROI) object (organ) from a medical image (2D or 3D).It separates an image into regions according to a given outline, for example, segmenting human tissues or organs in medical applications for border detection, tumor detection/segmentation, and mass detection [1].Furthermore, computed tomography (CT) medical imaging suffers from different uncertainty problems that affect the process of image segmentation.A CT is a gray-level image with large amounts of noise and a low level of intensity.Additionally, CT has poor edge representation and contrast regions.With so little data and low-quality images.These problems pose a challenge in the segmentation process because they can degrade the efficiency of the whole image processing operation.So, it's important to use methods that can handle and deal with uncertain information within images [2] The fuzzy set (FS), intuitionistic fuzzy set (IFS), and neutrosophic set (NS) were developed to deal with uncertainties.FS theory was introduced by Zadeh to deal with uncertainty based on the degree of membership [3].The FS theory is used widely in medical image segmentation.Zhang et al. [4] proposed the Reference-guided Fuzzy Integral GAN (RFI-GAN) generating ultrasound images by combining feature fusion between samples and reference sets.It generalizes feature additivity to nonadditivity using fuzzy integral.Two Fuzzy Integral Modules are proposed for the nonlinear fusion of texture and structure features.Another contribution by Zhao et al. [5] presents a BLS surrogateassisted evolutionary framework for improving time efficiency in clustering-based image segmentation.The BLS-MOEFC algorithm uses two fuzzy clustering objective functions, a BLS surrogate model-assisted multi-objective evolutionary framework, adaptive parameter updating, and a novel fuzzy clustering validity index.Also, Kumar et al. [6] introduced a new CoMHisP framework using a fuzzy support vector machine (SVM) with within-class density information.It extracts image micropatterns and computes the center of mass for each pixel.The framework performs well on a CMT dataset of histopathological images of canine mammary tumors and human In 1986, Atanassov introduced the IFS, which links each attribute in the universe with membership (M) and non-membership (non-M) degrees [7].Kumar et al. [8] proposed an optimization problem for the IFCM with spatial neighborhood information (IFCMSNI) method, incorporating intuitionistic fuzzy set theory and spatial regularization to handle noise in medical images.The method uses IFS and Sugeno's negation function.Also, Namburu et al. [9] proposed a simplified clustering method for melanoma detection, using the triangular membership function (TMF) to identify initial regions and intuitionistic fuzzy c-means clustering, achieving an average accuracy of 90%.Dahiya and Anjana Gosain [10] introduced a novel Type-II intuitionistic fuzzy C means clustering algorithm, combining Type-II membership with a hesitation degree.This algorithm offers advantages such as clear cluster definition, robustness to noise and outliers, and improved centroids' desired position.Compared to other fuzzy clustering algorithms, it outperforms others in accurately identifying lump shape and size in mammograms.The algorithm reduces the average error by 84% on synthetic data sets.
The segmentation methods goal under the FS, and IFS environment is to deal with the uncertainties within an image, but they suffer from some problems such as:  The segmentation approaches under the FS environment handle uncertainty by taking into consideration only the membership degree for image pixel values between[0,1]. The segmentation approaches under the FS environment handle uncertainty by taking into consideration only a hesitant degree in conditions of 'Membership' and "Non-Membership" degrees of image pixel values.Smarandache [11] proposed NS to associate each element with a {truth membership, Indeterminacy membership, and falsity membership} function independently.The NS has values ranging ] 0 − , 1 + [on real standard or non-standard subsets.Many applications can deal with the interval [0,1] because dealing with ] 0 − , 1 + [ in real situations is difficult [12].
On the other hand, a variety of segmentation approaches have been developed to address CT image segmentation, ranging from conventional methods to swarm intelligence techniques and metaheuristics.Anter et al. [13] proposed a dynamic approach to improve the fuzzy c-means clustering algorithm for automatic localization and segmentation of liver and hepatic lesions from CT scans.The approach uses fast-FCM, chaos theory, and bio-inspired ant lion optimizer (ALO) to determine optimal cluster centroids.Another contribution presented a novel multi-disease diagnosis model using chest X-ray images using deep learning approaches.The model uses standard datasets, pre-processing, segmentation, and classification using Optimized DeepLabv3, optimized by the Mutation Rate-based Lion Algorithm (MR-LA).The model improves sensitivity, precision, and specificity, achieving higher classification and detection accuracy.The recommended method outperforms other models in relative analysis [14].Chouksey et al. [15] investigated the effectiveness of antlion optimization (ALO) and multiverse optimization (MVO), two nature-inspired algorithms, in detecting tumors in medical images.ALO mimics antlion hunting behavior, while MVO is based on multiverse theory.The proposed algorithm outperforms other evolutionary algorithms and is faster than MVO.The results are analyzed using a Wilcoxon test.
The previous studies have outlined some challenges in CT brain segmentation:  The segmentation technique is complicated by bias areas and inconsistent borders present in CT images. Unfortunately, several factors make the segmentation of CT images difficult, including the patient's condition, and operator error. The increasing dimension of membership functions may pose challenges for high precision in addressing uncertainty.
An International Journal on Informatics, Decision Science, Intelligent Systems Applications Doaa El-Shahat, Nourhan Talal, Jun Ye, and Wen-Hua Cui; CT Image Segmentation Using Optimization Techniques under Neutrosophic Domain These problems highlight the critical need for a more thorough method in medical image segmentation to effectively handle fuzziness and uncertainty in CT brain images.This study presented a segmentation strategy based on optimization techniques under the NS domain.A comparison between Differential Evolution (DE), Spider Wasp Optimization (SWO), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA) optimization algorithm under the NS domain was implemented.Consequently, the following are this paper's main contributions:  Propose a segmentation approach based on NS that can deal with uncertainty by presenting a degree of indeterminacy. Compare five optimization algorithms under the NS domain. The NS image is obtained from the image guided by a DE, SWO, GWO, PSO, and WOA for optimized clustering for segmenting the medical images with reduced time consumption and efficient accuracy.The remainder of the paper is divided as follows.Section 2 provides the background needed for this study.Section 3 presents preliminaries for neutrosophic theory and optimization algorithms.Section 4 presents the steps of the proposed approach.Section 5 presents experimental results.Section 6 illustrates the conclusion and future directions of this proposal.

