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

Breast cancer is a prevalent disease and the second leading cause of death in women globally. Various imaging techniques, including mammography, ultrasonography, X-ray, and magnetic resonance, are employed for detection. Thermography shows significant promise for early breast disease detection, offering advantages such as being non-ionizing, non-invasive, cost-effective, and providing real-time results. Medical image segmentation is crucial in image analysis, and this study introduces a thermographic image segmentation algorithm using the improved Black Widow Optimization Algorithm (IBWOA). While the standard BWOA is effective for complex optimization problems, it has issues with stagnation and balancing exploration and exploitation. The proposed method enhances exploration with Levy flights and improves exploitation with quasi-opposition-based learning. Comparing IBWOA with other algorithms like Harris Hawks Optimization (HHO), Linear Success-History based Adaptive Differential Evolution (LSHADE), and the whale optimization algorithm (WOA), sine cosine algorithm (SCA), and black widow optimization (BWO) using otsu and Kapur's entropy method. Results show IBWOA delivers superior performance in both qualitative and quantitative analyses including visual inspection and metrics such as fitness value, threshold values, peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and feature similarity index (FSIM). Experimental results demonstrate the outperformance of the proposed IBWOA, validating its effectiveness and superiority.

Multilevel thresholding segmentation of color images plays an important role in many fields. The pivotal procedure of this technique is determining the specific threshold of the images. In this paper, a hybrid preaching optimization algorithm (HPOA) for color image segmentation is proposed. Firstly, the evolutionary state strategy is adopted to evaluate the evolutionary factors in each iteration. With the introduction of the evolutionary state, the proposed algorithm has more balanced exploration-exploitation compared with the original POA. Secondly, in order to prevent premature convergence, a randomly occurring time-delay is introduced into HPOA in a distributed manner. The expression of the time-delay is inspired by particle swarm optimization and reflects the history of previous personal optimum and global optimum. To better verify the effectiveness of the proposed method, eight well-known benchmark functions are employed to evaluate HPOA. In the interim, seven state-of-the-art algorithms are utilized to compare with HPOA in the terms of accuracy, convergence, and statistical analysis. On this basis, an excellent multilevel thresholding image segmentation method is proposed in this paper. Finally, to further illustrate the potential, experiments are respectively conducted on three different groups of Berkeley images. The quality of a segmented image is evaluated by an array of metrics including feature similarity index (FSIM), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and Kapur entropy values. The experimental results reveal that the proposed method significantly outperforms other algorithms and has remarkable and promising performance for multilevel thresholding color image segmentation.

In this paper, a new hybrid whale optimization algorithm (WOA) called WOA-DE is proposed to better balance the exploitation and exploration phases of optimization. Differential evolution (DE) is adopted as a local search strategy with the purpose of enhancing exploitation capability. The WOA-DE algorithm is then utilized to solve the problem of multilevel color image segmentation that can be considered as a challenging optimization task. Kapur’s entropy is used to obtain an efficient image segmentation method. In order to evaluate the performance of proposed algorithm, different images are selected for experiments, including natural images, satellite images and magnetic resonance (MR) images. The experimental results are compared with state-of-the-art meta-heuristic algorithms as well as conventional approaches. Several performance measures have been used such as average fitness values, standard deviation (STD), peak signal to noise ratio (PSNR), structural similarity index (SSIM), feature similarity index (FSIM), Wilcoxon’s rank sum test, and Friedman test. The experimental results indicate that the WOA-DE algorithm is superior to the other meta-heuristic algorithms. In addition, to show the effectiveness of the proposed technique, the Otsu method is used for comparison.

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.

Digital image segmentation is often used as a preprocessing step in image analysis where different objects in the image need to be separated. One of the most used techniques for image segmentation is multilevel thresholding. Different criteria are used for determination of optimal thresholds, but in all cases, multilevel thresholding is a hard optimization problem that cannot be solved by deterministic methods. Swarm intelligence stochastic optimization metaheuristics have been proven to be very successful for such problems. In this chapter, we propose adjusted guided fireworks algorithm (GFWA) for multiple optimal threshold determination based on Kapur's entropy, Otsu's criteria and Tsallis' entropy. Comparison with other state-of-the-art techniques shows that the GFWA exhibits superior performance.

Modified hybrid bat algorithm with genetic crossover operation and smart inertia weight for multilevel image segmentation

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.

Entropy-based thresholding techniques are quite popular and effective for image segmentation. Among different entropy-based techniques, minimum cross-entropy thresholding (MCET) has received wide attention in the field of image segmentation. Considering the high time complexity of MCET technique for multilevel thresholding, recursive approach to reducing its computational cost is highly desired. To reduce the complexity, further optimization techniques can be applied to find optimal multilevel threshold values. In this paper, a novel improved particle swarm optimization (IPSO)-based multilevel thresholding algorithm is proposed to search the near-optimal MCET thresholds. The general PSO algorithm often suffers from premature convergence problem which has been addressed in the IPSO by decomposing a high-dimensional swarm into several one-dimensional swarms, and then premature convergence is removed from each one-dimensional swarm. The proposed technique is applied to the set of grayscale images, and the experimental results infer that it produces better MCET optimal threshold values at a higher and faster convergence rate. The qualitative and quantitative results are compared with existing optimization techniques like modified artificial bee colony, Cuckoo search, Firefly, particle swarm optimization, and genetic algorithm. It has been observed that the proposed technique performs better in terms of producing better fitness value, less CPU time as quantitative measurements, and effective misclassification error, peak signal-to-noise ratio, feature similarity index measurement, complex wavelet structural similarity index measurement values as qualitative measurements compared to other considered state-of-the-art methods.

