Multilevel Thresholding Research Articles

Simplified expression and recursive algorithm of multi-threshold Tsallis entropy

Image segmentation is an important step in obtaining image information, and it has always been an extremely critical link in the fields of computer vision and pattern recognition. Because of its simplicity and effectiveness, threshold-based image segmentation technology has received significant attention and research by researchers. Tsallis entropy and Renyi entropy are two important global threshold selection methods in image thresholding. They not only have a special correspondence in mathematical expression, but also have a certain relationship in the field of image segmentation. Considering the number of thresholds increases, the complexity of the expression of Tsallis entropy criterion function also increases sharply, which is difficult to apply in multiple thresholds. Given this, this paper proposes a simplified expression of Tsallis entropy with multiple thresholds, which is proved by mathematical induction. Simultaneously, it is concluded that the multiple-threshold segmentation of Tsallis entropy and Renyi entropy with the same parameters is equivalent. To overcome the inconvenience of high calculation cost under multi-threshold and to improve calculation efficiency, recursive algorithms based on simplified Tsallis entropy and Renyi entropy under multi-threshold are given. The calculation costs of the traditional Tsallis entropy and Renyi entropy threshold, simplified Tsallis entropy and Renyi entropy threshold, and the recursive simplified Tsallis entropy and Renyi entropy are compared through experiments. The results have revealed that the calculation time of simplified Tsallis entropy and Renyi entropy is shorter than the traditional methods, and the calculation time of the recursive simplified Tsallis entropy and Renyi entropy is much lower than that of the simplified expression. Finally, we use the three optimization algorithms including particle swarm, differential evolution and Harris hawks algorithm to solve the optimal solutions of the six expressions in the case of multilevel thresholds. Experiments also show that recursive simplified Tsallis entropy and Renyi entropy have the lowest calculation time cost under the same parameters.

Multilevel Threshold Segmentation of Skin Lesions in Color Images Using Coronavirus Optimization Algorithm.

Skin Cancer (SC) is among the most hazardous due to its high mortality rate. Therefore, early detection of this disease would be very helpful in the treatment process. Multilevel Thresholding (MLT) is widely used for extracting regions of interest from medical images. Therefore, this paper utilizes the recent Coronavirus Disease Optimization Algorithm (COVIDOA) to address the MLT issue of SC images utilizing the hybridization of Otsu, Kapur, and Tsallis as fitness functions. Various SC images are utilized to validate the performance of the proposed algorithm. The proposed algorithm is compared to the following five meta-heuristic algorithms: Arithmetic Optimization Algorithm (AOA), Sine Cosine Algorithm (SCA), Reptile Search Algorithm (RSA), Flower Pollination Algorithm (FPA), Seagull Optimization Algorithm (SOA), and Artificial Gorilla Troops Optimizer (GTO) to prove its superiority. The performance of all algorithms is evaluated using a variety of measures, such as Mean Square Error (MSE), Peak Signal-To-Noise Ratio (PSNR), Feature Similarity Index Metric (FSIM), and Normalized Correlation Coefficient (NCC). The results of the experiments prove that the proposed algorithm surpasses several competing algorithms in terms of MSE, PSNR, FSIM, and NCC segmentation metrics and successfully solves the segmentation issue.

Levy Flight and Chaos Theory-Based Gravitational Search Algorithm for Image Segmentation

Image segmentation is one of the pivotal steps in image processing due to its enormous application potential in medical image analysis, data mining, and pattern recognition. In fact, image segmentation is the process of splitting an image into multiple parts in order to provide detailed information on different aspects of the image. Traditional image segmentation techniques suffer from local minima and premature convergence issues when exploring complex search spaces. Additionally, these techniques also take considerable runtime to find the optimal pixels as the threshold levels are increased. Therefore, in order to overcome the computational overhead and convergence problems of the multilevel thresholding process, a robust optimizer, namely the Levy flight and Chaos theory-based Gravitational Search Algorithm (LCGSA), is employed to perform the segmentation of the COVID-19 chest CT scan images. In LCGSA, exploration is carried out by Levy flight, while chaotic maps guarantee the exploitation of the search space. Meanwhile, Kapur’s entropy method is utilized for segmenting the image into various regions based on the pixel intensity values. To investigate the segmentation performance of ten chaotic versions of LCGSA, firstly, several benchmark images from the USC-SIPI database are considered for the numerical analysis. Secondly, the applicability of LCGSA for solving real-world image processing problems is examined by using various COVID-19 chest CT scan imaging datasets from the Kaggle database. Further, an ablation study is carried out on different chest CT scan images by considering ground truth images. Moreover, various qualitative and quantitative metrics are used for the performance evaluation. The overall analysis of the experimental results indicated the efficient performance of LCGSA over other peer algorithms in terms of taking less computational time and providing optimal values for image quality metrics.

