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The process of image segmentation is partitioning an image into its constituent parts and is a significant approach for extracting interesting features from images. Over a couple of decades, many efficient image segmentation approaches have been formulated for various applications. Still, it is a challenging and complex issue, especially for color image segmentation. To moderate this difficulty, a novel multilevel thresholding approach is proposed in this paper based on the electromagnetism optimization (EMO) technique with an energy curve, named multilevel thresholding based on EMO and energy curve (MTEMOE). To compute the optimized threshold values, Otsu's variance and Kapur's entropy are deployed as fitness functions; both values should be maximized to locate optimal threshold values. In both Kapur's and Otsu's methods, the pixels of an image are classified into different classes based on the threshold level selected on the histogram. Optimal threshold levels give higher efficiency of segmentation; the EMO technique is used to find optimal thresholds in this research. The methods based on an image's histograms do not possess the spatial contextual information for finding the optimal threshold levels. To abolish this deficiency an energy curve is used instead of the histogram and this curve can establish the spatial relationship of pixels with their neighbor pixels. To study the experimental results of the proposed scheme, several color benchmark images are considered at various threshold levels and compared with other meta-heuristic algorithms: multi-verse optimization, whale optimization algorithm, and so on. The investigational results are illustrated in terms of mean square error, peak signal-to-noise ratio, the mean value of fitness reach, feature similarity, structural similarity, variation of information, and probability rand index. The results reveal that the proposed MTEMOE approach overtops other state-of-the-art algorithms to solve engineering problems in various fields. [ABSTRACT FROM AUTHOR]

While yielding satisfactory segmentation results for images with low SNR and poor contrast, one-dimensional (1-D) and two-dimensional (2-D) Otsu’s thresholding methods have the downside of high computational complexity. So far, three-dimensional (3-D) Otsu method has been based on histogram, which has only probability distribution of pixels as an object of interest. Histogram-based segmentation methods do not consider the contextual information which is significant to enrich the quality of segmented image. In this paper, a context-based 3-D Otsu algorithm has been proposed that considers the pixel intensity values as well as spatial information along with same properties of histogram. The proposed method is evaluated comprehensively with respect to quality and a detailed analysis is presented to compare the results of histogram-based 1-D, 2-D, and 3-D Otsu and energy-based 1-D, 2-D, and 3-D Otsu method, respectively. Experimental outcomes demonstrate the superiority of energy-based 3-D Otsu algorithm compared to histogram-based methods in terms of improved performance metrics, including mean error (ME), mean square error (MSE), peak signal-to-noise ratio (PSNR), feature similarity index (FSIM), structure similarity index (SSIM), and entropy. Experiments on standard daily life color images have been carried out to prove the effectiveness of the proposed scheme. The results show that the proposed method can produce more promising segmentation results from the aspect of objective and subjective observations. [ABSTRACT FROM AUTHOR]

Multilevel thresholding image segmentation has attracted a lot of attention in the last several years since it has plenty of applications. The traditional exhaustive search methods are efficient for bi-level thresholding. However, they are time-consuming when extended to multilevel thresholding. To tackle this problem, a novel adaptive firefly algorithm (AFA) for multilevel thresholding using the minimum cross-entropy as its objective function has been proposed in this paper. The performance of the proposed algorithm has been examined on a set of benchmark images using various numbers of thresholds and has been compared with five different firefly variant algorithms. The experimental results indicated that the proposed algorithm outperformed the other five algorithms in terms of image segmentation quality, accuracy, and computation time. [ABSTRACT FROM AUTHOR]

