Fuzzy C-Means Clustering Algorithm for Image Classification and Processing

This document presents the implementation of the Fuzzy C-Means (FCM) clustering algorithm for image classification and digital image processing applications. The algorithm employs iterative optimization to assign membership values to each pixel, enabling soft clustering across multiple categories. Key implementation aspects include centroid initialization using k-means++ method, calculation of membership matrices through Euclidean distance metrics, and iterative updates until convergence criteria are met. We further explore multi-class segmentation techniques where the FCM algorithm partitions image data into distinct clusters based on feature similarity. For specialized applications, we integrate Synthetic Aperture Radar (SAR) image classification methodologies that incorporate texture analysis and speckle filtering to enhance classification accuracy. The implementation utilizes matrix operations for efficient membership calculations and includes parameters for controlling fuzziness index (m) and convergence threshold. Through these methods, we can effectively analyze and interpret various types of image data with improved precision and computational efficiency.