Spatial Models for Fuzzy Clustering

A novel approach to fuzzy clustering for image segmentation is described. The fuzzy C-means objective function is generalized to include a spatial penalty on the membership functions. The penalty term leads to an iterative algorithm that is only slightly different from the original fuzzy C-means algorithm and allows the estimation of spatially smooth membership functions. To determine the strength of the penalty function, a criterion based on cross-validation is employed. The new algorithm is applied to simulated and real magnetic resonance images and is shown to be more robust to noise and other artifacts than competing approaches.