To overcome the shortcomings of 1-D and 2-D Otsu’s thresholding methods, a 3-D Otsu method has been introduced. While yielding satisfactory segmentation results for images with a low signal-to-noise ratio (SNR) and poor contrast, it has the downside of high computational complexity. In this paper, the cuttlefish algorithm (CFA)-based 3-D Otsu thresholding method is proposed to pace up the conventional 3-D Otsu thresholding for color image segmentation. In order to decrease the effects of noises and weak edges, an optimally selected multilevel 3-D Otsu image thresholding technique is brought into the proposed segmentation scheme. The CFA is a newly developed stochastic meta-heuristic optimization algorithm based on observing, mimicking, and modeling the camouflaging feature of cuttlefish. It is used to simplify the problem of exhaustive search for the optimal threshold vector in 3-D space. Experimental results, when compared to 1-D Otsu, 1-D Otsu-Cuckoo search (CS) algorithm, 1-D Otsu-lightning search algorithm (LSA), 1-D Otsu-CFA, conventional 3-D Otsu, 3-D Otsu-CS, and 3-D Otsu-LSA, indicate that the proposed algorithm CFA-based 3-D Otsu thresholding is superior to all the other multilevel thresholding algorithms. The proposed 3-D-CFA method produces promising segmentation results from the objective and subjective aspects. [ABSTRACT FROM AUTHOR]

Multilevel thresholding image segmentation has always been a popular issue and attracted the attention of many researchers in recent years since it has many applications. However, the process of determining the optimal thresholds in the case of multilevel thresholding is time-consuming. To address this problem, in this paper, the optimal thresholds for multilevel thresholding image segmentation are obtained by maximizing the Rényi entropy using the Lévy flight firefly algorithm (FAFA), in which an adaptive parameter strategy based on Lévy flight is used to improve the performance of the standard firefly algorithm (FA). The performance of the proposed algorithm has been evaluated using several benchmark images and has been compared with five different heuristic algorithms. The experimental results showed that the proposed algorithm prevailed over the other five competitive algorithms in terms of the objective function value, image quality measures, and computational efficiency. [ABSTRACT FROM AUTHOR]

Multilevel thresholding is a basic method in image segmentation. The conventional image multilevel thresholding algorithms are computationally expensive when the number of decomposed segments is high. In this paper, a novel and powerful technique is suggested for Crow Search Algorithm (CSA) devoted to segmentation applications. The main contribution of our work is to adapt Darwinian evolutionary theory with heuristic CSA. First, the population is divided into specified groups and each group tries to find better location in the search space. A policy of encouragement and punishment is set on searching agents to avoid being trapped in the local optimum and premature solutions. Moreover, to increase the convergence rate of the proposed method, a gray-scale map is applied to out-boundary agents. Ten test images are selected to measure the ability of our algorithm, compared with the famous procedure, energy curve method. Two popular entropies i.e. Otsu and Kapur are employed to evaluate the capability of the introduced algorithm. Eight different search algorithms are implemented and compared to the introduced method. The obtained results show that our method, compared with the original CSA, and other heuristic search methods, can extract multi-level thresholding more efficiently. [ABSTRACT FROM AUTHOR]

Image segmentation is a prime operation to understand the content of images. Multilevel thresholding is applied in image segmentation because of its speed and accuracy. In this paper, a novel multilevel thresholding algorithm based on Cuckoo search (CS) is introduced. One of the major drawbacks of metaheuristic algorithms is the stagnation phenomenon which leads to a fall into local optimums and premature convergence. To overcome this shortcoming, the idea of Darwinian theory is incorporated with CS algorithm to increase the diversity and quality of the individuals without decreasing the convergence speed of CS algorithm. A policy of encouragement and punishment is considered to lead searching agents in the search space and reduce the computational time. The algorithm is implemented based on dividing the population into specified groups and each group tries to find a better location. Ten test images are selected to verify the ability of our algorithm using the famous energy curve method. Two popular entropies criteria, Otsu and Kapur, are employed to evaluate the capability of the introduced algorithm. Eight different search algorithms are also implemented and compared with our method. Experimental results manifest that DCS is a powerful tool for multilevel thresholding and the obtained results outperform the CS algorithm and other heuristic search methods. [ABSTRACT FROM AUTHOR]

