Multilevel Thresholding Image Segmentation Research Articles

Multilevel threshold image segmentation with diffusion association slime mould algorithm and Renyi's entropy for chronic obstructive pulmonary disease

Image segmentation is an essential pre-processing step and is an indispensable part of image analysis. This paper proposes Renyi's entropy multi-threshold image segmentation based on an improved Slime Mould Algorithm (DASMA). First, we introduce the diffusion mechanism (DM) into the original SMA to increase the population's diversity so that the variants can better avoid falling into local optima. The association strategy (AS) is then added to help the algorithm find the optimal solution faster. Finally, the proposed algorithm is applied to Renyi's entropy multilevel threshold image segmentation based on non-local means 2D histogram. The proposed method's effectiveness is demonstrated on the Berkeley segmentation dataset and benchmark (BSD) by comparing it with some well-known algorithms. The DASMA-based multilevel threshold segmentation technique is also successfully applied to the CT image segmentation of chronic obstructive pulmonary disease (COPD). The experimental results are evaluated by image quality metrics, which show the proposed algorithm's extraordinary performance. This means that it can help doctors analyze the lesion tissue qualitatively and quantitatively, improve its diagnostic accuracy and make the right treatment plan. The supplementary material and info about this article will be available at https://aliasgharheidari.com.

A Lévy Flight Based Firefly Algorithm for Multilevel Thresholding Image Segmentation

Traditional exhaustive search methods have high time complexity in solving multilevel threshold problems. To address this problem, a Levy flight based firefly algorithm called LFA is proposed. Otsu is regard as its objective function. A series of standard test images were used to evaluate the performance of the algorithm. The Peak signal to noise ratio(PSNR) and Structural similarity index (SSIM) are utilized to evaluate the segmented image. The experimental results show that the LFA is better than FA for multilevel thresholding image segmentation.

An Improved Teaching–Learning-Based Optimization for Multilevel Thresholding Image Segmentation

Due to its successful application image processing or computer vision system, image segmentation plays a significant role and has become a hot research hotspot. In this paper, we propose an improved teaching–learning-based optimization (NFDR-TLBO) to segment grayscale images via multilevel thresholding. In the proposed teaching–learning-based optimization variant, the neighborhood topology is introduced into the original teaching–learning-based optimization algorithm to maintain the exploration ability of the population and the fitness-distance-ratio mechanism is introduced into the original teaching–learning-based optimization algorithm to improve its optimization performance on complex numerical optimization problems. Moreover, the experimental results on 18 typical benchmark functions with different characteristics verify the feasibility and effectiveness of the proposed algorithm. Furthermore, the proposed algorithm is used to optimize Kapur entropy function in order to find the optimal threshold for image segmentation. Finally, the experimental simulations on different benchmark images show that the proposed algorithm is effective and efficient in improving the image segmentation performance in terms of peak-signal-to-noise ratio, structure similarity index and feature similarity.

A multi-leader whale optimization algorithm for global optimization and image segmentation

In this paper, a multilevel thresholding image segmentation method base on the enhancement of the performance of the whale optimization algorithm (WOA). The developed method, called the multi-leader whale optimization algorithm (MLWOA), aims to avoid the limitations of traditional WOA during the searching process, such as stagnation at the local optimum. This was achieved by integrating the different tools with WOA, such as memory mechanism, multi-leader method, self-learning strategy, and levy flight method. Each of these techniques has its own task, for example, the memory structure of traditional WOA and add a multi-leader mechanism to enhance the ability of exploration. The superiority of leaders will make more influence in MLWOA by adding a self-learning strategy. Also, it used levy flight trajectory to make the algorithm more robust and avoid premature convergence. To evaluate the performance of the developed MLWOA, a set of experiments are conducted using the CEC2017 benchmark. In addition, it is applied to determine the optimal threshold values to segment a set of images using the Otsu method, fuzzy entropy, and Kapur's entropy as a fitness function. The results of MLWOA are compared with well-known meta-heuristic algorithms inside the experiments. The comparison results indicated that MLWOA provides better performance in CEC2017 benchmark functions and shows high superiority in image segmentation in terms of performance measures. In addition, the MLWOA provides better results using Otsu, followed by the Fuzzy entropy and Kapur in terms of PSNR. In terms of SSIM, fuzzy entropy and Otsu have nearly the same SSIM value, but the fuzzy entropy provides better results.