Related Work
Many studies aim to integrate NS with optimization and metaheuristics methods.Palanisamy et al. [16] proposed a method using NS combined with fuzzy c-means clustering (FCM) and modified particle swarm optimization (PSO) for brain tumor segmentation, achieving superior sensitivity, specificity, Jaccard, and dice values compared to FCM alone and FCM with NS.Ashour et al. [17] introduced a skin lesion detection method called optimized neutrosophic k-means (ONKM), based on genetic algorithms.The method optimizes the neutrosophic set operation to reduce indeterminacy in dermoscopy images.The Jaccard index is used as the fitness function.The ONKM method is applied to segment dermoscopy images, and its performance is evaluated using metrics like Dice coefficient, specificity, sensitivity, and accuracy.The ONKM method outperforms k-means and -kmeans methods in accuracy.
Another contribution by Anter et al. [18] proposed a segmentation approach for abdominal CT liver tumors using neutrosophic sets, PSO, and fast fuzzy C-mean algorithm (FFCM).The method involves removing intensity values and high frequencies, transforming the image to the NS domain, optimizing FFCM using PSO, and clustering the livers using PSOFCM.The results showed neutrosophic sets offer accurate, less time-consuming, and noise-sensitive segmentation on nonuniform CT images.
Sayed et al. [19] presented an automatic mitosis detection approach for histopathology slide imaging using NS and moth-flame optimization (MFO).The approach involves two phases: candidate extraction and classification.The Gaussian filter is applied to the image, and morphological operations are applied to enhance it.The best features are selected using the meta-heuristic MFO algorithm.The approach is tested on a benchmark dataset of 50 histopathological images, including breast pathology slides.The results show the MFO feature selection algorithm maximizes classification performance, with high accuracy, recall, precision, and f-score.
Hanbay and Talu [20] introduces a novel SAR image segmentation algorithm based on the neutrosophic set and an improved artificial bee colony (I-ABC) algorithm.The algorithm uses threshold value estimation to search for a proper value in grayscale intervals.The I-ABC optimization algorithm is used to find the optimal threshold value.The paper contributes to SAR image segmentation by introducing a hybrid model with two feature extraction methods and demonstrating its effectiveness in real SAR images.
An International Journal on Informatics, Decision Science, Intelligent Systems Applications Doaa El-Shahat, Nourhan Talal, Jun Ye, and Wen-Hua Cui; CT Image Segmentation Using Optimization Techniques under Neutrosophic Domain Another study introduced a new methodology for license plate (LP) recognition using image processing algorithms and an optimized neutrosophic set (NS) based on genetic algorithm (GA).The methodology uses edge detection, morphological operations, and a new methodology using GA to optimize NS operations.The k-means clustering algorithm and connected components labeling analysis (CCLA) algorithm are used to segment characters.The proposed methodology is suitable for both Arabic-Egyptian and English LP, achieving high recognition accuracy in high-resolution Egyptian and low-resolution-corrupted English.The system also achieves 92.5% accuracy in image disturbances [21].From previous studies, we conclude that  No studies are comparing different optimization techniques under the neutrosophic domain. Few studies investigate the results of hybrid NS and optimization in medical images.

