Multilevel Thresholding Medical Image Segmentation Using Adaptive Entropy-Regulated Particle Swarm Optimization

Abstract

Image segmentation clusters pixels with common intensity characteristics into different
regions. Multilevel thresholding is one of the most commonly used segmentation
techniques because it requires relatively low computational effort while producing
satisfactory results for many applications. The main challenge is selecting threshold values
that maximize segmentation quality. Standard Particle Swarm Optimization (PSO) may get
trapped in local optima before finding better threshold combinations, especially when
dealing with complicated search spaces. To overcome this limitation, an Adaptive Entropy-
Regulated Particle Swarm Optimization (AER-PSO) algorithm is developed for multilevel
threshold selection. In the proposed algorithm, a particle encodes a set of threshold values,
and Kapur's entropy defines the optimization objective. Normalized swarm entropy is used
to estimate swarm diversity and adaptively regulate the inertia weight, while Gaussian
perturbation is applied to particle velocities during low-diversity states to enhance
exploration and prevent premature convergence. The proposed method is evaluated against
PSO, Quantum Particle Swarm Optimization (QPSO), and Pyramid Particle Swarm
Optimization with Complementary Inertia Weights (CIWP-PSO). The evaluation is
performed using the same high-bit-depth medical image dataset employed in the original
CIWP-PSO study, as well as the publicly available BrainWeb and Internet Brain
Segmentation Repository (IBSR) datasets. Experimental results show that AER-PSO
consistently achieves higher Kapur entropy and outperforms the compared algorithms in
terms of Segmentation Accuracy, Jaccard Similarity, Dice Similarity, Sensitivity, Peak
Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Feature
Similarity Index Measure (FSIM). The novelty of AER-PSO lies in its entropy-regulated
adaptive inertia weight mechanism integrated with Gaussian velocity perturbation, which
dynamically balances exploration and exploitation, maintains swarm diversity, prevents premature convergence, and achieves superior multilevel threshold optimization and image
segmentation performance compared with existing PSO-based methods.