Fuzzy clustering with spatial constraints

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 term, 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 the standard algorithm.