Neutrosophic Sets
The NS can deal with uncertainty and fuzziness within any data by describing the attribute with three components such as the True (T), Indeterminate(I), False (F) subsets.The CT images are mapped into the NS domain.Where a pixel P in the image is defined as P(T, I, F) where t, i, and f are the true, indeterminate, and false in the set, respectively, as t diverges in T, i diverges in I, and f diverges in F.Then, the pixel P(x, y)in the image space is transformed into the NS space PNS (x, y) = {T(x, y), I(x, y), F(x, y)}.T(x, y), I(x, y) and F(x, y)are the corresponding probabilities which are given by [27]: (2) (, ) = ((, ) − (, ) (, ) = (, ) −     −   (5) where the pixels in the window have (, ) local mean, and (, ) implies the absolute value of difference among intensity (, ) and its  (, ).
The entropy is computed for a grayscale image to evaluate the distribution of gray levels.When the intensities have a uniform distribution and equal probability, maximum entropy occurs.When intensities have nonuniform distribution and varying probabilities, little entropy arises.The totality of the T, I, and F entropies is referred to as the entropy in the neutrosophic image, and it is used to calculate the element distribution in the NS domain [27].The entropy can be donated by the following where the entropies are   ,   , and   for T, I, and F, respectively.Furthermore, the probabilities of the element  are   (),   (),    () in T, I, and F, respectively.

Proposed Algorithm
The neutrosophic set theory allows us to uncertainties, imprecision, and vagueness in image data.By combining optimization algorithms with neutrosophic image segmentation, we can improve the adaptability of the segmentation process to different image types and conditions.Optimization algorithms can also help refine the segmentation process by iteratively adjusting the parameters of some membership functions to maximize the entropy, thereby aiding in segmenting the images more accurately.In this study, we employ the S membership function to generate both T and F domains in NS theory.This function is mathematically defined as follows: where , , and  are three parameters that need to be accurately estimated to better separate the true and false NS domains.  is used as an objective function to be optimized for reaching the near-optimal values for those parameters.To perform this optimization process, the DE algorithm is herein employed due to its high performance and stability for several optimization problems [22].

Results and Discussion
This section assesses the performance of the DE algorithm when applied to search for the nearoptimal intervals of the S membership function that could accurately segment the true (object) and false (background) NS domains from eight brain tumor MRI images.The MRI images used in our experiments are shown in Table 1.The performance of this algorithm is compared to four metaheuristic algorithms, such as spider wasp optimizer (SWO) [23], grey wolf optimizer (GWO) [24], particle swarm optimization (PSO) [25], and whale optimization algorithm (WOA) [26] in terms of four performance metrics, such as best entropy, worst entropy, average (Avg) entropy, and standard deviation (SD).All algorithms are executed 25 independent times, and those performance metrics are computed under the estimated outcomes and reported in Table 2. Inspecting this table shows that DE is the highest-performing algorithm because it could achieve the best outcomes for all test images.To show those findings more clearly, Figure 1 is presented to compute the average entropy obtained by each algorithm on all test images.From this figure, DE is the best, WOA is the second best, and PSO is the worst algorithm.Table 3 displays the NS domains for three test images obtained by the intervals optimized by DE.Finally, Figure 2 shows the convergence curves of various algorithms on three test images, showing the superiority of DE.

Conclusion and Future Work
In this paper, a novel segmentation algorithm based on a Neutrosophic set and optimization techniques has been introduced.The applicability of the image segmentation under the neutrosophic domain was demonstrated on CT images.In our approach, Neutrosophic was obtained to transform the grayscale CT image to the NS domain and measure uncertainties using Neutrosophic entropy.The experiments were presented on 8 CT images.

Figure 1 .Figure 2 .
Figure 1.Average entropy obtained by each algorithm on all test images.
An International Journal on Informatics, Decision Science, Intelligent Systems Applications It achieves a classification accuracy of 97.25%, outperforming traditional ML and deep FE-VGGNET16-based feature descriptors.

Table 1 .
An International Journal on Informatics, Decision Science, Intelligent Systems Applications Doaa El-Shahat, Nourhan Talal, Jun Ye, and Wen-Hua Cui; CT Image Segmentation Using Optimization Techniques under Neutrosophic Domain Brain tumor MRI images used in this study.

Table 2 .
Comparison among algorithms under various performance indicators.