A Bipolar Fuzzy Approach to Image Segmentation: Enhancing Similarity Measures and Entropy Computation

Abstract

Image segmentation is a fundamental process in digital image analysis, with applications in object recognition, medical imaging, and computer vision. Traditional segmentation techniques often struggle with uncertainty, imprecise boundaries, and misclassified regions due to their inability to effectively model both positive and negative information. This study introduces a bipolar fuzzy-based computational approach that enhances segmentation accuracy by incorporating dual membership functions to represent both the presence and absence of image features. To further improve segmentation robustness, we extend classical similarity measures by formulating a Bipolar Fuzzy Jaccard Similarity, which quantifies both positive and negative membership interactions, leading to more precise region classification. Additionally, a novel Bipolar Rényi Entropy (BRE) measure is developed to capture uncertainty in segmentation by integrating bipolar fuzzy probability distributions, allowing for adaptive sensitivity to dominant and rare features. Experimental validation on grayscale image datasets demonstrates the superiority of the proposed approach over conventional fuzzy and graph-based segmentation methods, particularly in applications requiring high precision, such as medical imaging and AI-driven pattern recognition. The integration of bipolar fuzzy similarity and entropy measures provides a powerful computational framework for more accurate and interpretable image segmentation.