Automated Segmentation and Morphometry of Zebrafish Anterior Chamber OCT Scans

Zebrafish (Danio rerio) eyes are widely used in modeling studies of human ophthalmic diseases, including glaucoma and myopia. These pathologies cause morphological variations in the anterior chamber elements, which can be quantitatively measured using morphometric parameters, such as the corneal curvature, central corneal thickness, and anterior chamber angle. In the present work, an automated method is presented for iris and corneal segmentation, as well as the determination of the above-mentioned morphometry from optical coherence tomography (OCT) scans of zebrafish. The proposed method consists of four stages; namely, preprocessing, segmentation, postprocessing, and extraction of morphometric parameters. The first stage is composed of a combination of wavelet and Fourier transforms as well as gamma correction for artifact removal/reduction. The segmentation step is achieved using the U-net convolutional neural network. The postprocessing stage is composed of multilevel thresholding and morphological operations. Finally, three algorithms are proposed for automated morphological extraction in the last step. The morphology obtained using our automated framework is compared against manual measurements to assess the effectiveness of the method. The obtained results show that our scheme allows reliable determination of the morphometric parameters, thereby allowing efficient assessment for massive studies on zebrafish anterior chamber morphology using OCT scans.

Quadruple parameter adaptation growth optimizer with integrated distribution, confrontation, and balance features for optimization

Growth optimizer is a novel metaheuristic algorithm that has powerful numerical optimization capabilities. However, its parameters and search operators become crucial factors that significantly impact its optimization capability for engineering problems and benchmarks. Therefore, this paper proposes a quadruple parameter adaptation growth optimizer (QAGO) integrated with distribution, confrontation, and balance features. In QAGO, the quadruple parameter adaptation mechanism aims to reduce the algorithmic sensitivity for parameter setting and enhance the algorithmic adaptability. By employing parameter sampling that adheres to specific probability distributions, the parameter adaptation mechanism achieves dynamic tuning of the algorithm hyperparameters. Moreover, one-dimensional mapping and fitness difference methods are designed in the triple parameter self-adaptation mechanism based on the contradictory relationship to adjust the operator’s parameters. After that, ”spear” and ”shield” are balanced based on the Jensen–Shannon divergence in information theory. Furthermore, the topological structure of the operators is redesigned, and by combining the parameter adaptation mechanism, operator refinement is achieved. Refined operators can effectively utilize different evolutionary information to improve the quality of the solution. The experiment evaluates the performance of QAGO on distinct optimization problems on the CEC 2017 and CEC 2022 test suites. To demonstrate the capability of QAGO in solving real-world applications, it was applied to tackle two specific problems: multilevel threshold image segmentation and wireless sensor network node deployment. The results demonstrated that QAGO delivers highly promising optimization results compared to seventy-one high-performance competing algorithms, including the five IEEE CEC competition winners. The source code of the QAGO algorithm is publicly available at https://github.com/tsingke/QAGO.

Tangent hybrid leader coronavirus herd optimization for the foreground and background image segmentation using multilevel thresholding

ABSTRACT In this paper, multilevel thresholding with Tangent Hybrid Leader Coronavirus Herd Optimization (THLCHO) is introduced for the image segmentation of foreground and background, The input image is passed to the pre-processing that is done by the adaptive wiener filtering (AWF) technique and the Region of Interest (RoI) extraction. Multilevel thresholding approaches such as threshold and threshold levels are employed to segment the images by entropy-based Kapur, and ostu thresholding, masi entropy and Renyi’s entropy, then the threshold values are optimally selected by THLCHO and considered as the output of the techniques. Secondly, the pre-processed image is subjected to the background and foreground image segmentation utilizing the entropy-based Fuzzy C-Means (EFCM) algorithm, which is assumed as an output of EFCM. Lastly, both outcomes are merged to produce the resultant output. The evaluation metrics employed for Multithresholding- THLCHO, namely, dice co-efficient, peak signal-to-noise-ratio (PSNR) and uniformity measure acquired the maximal values of 0.900, 38.274 dB and 0.918, respectively.