An efficient method of multicolor detection using global optimum thresholding for image analysis

Image segmentation is a key step in the image analysis, pattern recognition, low-level vision, medical data analysis, objects tracking, recognition task and grasping of things from the field of robotics. Being a problematic and demanding chore in image processing, it governs the eminence of absolute outcomes of image analysis. The method aims to improve color detection using formulations in RGB arrays. First targeted color is selected and identified the desired color location by sliding window techniques. Then threshold has been calculated using the summation of within and between the class variance of the selected color. Proposed method overcomes the limitation of complex, the dearth incorrectness, and steadiness of conventional multilevel thresholding for image segmentation. This work is tested on a different kind of images such as two-dimensional images, low-quality images, complex images, blur images, and medical images. The simulated results designate the maximum accuracy and minimum computational time over other methods.

Multilevel thresholding image segmentation based on improved volleyball premier league algorithm using whale optimization algorithm.

Multilevel thresholding image segmentation has received considerable attention in several image processing applications. However, the process of determining the optimal threshold values (as the preprocessing step) is time-consuming when traditional methods are used. Although these limitations can be addressed by applying metaheuristic methods, such approaches may be idle with a local solution. This study proposed an alternative multilevel thresholding image segmentation method called VPLWOA, which is an improved version of the volleyball premier league (VPL) algorithm using the whale optimization algorithm (WOA). In VPLWOA, the WOA is used as a local search system to improve the learning phase of the VPL algorithm. A set of experimental series is performed using two different image datasets to assess the performance of the VPLWOA in determining the values that may be optimal threshold, and the performance of this algorithm is compared with other approaches. Experimental results show that the proposed VPLWOA outperforms the other approaches in terms of several performance measures, such as signal-to-noise ratio and structural similarity index.

Multilevel thresholding using an improved cuckoo search algorithm for image segmentation

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.

Kapur's entropy for multilevel thresholding image segmentation based on moth-flame optimization.

Multilevel thresholding is a reliable and efficacious method for image segmentation that has recently received widespread recognition. However, the computational complexity of the multilevel thresholding method increases as the threshold level increases, which causes the low segmentation accuracy of this method. To overcome this shortcoming, this paper presents a moth-flame optimization (MFO) established on Kapur's entropy to clarify the multilevel thresholding image segmentation. The MFO adjusts exploration and exploitation to achieve the best fitness value. To validate the overall performance, MFO is compared with other algorithms to realize the global optimal solution to maximize the target value of Kapur's entropy. Some critical evaluation indicators are used to determine the segmentation effect and optimization performance of each algorithm. The experimental results indicate that MFO has a faster convergence speed, higher calculation accuracy, better segmentation effect and better stability.

A Hybrid SSA and SMA with Mutation Opposition-Based Learning for Constrained Engineering Problems.

Based on Salp Swarm Algorithm (SSA) and Slime Mould Algorithm (SMA), a novel hybrid optimization algorithm, named Hybrid Slime Mould Salp Swarm Algorithm (HSMSSA), is proposed to solve constrained engineering problems. SSA can obtain good results in solving some optimization problems. However, it is easy to suffer from local minima and lower density of population. SMA specializes in global exploration and good robustness, but its convergence rate is too slow to find satisfactory solutions efficiently. Thus, in this paper, considering the characteristics and advantages of both the above optimization algorithms, SMA is integrated into the leader position updating equations of SSA, which can share helpful information so that the proposed algorithm can utilize these two algorithms' advantages to enhance global optimization performance. Furthermore, Levy flight is utilized to enhance the exploration ability. It is worth noting that a novel strategy called mutation opposition-based learning is proposed to enhance the performance of the hybrid optimization algorithm on premature convergence avoidance, balance between exploration and exploitation phases, and finding satisfactory global optimum. To evaluate the efficiency of the proposed algorithm, HSMSSA is applied to 23 different benchmark functions of the unimodal and multimodal types. Additionally, five classical constrained engineering problems are utilized to evaluate the proposed technique's practicable abilities. The simulation results show that the HSMSSA method is more competitive and presents more engineering effectiveness for real-world constrained problems than SMA, SSA, and other comparative algorithms. In the end, we also provide some potential areas for future studies such as feature selection and multilevel threshold image segmentation.

