Colour Image Multilevel Thresholding Segmentation Using Trees Social Relationship Algorithm

Abstract

Colour image segmentation via multilevel thresholding is a fundamental yet challenging task in computer vision, primarily due to the exponential growth of candidate thresholds. This paper introduces the Trees Social Relationship Algorithm (TSR), a novel metaheuristic inspired by the cooperative behaviour of trees in a forest. TSR integrates hierarchical parallel sub-populations (sub-jungles), a growth-rate-driven selection mechanism, and three tailored operators (proliferation, seedling-proliferation, and layering) to balance exploration and exploitation. The algorithm optimizes entropy-based (Kapur) and variance-based (Otsu) objectives across colour channels. To ensure reproducibility, detailed pseudocode, parameter settings, and complexity analysis are provided. Extensive experiments on BSDS benchmark images compare TSR against ten established metaheuristics (PSO, ABC, BAT, BFO, BSA, Cuckoo, DE, EFO, FA, WDO). Evaluation metrics include PSNR, SSIM, FSIM, GCE, PRI, and VOI. Results demonstrate that TSR achieves superior segmentation quality, robust convergence behaviour, and faster execution, consistently outperforming competitors. Statistical validation using the Wilcoxon rank-sum test further confirms the significance of the improvements.