Multilevel image thresholding is an essential step in the image segmentation process. Expectation Maximization (EM) is a powerful technique to find thresholds but is sensitive to the initial points. Differential Evolution (DE) is a robust metaheuristic algorithm that can find thresholds rapidly. However, it may be trapped in the local optimums and premature convergence occurs. In this paper, we incorporate EM algorithm to DE and introduce a novel algorithm called EM+DE which overcomes these shortages and can segment images better than EM and DE algorithms. In the proposed method, EM estimates Gaussian Mixture Model (GMM) coefficients of the histogram and DE tries to provide good volunteer solutions to EM algorithm when EM converges in local areas. Finally, DE fits GMM parameters based on Root Mean Square Error (RMSE) to reach the fittest curve. Ten standard test images and six famous metaheuristic algorithms are considered and result on global fitness. PSNR, SSIM, FSIM criteria and the computational time are given. The experimental results prove that the proposed algorithm outperforms the EM and DE as well as EM+ other natural-inspired algorithms in terms of segmentation criteria. [ABSTRACT FROM AUTHOR]

Image segmentation is a prime operation to understand the content of images. Multilevel thresholding is applied in image segmentation because of its speed and accuracy. In this paper, a novel multilevel thresholding algorithm based on differential evolution (DE) search is introduced. One of the major drawbacks of metaheuristic algorithms is the stagnation phenomenon which leads to falling into local optimums and premature convergence. To overcome this shortcoming, the idea of Darwinian theory is incorporated with DE algorithm to increase the diversity and quality of the individuals without decreasing the convergence speed of DE algorithm. A policy of encouragement and punishment is considered to lead searching agents in the search space and reduce the computational time. The algorithm is implemented based on dividing the population into specified groups and each group tries to find a better location. Ten test images are selected to verify the ability of our algorithm using the famous energy curve method. Kapur entropy and Type 2 fuzzy entropy are employed to evaluate the capability of the introduced algorithm. Nine different metaheuristic algorithms with Darwinian modes are also implemented and compared with our method. Experimental results manifest that the proposed method is a powerful tool for multilevel thresholding and the obtained results outperform the DE algorithm and other methods. [ABSTRACT FROM AUTHOR]

One of the most crucial aspects of image segmentation is multilevel thresholding. However, multilevel thresholding becomes increasingly more computationally complex as the number of thresholds grows. In order to address this defect, this paper proposes a new multilevel thresholding approach based on the Evolutionary Arithmetic Optimization Algorithm (AOA). The arithmetic operators in science were the inspiration for AOA. DAOA is the proposed approach, which employs the Differential Evolution technique to enhance the AOA local research. The proposed algorithm is applied to the multilevel thresholding problem, using Kapur's measure between class variance functions. The suggested DAOA is used to evaluate images, using eight standard test images from two different groups: nature and CT COVID-19 images. Peak signal-to-noise ratio (PSNR) and structural similarity index test (SSIM) are standard evaluation measures used to determine the accuracy of segmented images. The proposed DAOA method's efficiency is evaluated and compared to other multilevel thresholding methods. The findings are presented with a number of different threshold values (i.e., 2, 3, 4, 5, and 6). According to the experimental results, the proposed DAOA process is better and produces higher-quality solutions than other comparative approaches. Moreover, it achieved better-segmented images, PSNR, and SSIM values. In addition, the proposed DAOA is ranked the first method in all test cases. [ABSTRACT FROM AUTHOR]

