Fast and Robust Fuzzy C-Means Clustering Algorithm Based on Morphological Reconstruction and Membership Filtering

In this paper, we introduce an enhanced FCM algorithm called FRFCM, which utilizes morphological reconstruction and membership filtering to achieve substantial improvements in efficiency and robustness over traditional FCM. The core innovation involves integrating a membership function filter into the standard FCM framework to mitigate instabilities caused by noise and outliers. Our Python implementation features morphological reconstruction operations for image preprocessing and a specialized membership filtering function that processes cluster affiliation matrices during iteration. Experimental evaluations across multiple datasets demonstrate that FRFCM achieves notable gains in both clustering accuracy and computational efficiency compared to conventional FCM. These advantages make FRFCM particularly suitable for practical applications requiring reliable clustering under noisy conditions. The algorithm's key functions include morphological reconstruction for noise suppression and adaptive membership filtering for outlier resistance, implemented through optimized matrix operations and iterative membership updates.