Adaptively Weighted Residual-Driven Fuzzy $C$-Means for Image Segmentation in Presence of Mixed or Unknown Noise

Image segmentation in the presence of mixed or unknown noise is a persistent challenge. Traditional Fuzzy $C$-Means (FCM) algorithms often struggle with complex noise, necessitating either prior knowledge of the noise characteristics or separate noise removal steps. To address this limitation, this work elaborates a novel residual-driven FCM framework, adaptively handling a wide variety of noise types within a unified model. The residual (the difference between the noisy and estimated clean images) is decomposed into two components, i.e., Gaussian-like noise and impulse noise, thus generating a weighted $\ell _{2}/\ell _{1}$-norm regularization term for the accurate estimation of mixed or unknown noise. An exponential function of the residual magnitude governs this adaptive weighting, promoting $\ell _{2}$-norm-based smoothing for Gaussian-like noise and $\ell _{1}$-norm-based robustness to impulse noise. The regularization term is integrated into FCM's objective function. To further enhance the robustness of the newly generated objective function, spatial constraints are used to refine the clustering process. Experimental results on synthetic, medical, and real-world images demonstrate the superior effectiveness and efficiency of the proposed algorithm compared to existing methods, significantly enhancing FCM's applicability and providing a more accurate solution in real-world or noisy scenarios.