How effective are current population-based metaheuristic algorithms for variance-based multi-level image thresholding?

Multi-level image thresholding is a common approach to image segmentation where an image is divided into several regions based on its histogram. Otsu’s method is the most popular method for this purpose, and is based on seeking for threshold values that maximise the between-class variance. This requires an exhaustive search to find the optimal set of threshold values, making image thresholding a time-consuming process. This is especially the case with increasing numbers of thresholds since, due to the curse of dimensionality, the search space enlarges exponentially with the number of thresholds. Population-based metaheuristic algorithms are efficient and effective problem-independent methods to tackle hard optimisation problems. Over the years, a variety of such algorithms, often based on bio-inspired paradigms, have been proposed. In this paper, we formulate multi-level image thresholding as an optimisation problem and perform an extensive evaluation of 23 population-based metaheuristics, including both state-of-the-art and recently introduced algorithms, for this purpose. We benchmark the algorithms on a set of commonly used images and based on various measures, including objective function value, peak signal-to-noise ratio, feature similarity index, and structural similarity index. In addition, we carry out a stability analysis as well as a statistical analysis to judge if there are significant differences between algorithms. Our experimental results indicate that recently introduced algorithms do not necessarily achieve acceptable performance in multi-level image thresholding, while some established algorithms are demonstrated to work better.</p

A grouping differential evolution algorithm boosted by attraction and repulsion strategies for masi entropy-based multi-level image segmentation

Masi entropy is a popular criterion employed for identifying appropriate threshold values in image thresholding. However, with an increasing number of thresholds, the efficiency of Masi entropy-based multi-level thresholding algorithms becomes problematic. To overcome this, we propose a novel differential evolution (DE) algorithm as an effective population-based metaheuristic for Masi entropy-based multi-level image thresholding. Our ME-GDEAR algorithm benefits from a grouping strategy to enhance the efficacy of the algorithm for which a clustering algorithm is used to partition the current population. Then, an updating strategy is introduced to include the obtained clusters in the current population. We further improve the algorithm using attraction (towards the best individual) and repulsion (from random individuals) strategies. Extensive experiments on a set of benchmark images convincingly show ME-GDEAR to give excellent image thresholding performance, outperforming other metaheuristics in 37 out of 48 cases based on cost function evaluation, 26 of 48 cases based on feature similarity index, and 20 of 32 cases based on Dice similarity. The obtained results demonstrate that population-based metaheuristics can be successfully applied to entropy-based image thresholding and that strengthening both exploitation and exploration strategies, as performed in ME-GDEAR, is crucial for designing such an algorithm