A Grunwald–Letnikov based Manta ray foraging optimizer for global optimization and image segmentation

This paper presents a modified version of Manta ray foraging optimizer (MRFO) algorithm to deal with global optimization and multilevel image segmentation problems. MRFO is a meta-heuristic technique that simulates the behaviors of manta rays to find the food. MRFO established its ability to find a suitable solution for a variant of optimization problems. However, by analyzing its behaviors during the optimization process, it is observed that its exploitation ability is less than exploration ability, which makes MRFO more sensitive to attractive to a local point. Therefore, we enhanced MRFO by using the fractional-order (FO) calculus during the exploitation phase. We used the heredity and non-locality properties of the Grunwald–Letnikov fractional differ-integral operator to simulate the after effect of the previous locations of manta rays on their future movement directions. The proposed Fractional-order MRFO (FO-MRFO) quality is confirmed using a set of two experimental series. Firstly, it is applied to find the solution for CEC2017 benchmark functions with different dimensions of 10, 30, and 50. Through performing the non-parametric statistical analysis, the FO-MRFO shows its superiority in comparison with the basic MRFO. For the second series of experiments, the developed algorithm is implemented as a multilevel threshold image segmentation technique. In this experiment, a variant of natural images is used to assess FO-MFRO. According to different performance measures, the FO-MRFO outperforms the compared algorithms in the global optimization and image segmentation.

A novel Black Widow Optimization algorithm for multilevel thresholding image segmentation

Segmentation is a crucial step in image processing applications. This process separates pixels of the image into multiple classes that permits the analysis of the objects contained in the scene. Multilevel thresholding is a method that easily performs this task, the problem is to find the best set of thresholds that properly segment each image. Techniques as Otsu’s between class variance or Kapur’s entropy helps to find the best thresholds but they are computationally expensive for more than two thresholds. To overcome such problem this paper introduces the use of the novel meta-heuristic algorithm called Black Widow Optimization (BWO) to find the best threshold configuration using Otsu or Kapur as objective function. To evaluate the performance and effectiveness of the BWO-based method, it has been considered the use of a variety of benchmark images, and compared against six well-known meta-heuristic algorithms including; the Gray Wolf Optimization (GWO), Moth Flame Optimization (MFO), Whale Optimization Algorithm (WOA), Sine–Cosine Algorithm (SCA), Slap Swarm Algorithm (SSA), and Equilibrium Optimization (EO). The experimental results have revealed that the proposed BWO-based method outperform the competitor algorithms in terms of the fitness values as well as the others performance measures such as PSNR, SSIM and FSIM. The statistical analysis manifests that the BWO-based method achieves efficient and reliable results in comparison with the other methods. Therefore, BWO-based method was found to be most promising for multi-level image segmentation problem over other segmentation approaches that are currently used in the literature.

Multilevel thresholding image segmentation based on energy curve with harmony Search Algorithm

Image segmentation is a process of portion image into regions. From image segmentation schemes available, multilevel thresholding on the histogram is a highly established method. Otsu’s method is a significant multilevel thresholding technique, in this multiple threshold levels selected on histogram and group the pixels of an image into different regions. The optimized threshold levels computed with an Optimized technique by maximizing the inter-class variance. Methods with histograms are incapable to possess spatial details of contextual information for finding optimal threshold levels. As a remedy, a novel method proposed the Energy Curve is used instead of a histogram with Otsu’s method and Harmony Search Algorithm to compute optimized gray levels. The proposed method experimented on several benchmark images, and results compared with various optimization algorithms with histogram by Dunn Index, DB Index, SD Index, mean of fitness and PSNR, comparison clarifies that the proposed method is superior to histogram-based methods.