Multilevel Thresholding of Color Image Segmentation Using Memory-based Grey Wolf Optimizer With Otsu Method, Kapur, and M.Masi Entropy

Determining the optimal threshold value for image segmentation has become more attention in recent years because of its varied uses. Otsu-based thresholding methods, minimum cross entropy, and Kapur entropy are efficient for solving bi-level thresholding image segmentation problems (BL-ISP), but not with multi-level thresholding image segmentation problems (ML-ISP). The main problem is exponentially increasing computational complexity. This study uses the memory-based Gray Wolf Optimizer (mGWO) to determine the optimal threshold value for solving ML-ISP on RGB images. The mGWO method is a variant of the standard grey wolf optimizer (GWO) that utilizes the best track record of each individual grey wolf for the global exploration and local exploitation phases of the problem solution space. The solution candidates are represented by each grey wolf using the image intensity values and optimized according to mGWO characteristics. Three objective functions, namely the Otsu method, Kapur Entropy, and M.Masi Entropy are used to evaluate the solutions generated in the optimization process. The GridSearch method is used to determine the optimal parameter combination of each method based on 10 training images. Evaluation of the performance of the mGWO method was measured using several benchmark images and compared with five standard swarm intelligence (SI) methods as benchmarks. Analysis of the results was carried out qualitatively and quantitatively based on the average PSNR, RMSE, SSIM, UQI, fitness value, and CPU processing time from 30 tests. The results were analyzed further with the Wilcoxon signed-rank test. The experimental results show that the performance of the mGWO method outperforms the benchmark method in most experiments and metrics. The mGWO variant also proved to be superior to the standard GWO in resolving multi-level color image segmentation problems. The mGWO performance results are also compared with other state-of-the-art SI methods in solving ML-ISP on grayscale images and was able to outperform those methods in most experiments.

Cooperative Swarm Intelligence Algorithms for Adaptive Multilevel Thresholding Segmentation of COVID-19 CT-Scan Images

The Coronavirus Disease 2019 (COVID-19) is widespread throughout the world and poses a serious threat to public health and safety. A COVID-19 infection can be recognized using computed tomography (CT) scans. To enhance the categorization, some image segmentation techniques are presented to extract regions of interest from COVID-19 CT images. Multi-level thresholding (MLT) is one of the simplest and most effective image segmentation approaches, especially for grayscale images like CT scan images. Traditional image segmentation methods use histogram approaches; however, these approaches encounter some limitations. Now, swarm intelligence inspired meta-heuristic algorithms have been applied to resolve MLT, deemed an NP-hard optimization task. Despite the advantages of using meta-heuristics to solve global optimization tasks, each approach has its own drawbacks. However, the common flaw for most meta-heuristic algorithms is that they are unable to maintain the diversity of their population during the search, which means they might not always converge to the global optimum. This study proposes a cooperative swarm intelligence-based MLT image segmentation approach that hybridizes the advantages of parallel meta-heuristics and MLT for developing an efficient image segmentation method for COVID-19 CT images. An efficient cooperative model-based meta-heuristic called the CPGH is developed based on three practical algorithms: particle swarm optimization (PSO), grey wolf optimizer (GWO), and Harris hawks optimization (HHO). In the cooperative model, the applied algorithms are executed concurrently, and a number of potential solutions are moved across their populations through a procedure called migration after a set number of generations. The CPGH model can solve the image segmentation problem using MLT image segmentation. The proposed CPGH is evaluated using three objective functions, cross-entropy, Otsu’s, and Tsallis, over the COVID-19 CT images selected from open-sourced datasets. Various evaluation metrics covering peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and universal quality image index (UQI) were employed to quantify the segmentation quality. The overall ranking results of the segmentation quality metrics indicate that the performance of the proposed CPGH is better than conventional PSO, GWO, and HHO algorithms and other state-of-the-art methods for MLT image segmentation. On the tested COVID-19 CT images, the CPGH offered an average PSNR of 24.8062, SSIM of 0.8818, and UQI of 0.9097 using 20 thresholds.

