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.

中文翻译：

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基于压缩系数的粒子群优化和重力搜索算法用于多级图像阈值化

图像分割是图像处理的关键步骤之一。实际上，它根据像素强度将图像划分为不同的类。这项工作介绍了一种基于压缩系数的粒子群优化和引力搜索算法（CPSOGSA）的新图像分割方法。图像的随机样本充当 CPSOGSA 算法的搜索代理。使用 Kapur 的熵方法确定阈值的最佳数量。CPSOGSA 在图像分割中的有效性和适用性是通过将其应用于 USC-SIPI 图像数据库中的五个标准图像来实现的，即 Aeroplane、Cameraman、Clock、Lena 和 Pirate。各种性能指标被用来研究模拟结果，包括最佳阈值、标准偏差、MSE（均方误差）、运行时间分析、PSNR（峰值信噪比）、最佳适应值计算、收敛图、分割图像图和箱线图分析。此外，通过利用 SSIM（结构相似性指标度量）和 FSIM（特征相似性指标度量）指标对图像准确性进行基准测试。此外，成对非参数有符号 Wilcoxon 秩和检验用于模拟结果的统计验证。此外，将CPSOGSA的实验结果与标准PSO、经典GSA、PSOGSA、SCA（正余弦算法）、SSA（salp swarm算法）、GWO（灰狼优化器）、MFO（飞蛾火焰优化器）等八种不同算法进行了比较和 ABC（人工蜂群）。仿真结果清楚地表明，混合 CPSOGSA 成功地提供了最好的 SSIM、FSIM、