Modified Moth-Flame Optimization Algorithm-Based Multilevel Minimum Cross Entropy Thresholding for Image Segmentation

Multilevel thresholding is a widely used image segmentation technique. However, multilevel thresholding becomes more and more computationally expensive as the number of thresholds increase. Therefore, it is essential to incorporate some suitable optimization technique to make it practical. In this article, a modification is proposed to the Moth-Flame Optimization (MFO) algorithm and then it is applied to multilevel thresholding for image segmentation. Cross entropy is used as the objective function to select the optimal thresholds. A set of benchmark test images are used to evaluate the proposed technique. The Mean Structural SIMilarity (MSSIM) index is used to measure the quality of the segmented images. The results of the proposed technique are compared with the original MFO, PSO, BFO, and WOA. Experimental results and analysis suggest that the proposed technique outperforms other techniques in terms of segmentation quality images and stability. Moreover, computation time required for multilevel thresholding is also reduced to a manageable level.

Modified water wave optimization algorithm for underwater multilevel thresholding image segmentation

Multilevel thresholding is a simple and important method for image segmentation in various applications that has drawn widespread attention in recent years. However, the computational complexity increases correspondingly when the threshold levels increase. To overcome this drawback, a modified water wave optimization (MWWO) algorithm with the elite opposition-based learning strategy and the ranking-based mutation operator for underwater image segmentation is proposed in this paper. The elite opposition-based learning strategy increases the diversity of the population and prevents the search from stagnating to improve the calculation accuracy. The ranking-based mutation operator increases the selection probability. MWWO can effectively balance exploration and exploitation to obtain the optimal solution in the search space. To objectively evaluate the overall performance of the proposed algorithm, MWWO is compared with six state-of-the-art meta-heuristic algorithms by maximizing the fitness value of Kapur’s entropy method to obtain the optimal threshold through experiments on ten test images. The fitness value, the best threshold values, the execution time, the peak signal to noise ratio (PSNR), the structure similarity index (SSIM), and the Wilcoxon’s rank-sum test are used as important metrics to evaluate the segmentation effect of underwater images. The experimental results show that MWWO has a better segmentation effect and stronger robustness compared with other algorithms and an effective and feasible method for solving underwater multilevel thresholding image segmentation.

Kapur’s Entropy for Underwater Multilevel Thresholding Image Segmentation Based on Whale Optimization Algorithm

Multilevel thresholding is an effective and indispensable technology for image segmentation that has attracted extensive attention in recent years. However, the multilevel thresholding method has some disadvantages, such as a large computational complexity and low segmentation accuracy. Therefore, this paper proposes a whale optimization algorithm (WOA) based on Kapur's entropy method to solve the image segmentation problem. The WOA can effectively balance exploration and exploitation to avoid falling into premature convergence and obtain the global optimal solution. To verify the segmentation performance of the WOA, a series of experiments on underwater images from the experimental pool of Harbin Engineering University are conducted, and the segmentation results are compared with those of the BA, the FPA, MFO, the MSA, PSO and WWO by maximizing the fitness value of Kapur's entropy method. The fitness value, peak signal-to-noise ratio (PSNR), structure similarity index (SSIM), execution time and Wilcoxon's rank-sum test are used to evaluate the overall performance of each algorithm. The experimental results reveal that the WOA is superior to the other comparison algorithms and has a higher segmentation accuracy, better segmentation effect and stronger robustness. In addition, the feasibility and efficiency of the WOA are verified.

An ameliorated teaching–learning-based optimization algorithm based study of image segmentation for multilevel thresholding using Kapur’s entropy and Otsu’s between class variance

In this paper, multi-threshold image segmentation approaches using an improved teaching–learning-based optimization algorithm (DI-TLBO) are presented and the proposed DI-TLBO-based methods obtain satisfactory segmentation results. This work is presented as follows. Firstly, two random numbers are introduced to determine the learning methods of the learner in the teacher phases and the learner phases of DI-TLBO. Randomness of the learning methods further improves global optimization ability of DI-TLBO. Self-feedback learning phase and mutation-crossover phase are also introduced into DI-TLBO algorithm, which makes DI-TLBO achieve better exploration ability. The comparative results of DI-TLBO with other evolutionary algorithms (EAs) on a set of benchmarks functions demonstrate that DI-TLBO acquires better solution accuracy than other EAs. Then the proposed DI-TLBO algorithm is applied to solve multi-level threshold image segmentation problems modeled by Otsu’s between class variance function and Kapur’s entropy function. Experiments comparing DI-TLBO-based methods with other EAs based approaches on standard test images show that DI-TLBO-based methods possess superior performance in terms of both solution accuracy and stability of segmentation results. Finally, the proposed DI-TLBO-based methods are successfully applied in casting X-ray image segmentation for multi-level threshold. Although the defects in high resolution X-ray image (3072×2400) are easy to be ignored and omitted when being detected artificially, all the defects are segmented perfectly using the proposed DI-TLBO-based methods.