Multilevel thresholding image segmentation is an important technique, which has attracted much attention in recent years. The conventional exhaustive search method for image segmentation is efficient for bilevel thresholding. However, they are time expensive when dealing with multilevel thresholding image segmentation. To better tackle this problem, an improved cuckoo search algorithm (ICS) is proposed to search for the optimal multilevel thresholding in this paper, and Otsu is considered as its objective function. In the ICS, two modifications are used to improve the standard cuckoo search algorithm. First, a parameter adaptation strategy is utilized to improve exploration performance. Second, a dynamic weighted random-walk method is adopted to enhance the local search efficiency. A total of six benchmark test images are used to perform the experiments, and seven state-of-the-art metaheuristic algorithms are introduced to compare with the ICS. A series of measure indexes such as objective function value and standard deviation, PSNR, FSIM, and SSIM as well as the Wilcoxon rank sum and convergence performance are performed in the experiments; the experimental results show that the proposed algorithm is superior to other seven well-known heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose an interval iteration multilevel thresholding method (IIMT). This approach is based on the Otsu method but iteratively searches for sub-regions of the image to achieve segmentation, rather than processing the full image as a whole region. Then, a novel multilevel thresholding framework based on IIMT for brain MR image segmentation is proposed. In this framework, the original image is first decomposed using a hybrid L1 − L0 layer decomposition method to obtain the base layer. Second, we use IIMT to segment both the original image and its base layer. Finally, the two segmentation results are integrated by a fusion scheme to obtain a more refined and accurate segmentation result. Experimental results showed that our proposed algorithm is effective, and outperforms the standard Otsu-based and other optimization-based segmentation methods. [ABSTRACT FROM AUTHOR]

• A color image segmentation based on Exchange Market Algorithm (EMA) is proposed. • Between class variance and entropy functions are used as objective functions. • The proposed EMA approach is compared with other state-of-the-art algorithms. • Results reveal that the EMA is the effective approach for multilevel thresholding. Color image segmentation is the primary step to elicit detailed information of the image with RGB color space. The key to acquire the region of interest is the straightforward, instinctual technique called thresholding. Bi-level thresholding can be assessed concretely for simple images, whereas revealing various classes from a complex image is achieved only through multiple threshold values. Hence, multilevel thresholding with the most propitious maximizing objective functions such as Kapur, Otsu and Minimum Cross Entropy (MCE) to extract the precise threshold are employed in this paper. As the segmentation level increases, execution of non-parametric objective functions leads to exponential increase in computational time. Several researches to enhance the speed of objective functions along with various metaheuristics such as Krill Herd Algorithm (KHA), Teaching-Learning Based Optimization (TLBO) and Cuckoo Search Algorithm (CSA) are performed. The need to unlock the computational complexity drifted our view towards the most powerful, robust, recently introduced metaheuristic Exchange Market Algorithm (EMA). EMA involves exchange of shares among investors to gain profit. The strategic approach of share members in stable and unstable modes of the market results in precise exploration and exploitation. Furthermore, low fitness shareholders gaining experience from their high and moderate counterparts, stands out as an exceptional step to reduce the time consumption. This concept is utilized in our paper for the first time to obtain the exact details from the image without any delay. Empirical outcome of the results indicates that exceptional image segmentation is achieved by EMA in less time compared to extensive search techniques such as KHA, TLBO and CSA. Quantitative and qualitative validation furnished by metrics such as Structural Similarity Index (SSIM), computational time, Peak Signal to Noise Ratio (PSNR) and statistical Wilcoxon test affirm that Otsu, Kapur and MCE based EMA outperforms the existing techniques to analyze the real-world images. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced Harris Hawks Optimizer (HHO) to tackle global optimization and determine the optimal threshold values for multi-level image segmentation problems. HHO is a new swarm-based metaheuristic technique that simulates the behaviors of Harris hawks during the process of catching the rabbits. The HHO established its strong performance as a swarm-based optimization technique. However, population-based HHO still may face some limitations in dealing with more multi-modal and composition problems. For example, this optimizer may be stagnated to local optima and turned to immature convergence when performing phases of exploration and exploitation. To mitigate these drawbacks, an improved HHO is proposed that considers the salp swarm algorithm (SSA) as a competitive method to enhance the balance between its exploration and exploitation trends. Firstly, a set of solutions is generated. Then, we divide those solutions into two halves, where the exploratory and exploitative phases of HHO will be applied to the first half, and the searching stages of SSA will be used to update the solutions in the second half. Thereafter, the best solutions from the union sub-populations are selected to continue the iterative process. According to the improved HHO, which is called HHOSSA, an effective multi-level image segmentation approach is also developed in this research. A comprehensive set of experiments are performed using 36 IEEE CEC 2005 benchmark functions and 11 natural gray-scale images. Extensive results and comparisons show the high ability of the SSA to improve the HHO's performance since the proposed HHOSSA achieves a more stable performance compared to HHO, SSA, and many other well-known methods. • This paper presents an enhanced Harris Hawks Optimizer (HHO). • A comprehensive experiment is performed using more than forty five benchmark problems. • Extensive results show the more stable performance of the proposed variant of HHO. [ABSTRACT FROM AUTHOR]