Editorial

Dear Readers,  Welcome to the seventh issue in 2023. I am very pleased to announce the journal’s continued high Scopus CiteScore of 2.7 and Web of Science Impact Factor of 1.0 for 2022, indicating another scientifically successful year. On behalf of the J.UCS team, I would like to thank all the authors for their sound research contributions, the reviewers for their very helpful suggestions for improvements, and the consortium members for their financial support. Your commitment and dedicated work have contributed significantly to the long-lasting success of our journal.  As we want to secure the financial support also for the years to come, we are looking for institutions and libraries to financially support our diamond open access journal as consortium members, who will then benefit from the research community, international visibility, and the opportunity to manage special issues and focused topics within the journal. Please think about the possibility of such financial participation of your institution, we would be very grateful for any kind of support.  In this regular issue, I am very pleased to introduce six accepted papers from seven different countries and 20 involved authors.  Ana P. Allian, Leandro F. Silva, Edson OliveiraJr and Elisa Y. Nakagawa from Brazil present VMTools-RA, a reference architecture that encompasses the knowledge and practice for developing and evolving variability tools. In a collaboration between researchers from the UK and Estonia, Vimal Dwivedi, Mubashar Iqbal, Alex Norta and Raimundas Matulevičius are focusing their research on the evaluation of a legally binding smart-contract language for blockchain applications. Monika, Seema Verma, and Pardeep Kumar from India discuss an intelligent vision-based decision-making system for the exploration of past aviation accidents and incidents, which is based on a visual query-based model capable of analyzing the major factors including flight phases, human factors, weather conditions, and faulty components in particular aircraft models. Luis Eduardo Ordoñez Palacios, Víctor Bucheli Guerrero and Hugo Ordoñez from Colombia present their research on integrating satellite imagery and meteorological data to estimate solar radiation applying and evaluating five machine learning models. In a collaboration between researchers from Palestine and Egypt, Muath Sabha, Thaer Thaher, and Marwa M. Emam apply cooperative swarm intelligence algorithms to adaptive multilevel thresholding segmentation of COVID-19 CT scan images. Geovana Ramos Sousa Silva, Genaína Nunes Rodrigues and Edna Dias Canedo from Brazil introduce their work on a modeling strategy to design and verify chatbot conversational flows via the Uppaal model checking tool.  Enjoy Reading! Cordially, Christian Gütl, Managing Editor 

Automatic multi-structure pediatric knee bone segmentation using optimal multi-level Otsu thresholding to tackle intensity homogeneity in bone structures.

Recent studies in medical image segmentation involve new automatic approaches where active learning models are useful with less training samples. Presence of homogenous and heterogenous intensities for a single anatomical structure in pediatric musculoskeletal MR images affects the accuracy in terms of segmentation and classification of labels. This study addresses the homogeneity in intensity issues and introduces a new pre-training pipeline framework of Multi-level Otsu thresholding image as separate channel for 3D UNet model training. The proposed framework achieved higher performance of up to 85% when compared with the Baseline 3D UNet model and the Histogram threshold with 3D UNet. All algorithms are run through MONAI core framework.Clinical Relevance- This study will be of major interest to practicing pediatric clinicians and surgeons for its ability to provide accurate morphological assessment of underlying musculoskeletal structure. For researchers, it provides a new approach in dealing with heterogeneity in intensity problem which is common in pediatric MR imaging.

An improved African vultures optimization algorithm using different fitness functions for multi-level thresholding image segmentation

An improved African vultures optimization algorithm using different fitness functions for multi-level thresholding image segmentation

Identification of breast lesion through integrated study of gorilla troops optimization and rotation-based learning from MRI images