Multilevel Thresholding Image Segmentation based on Autonomous Groups Particle Swarm Optimization

Multilevel thresholding problems based on Otsu criteria are discussed in this paper. One weakness of the Otsu method is that computational time increases exponentially according to the number of thresholding dimensions. In this paper, a modified Particle Swarm Optimization (PSO) algorithm called Autonomous Groups Particles Swarm Optimization (AGPSO) is proposed to reduce two problems trapped in local minima and a slow convergence rate in solving high-dimensional problems. AGPSO is used for multilevel thresholding image segmentation. The performance of AGPSO is compared with standard PSO on three natural images. The parameters used to compare the performance of AGPSO and PSO are SSIM, PSNR, Computation Time, optimal threshold obtained from each algorithm. From the experimental results show that AGPSO is better when compared to PSO in image segmentation, from the resulting fitness value and higher SSIM and PNSR values.

A fuzzy adaptive gravitational search algorithm for two-dimensional multilevel thresholding image segmentation

Two-dimensional (2D) multilevel thresholding is an important technique for noisy image segmentation which has drawn much attention during the past few years. The conventional image segmentation methods are efficient for 2D bi-level thresholding. However, the computational complexity grows exponentially when extended to 2D multilevel thresholding since they search the optimal thresholds by exhaustive strategy. To tackle this problem, a fuzzy adaptive gravitational search algorithm (FAGSA) using Tsallis entropy as its objective function has been presented to find the optimal 2D multilevel thresholds in this paper. In the FAGSA, fuzzy logic controllers are designed to tune the control parameters. The state-of-the-art heuristic algorithms are compared with this proposed algorithm. Both test images and noisy images are utilized in the experiments to evaluate the performance of the involved algorithms. The experimental results significantly demonstrate the superiority of our algorithm in terms of the objective function value, image quality measures and time consumption.

Hyper-heuristic method for multilevel thresholding image segmentation

In digital image processing, one of the most relevant tasks is to classify pixels depending on their intensity level. To perform this process there exist different traditional methods as Otsu or Kapur, such methods are used to compute the thresholds that divide the histogram of the image into different groups. These methods are easy to implement for a single threshold; however, the computational effort is affected when more thresholds are required. Therefore, different meta-heuristic based approaches have been proposed, but each of them has its properties and limitations. So, this paper introduces an alternative concept to the image segmentation which is called hyper-heuristic that at each iteration determines the optimal execution sequence of meta-heuristic algorithms that provides the optimal thresholds. The proposed method consists of two layers, in the first layer, the genetic algorithm (GA) is used to determine the execution sequence of the meta-heuristic algorithms. While the second layer contains the set of four meta-heuristic algorithms that executed in a specific order, assigned by the current solution of GA, to update the threshold population. In order to evaluate the performance of the proposed approach, it has been tested over a set of benchmark images and the results provide a good performance in terms of quality of segmentation. Moreover, experimental comparisons support that the proposed hyper-heuristic is able to find more accurate solutions than other algorithms.

Bee Foraging Algorithm Based Multi-Level Thresholding For Image Segmentation

Multi-level thresholding is one of the essential approaches for image segmentation. Determining the optimal thresholds for multi-level thresholding needs exhaustive searching which is time-consuming. To improve the searching efficiency, a novel population based bee foraging algorithm (BFA) for multi-level thresholding is presented in this paper. The proposed algorithm provides different flying trajectories for different types of bees and takes both single-dimensional and multi-dimensional search aiming to maintain a proper balance between exploitation and exploration. The bee swarm is divided into a number of sub-swarms to enhance the diversity. A neighbourhood shrinking strategy is applied to mitigate stagnation and accelerate convergence. Experiments have been performed on eight benchmark images using between-class variance as the thresholding criterion. The performance of the proposed algorithm is compared with some state-of-art meta-heuristic algorithms. The results show that BFA is efficient and robust, produces excellent results with few control parameters, and outperforms other algorithms investigated in this consideration on most of the tested images.