A Symmetry-Aware BAS for Improved Fuzzy Intra-Class Distance-Based Image Segmentation

At present, the Beetle Antennae Search (BAS) algorithm has achieved remarkable success in image segmentation. However, when dealing with some complex image segmentation problems, particularly in the context of instance segmentation, which aims to identify and delineate each distinct object of interest, even within the same semantic class, there are problems such as poor optimization performance, slow convergence speed, and low stability. Therefore, to address the challenges of instance segmentation, an improved image segmentation model is proposed, and a novel BAS algorithm called the Crossover and Mutation Beetle Antennae Search (CMBAS) algorithm is designed to optimize it. The core of our approach treats instance segmentation as a sophisticated clustering problem, where each cluster center corresponds to a unique object instance. Firstly, an improved intra-class distance based on fuzzy membership weighting is designed to enhance the compactness of individual instances. Secondly, to quantify the genetic potential of individuals through their fitness performance, CMBAS uses an adaptive crossover rate mechanism based on fitness ranking and establishes a ranking-driven crossover probability allocation model. Thirdly, to guide individuals to evolve towards excellence, CMBAS uses a strategy for individual mutation of longicorn beetle antennae based on DE/current-to-best/1. Furthermore, the symmetry-aware adaptive crossover and mutation operations enhance the balance between exploration and exploitation, leading to more robust and consistent instance-level segmentation results. Experimental results on five typical benchmark functions demonstrate that CMBAS achieves superior accuracy and stability compared to the BAGWO, BAS, GWO, PSO, GA, Jaya, and FA algorithms. In image segmentation applications, CMBAS exhibits exceptional instance segmentation performance, including an enhanced ability to distinguish between adjacent or overlapping objects of the same class, resulting in smoother and more continuous instance boundaries, clearer segmented targets, and excellent convergence performance.