A New Fuzzy Clustering Algorithm for Image Segmentation

Abstract

The fuzzy c-means (FCM) algorithm is widely used image segmentation but, has several limitations. It is sensitive to noise, demonstrates variable convergence rate depending on data distribution, and its reliance on Euclidean distance fails to account for intra-cluster variations, particularly in complex and color images. Furthermore, FCM’s non-adaptive distance metric struggles with diverse cluster shapes, and most FCM-based approaches face difficulties in color image segmentation due to the challenges in spatial information acquisition. To address these limitations, we propose an Improved Gustafson-Kessel (IGK) algorithm that offers superior robustness compared to both FCM and traditional Gustafson-Kessel (GK) clustering. Our approach first applies morphological reconstruction (MR) for grayscale images and multivariate morphological reconstruction (MMR) for color images to ensure noise immunity while preservation image details. We then replace the Euclidean distance metric with Mahalanobis distance to adapt to varying cluster shapes. The algorithm iteratively updates cluster centers, membership matrix, and positive definite symmetric matrices, followed by a median filter refinement of the membership partition matrix. Unlike previous approaches, IGK eliminates the need for computing distances within local spatial neighbors during clustering. Experimental results on both grayscale and color images demonstrate that the proposed IGK algorithm achieves superior segmentation performance compared to existing FCM-based methods.