Breast cancer has emerged as the most life-threatening disease among women around the world. Early detection and treatment of breast cancer are thought to reduce the need for surgery and boost the survival rate. The Magnetic Resonance Imaging (MRI) segmentation techniques for breast cancer diagnosis are investigated in this article. Kapur’s entropy-based multilevel thresholding is used in this study to determine optimal values for breast DCE-MRI lesion segmentation using Gorilla Troops Optimization (GTO). An improved GTO, is developed by incorporating Rotational opposition based-learning (RBL) into GTO called (GTORBL) and applied it to the same problem. The proposed approaches are tested on 20 patients’ T2 Weighted Sagittal (T2 WS) DCE-MRI 100 slices. The proposed approaches are compared with Tunicate Swarm Algorithm (TSA), Particle Swarm Optimization (PSO), Arithmetic Optimization Algorithm (AOA), Slime Mould Algorithm (SMA), Multi-verse Optimization (MVO), Hidden Markov Random Field (HMRF), Improved Markov Random Field (IMRF), and Conventional Markov Random Field (CMRF). The Dice Similarity Coefficient (DSC), sensitivity, and accuracy of the proposed GTO-based approach is achieved 87.04%, 90.96%, and 98.13% respectively. Another proposed GTORBL-based segmentation method achieves accuracy values of 99.31% , sensitivity of 95.45% , and DSC of 91.54%. The one-way ANOVA test followed by Tukey HSD and Wilcoxon Signed Rank Test are used to examine the results. Furthermore, Multi-Criteria Decision Making is used to evaluate overall performance focused on sensitivity, accuracy, false-positive rate, precision, specificity, F_1-score, Geometric-Mean, and DSC. According to both quantitative and qualitative findings, the proposed strategies outperform other compared methodologies.

A multilevel threshold public good perspective on place branding: evidence from Italy

ABSTRACT This paper proposes a new interpretation of place brand as a multilevel threshold public good (MTPG) produced by the interaction of narratives from different geographical levels. Using an original dataset of Google trends and tweets from Italian provinces and regions, we test the hypothesis that place branding has a multilevel structure. We further test the MTPG framework applied to place branding, showing that place branding is influenced by different geographical levels which can trigger a spillover in terms of attractiveness if they contribute to crossing a threshold point. The results confirm the presence of a provision point in place branding, showing that the proposed MTPG framework fits the phenomenon. This article contributes to the literature on place branding and brands by providing a new lens through which to interpret the phenomenon, which may be useful for a better understanding and measuring of the interaction of branding strategies operating at different spatial scales.

A solution to the stagnation of multi-verse optimization: An efficient method for breast cancer pathologic images segmentation

The multi-verse optimizer (MVO) algorithm has been applied to image segmentation, feature selection, engineering problems, and many other fields. MVO, like other metaheuristic algorithms, still has shortcomings, such as poor convergence speed and quickly falling into local optimum. To address these concerns, this paper proposes CBQMVO, extending the original MVO algorithm with three strategies: covariance matrix adaptation strategy (CMAES), biogeography-based learning strategy (BLS), quasi-reflected and quasi-opposition strategy (QROS). CMAES can make the algorithm approach quickly the current local optimal solution and accelerate the convergence. BLS can enrich the population’s diversity to discourage prematurely and assist the algorithm in jumping out of the local optimum. QROS can increase the probability of search particles falling near the optimal solution. A set of experiments were conducted to evaluate the performance of the CBQMVO. First, the original algorithm comparison experiment on IEEE CEC2014 includes strategy comparison, dimension comparison, exploration/exploitation balance, and population diversity experiments. Then, the advanced algorithm comparison experiment was carried out on IEEE CEC 2014. Furthermore, the champion algorithm comparison experiment was conducted on IEEE CEC2017 and IEEE CEC2020. A series of comparative experimental data demonstrate that CBQMVO has high performance, especially on some unimodal and complex competition functions. In addition, this paper also applied CBQMVO to implement Renyi’s entropy multilevel threshold image segmentation based on the non-local mean 2D histogram (RMIS-2D) on breast cancer pathologic images. Compared with other metaheuristic algorithms and Kapur’s entropy image segmentation, the proposed scheme in this paper has a better segmentation effect.

Prostate Cancer Detection through MR Images based on Black Hole Optimization Algorithm

Introduction: Prostate cancer is the most common type of malignant cancer among men and is known as one of the leading causes of cancer mortality in men. The complexity of diagnostic procedures such as mass biopsy has made new diagnostic strategies for prostate cancer, such as MRI imaging, a research priority in recent years. Methods: In this applied-descriptive study, a four steps method for diagnosing prostate cancer through MR image is presented. In the first step, the destructive effect of noise on the input images by using two-dimensional wavelet transform and histogram equalization is reduced. In the second step, the black hole optimization algorithm is used for segmentation of the input image based on the multilevel threshold technique. By doing this, the suspicious areas are identified in the image and in the third step, the features of each target area are extracted. In the fourth step, a combination of three learning algorithms, including: artificial neural network, decision and support vector machine is used to diagnose prostate cancer. Results: The effectiveness of the proposed method in diagnosing prostate cancer has been evaluated from various aspects and its performance has been compared with other learning models. Based on the results, the proposed method can diagnose prostate cancer through MRI images with an average accuracy of 99%. Discussion & Conclusion: The proposed method uses a combination of image processing, optimization and machine learning techniques to achieve this goal. Compared with other models, this proposed method was of the highest accuracy.