Medical image segmentation using exchange market algorithm

A fast image segmentation method with multilevel threshold of two-dimensional entropy was proposed based on the firefly algorithm to overcome the large amount of calculation and long computing time.Firstly,the principle of two-dimensional entropy threshold segmentation was analyzed,and the single threshold segmentation of two-dimensional entropy was extended to multilevel threshold segmentation.Then,the bionic mechanism and searching optimization process of the firefly algorithm were analyzed,and the multilevel threshold segmentation method of two-dimensional entropy combined with firefly algorithm was proposed.Finally,typical image segmentation experiments by using the proposed method were performed and the results were compared with those of two-dimensional entropy exhaustive segmentation method and the multilevel threshold segmentation method of two-dimensional entropy based on Particle Swarm Optimization(PSO).Experimental results show that the speeds of the proposed method in single threshold segmentation,dual-threshold segmentation and thethree threshold segmentation are 3.91,1 040.32and 8 128.85times faster than those of the two-dimensional entropy exhaustive segmentation method respectively.Moreover,the threshold selection accuracy and running speed of the proposed method are both better than those of the multilevel threshold segmentation method of two-dimensional entropy based on PSO.Therefore,the fast image segmentation method with multilevel threshold of two-dimensional entropy based on firefly algorithm can quickly and efficiently resolve complex and multi-target image segmentation problems.

Optimal multi-level thresholding with membrane computing

Image enhancement is an important step in image processing to improve contrast and information quality. Intelligent enhancement algorithms are gaining popularity due to the limitations of traditional methods. This paper utilizes a transformation function to enhance the global and local information of grayscale images, but the parameters of this function can produce significant changes in the processed images. To address this, the whale optimization algorithm (WOA) is employed for parameter optimization. New equations are incorporated into WOA to improve its global optimization capability, and exemplars and advanced spiral updates improve the convergence of the algorithm. Its performance is validated on four different types of images. The algorithm not only outperforms comparison algorithms in the objective function but also excels in other image enhancement metrics, including peak signal-to-noise ratio (PSNR), feature similarity index (FSIM), structural similarity index (SSIM), and patch-based contrast quality index (PCQI). It is superior to the comparison algorithms in 11, 6, 11, 13, and 7 images in these metrics, respectively. The results demonstrate that the algorithm is suitable for image enhancement both subjectively and statistically.

Reversible image watermarking schemes are used to protect ownership and copyrights of digital images. This paper proposes a novel reversible image watermarking scheme based on adaptive image interpolation, segmentation and additive prediction error expansion (PEE). Proposed interpolation comprises of weighted average of neighboring pixels by allocating higher and lower weights to less and more distant neighboring pixel values respectively. The proposed adaptive image interpolation focuses on detection of edges thus minimizing artifacts imposed by interpolation. The idea of embedding varying amount of watermark bits in different image segments has been explored. Simple linear iterative clustering (SLIC) based image segmentation is performed to separate very sharp, sharp, smooth and very smooth regions in image. Higher number of watermark bits are embedded in sharp regions by using additive prediction error expansion embedding technique. Simulations of proposed and existing techniques were performed on different images and compared using embedding capacity (EC), peak signal to noise ratio (PSNR), computational efficiency, image quality, mean square error (MSE), normalized cross correlation (NCC) and structural similarity index (SSIM). The experimental results show that proposed scheme achieves better results in terms of EC, PSNR, computational efficiency, image quality, MSE, NCC and SSIM as compared to existing techniques.

Segmentation is one of the most important tasks in image processing that endeavors to classify pixels into two or more groups according to their intensity levels and a threshold value. Since traditional image processing techniques exhibit several difficulties when they are employed to segment images, the use of evolutionary algorithms has been extended to segmentation tasks in last years. The Harmony Search Algorithm (HSA) is an evolutionary method which is inspired in musicians improvising new harmonies while playing. Different to other evolutionary algorithms, HSA exhibits interesting search capabilities still keeping a low computational overhead. In this chapter, a multilevel thresholding (MT) algorithm based on the HSA is presented. The approach combines the good search capabilities of HSA with objective functions suggested by the popular MT methods of Otsu and Kapur. The presented algorithm takes random samples from a feasible search space inside the image histogram. Such samples build each harmony (candidate solution) in the HSA context whereas its quality is evaluated considering the objective function that is employed by the Otsu’s or Kapur’s method. Guided by these objective values, the set of candidate solutions are evolved through HSA operators until an optimal solution is found. The approach generates a multilevel segmentation algorithm which can effectively identify threshold values of a digital image in a reduced number of iterations. Experimental results show a high performance of the presented method for the segmentation of digital images.

Three-dimensional path planning for autonomous underwater vehicles based on a whale optimization algorithm