Image segmentation is one of the pivotal steps in image processing. Actually, it deals with the partitioning of the image into different classes based on pixel intensities. This work introduces a new image segmentation method based on the constriction coefficient‐based particle swarm optimization and gravitational search algorithm (CPSOGSA). The random samples of the image act as searcher agents of the CPSOGSA algorithm. The optimal number of thresholds is determined using Kapur's entropy method. The effectiveness and applicability of CPSOGSA in image segmentation is accomplished by applying it to five standard images from the USC‐SIPI image database, namely Aeroplane, Cameraman, Clock, Lena, and Pirate. Various performance metrics are employed to investigate the simulation outcomes, including optimal thresholds, standard deviation, MSE (mean square error), run time analysis, PSNR (peak signal to noise ratio), best fitness value calculation, convergence maps, segmented image graphs, and box plot analysis. Moreover, image accuracy is benchmarked by utilizing SSIM (structural similarity index measure) and FSIM (feature similarity index measure) metrics. Also, a pairwise non‐parametric signed Wilcoxon rank‐sum test is utilized for statistical verification of simulation results. In addition, the experimental outcomes of CPSOGSA are compared with eight different algorithms including standard PSO, classical GSA, PSOGSA, SCA (sine cosine algorithm), SSA (salp swarm algorithm), GWO (grey wolf optimizer), MFO (moth flame optimizer), and ABC (artificial bee colony). The simulation results clearly indicate that the hybrid CPSOGSA has successfully provided the best SSIM, FSIM, and threshold values to the benchmark images. [ABSTRACT FROM AUTHOR]

Multilevel thresholding method is one of the most popular techniques in image segmentation. However, the multilevel thresholding method is time-consuming, its time complexity increases exponentially with the number of threshold levels. In this paper, in order to improve the computation efficiency of the multilevel minimum cross entropy thresholding, the iterative formula of the multilevel cross entropy thresholding algorithm is proposed and compared with the modern meta-heuristic optimization algorithms. The iterative multilevel cross entropy thresholding algorithm can find the thresholds close to the global optimums with less time. The computation cost of the iterative multilevel cross entropy thresholding algorithm is linear in the number of the threshold levels. We prove the convergence of the iterative algorithm and compare the iterative multilevel cross entropy thresholding algorithm with multilevel cross entropy thresholding methods combined with the state-of-the-art meta-heuristic optimization techniques including particle swarm optimization (PSO), cuckoo search algorithm (CS), differential evolution (DE), crow search algorithm (CSA) and genetic algorithm (GA). Experimental results show that the iterative multilevel cross entropy thresholding algorithm is efficient and effective. Therefore, iterative algorithm for the multilevel cross entropy thresholding is an effective method to improve the computation efficiency. • Propose the iterative formula of the multilevel minimum cross entropy thresholding (MMCET) method. • Prove the convergence of the iterative algorithm. • Compare the iterative algorithm with the MMCET method optimized by swarm search algorithm. • Validate the effectiveness of the iterative MMCET algorithm. [ABSTRACT FROM AUTHOR]