Fabric defect detection using ACS-based thresholding and GA-based optimal Gabor filter

Fabric defect detection is closely related to quality control. Therefore, it is an important topic in the modern textile field. In this article, a new fabric defect detection method using ACS-based thresholding and GA-based optimal Gabor filter is proposed. The multi-level gray-scale image thresholding is improved by using Adaptive cuckoo search (ACS) to calculate the best threshold. In order to suppress texture interference, the optimal Gabor filter calculated by genetic algorithm (GA) is used to achieve the optimal feature extraction of fabric defects. A specific image acquisition system is set up to obtain clear defective fabric images and corresponding defect-free images which are used to build the database. The performance of the method is evaluated by extensive experiments on various types of fabric defects. Experimental results show that the proposed method, effective and robust, is superior than the other six methods.

Symmetric cross-entropy multi-threshold color image segmentation based on improved pelican optimization algorithm.

To address the problems of low accuracy and slow convergence of traditional multilevel image segmentation methods, a symmetric cross-entropy multilevel thresholding image segmentation method (MSIPOA) with multi-strategy improved pelican optimization algorithm is proposed for global optimization and image segmentation tasks. First, Sine chaotic mapping is used to improve the quality and distribution uniformity of the initial population. A spiral search mechanism incorporating a sine cosine optimization algorithm improves the algorithm's search diversity, local pioneering ability, and convergence accuracy. A levy flight strategy further improves the algorithm's ability to jump out of local minima. In this paper, 12 benchmark test functions and 8 other newer swarm intelligence algorithms are compared in terms of convergence speed and convergence accuracy to evaluate the performance of the MSIPOA algorithm. By non-parametric statistical analysis, MSIPOA shows a greater superiority over other optimization algorithms. The MSIPOA algorithm is then experimented with symmetric cross-entropy multilevel threshold image segmentation, and eight images from BSDS300 are selected as the test set to evaluate MSIPOA. According to different performance metrics and Fridman test, MSIPOA algorithm outperforms similar algorithms in global optimization and image segmentation, and the symmetric cross entropy of MSIPOA algorithm for multilevel thresholding image segmentation method can be effectively applied to multilevel thresholding image segmentation tasks.

A chimp-inspired remora optimization algorithm for multilevel thresholding image segmentation using cross entropy

A chimp-inspired remora optimization algorithm for multilevel thresholding image segmentation using cross entropy

Multi-level Threshold Switching and Crystallization Characteristics of Nitrogen Alloyed GaSb for Phase Change Memory Application

Multi-level Threshold Switching and Crystallization Characteristics of Nitrogen Alloyed GaSb for Phase Change Memory Application

MSWOA: A Mixed-Strategy-Based Improved Whale Optimization Algorithm for Multilevel Thresholding Image Segmentation

Multilevel thresholding image segmentation is one of the most widely used segmentation methods in the field of image segmentation. This paper proposes a multilevel thresholding image segmentation technique based on an improved whale optimization algorithm. The WOA has been applied to many complex optimization problems because of its excellent performance; however, it easily falls into local optimization. Therefore, firstly, a mixed-strategy-based improved whale optimization algorithm (MSWOA) is proposed using the k-point initialization algorithm, the nonlinear convergence factor, and the adaptive weight coefficient to improve the optimization ability of the algorithm. Then, the MSWOA is combined with the Otsu method and Kapur entropy to search for the optimal thresholds for multilevel thresholding gray image segmentation, respectively. The results of algorithm performance evaluation experiments on benchmark functions demonstrate that the MSWOA has higher search accuracy and faster convergence speed than other comparative algorithms and that it can effectively jump out of the local optimum. In addition, the image segmentation experimental results on benchmark images show that the MSWOA–Kapur image segmentation technique can effectively and accurately search multilevel thresholds.