FUZZY C-MEANS CLUSTERING METHOD WITH THE GIBBS PENALTY FUNCTION AND ARBITRARY POWERS OF THE VECTOR ACCESSORIES

Abstract

A new version of the Fuzzy C-means clustering method, which we have called the Fuzzy C-means with the Gibbs Penalty (GPFCM), is introduced. The algorithm is designed to cluster gray scale, color and multichannel images. The specificity of the algorithm is to use the additive Gibbs penalty function in order to control the local smoothness of cluster representations of images in the regions of image homogeneity. The local smoothness of the solutions found by the GPFCM depends on the values of the coefficients of the penalty function. In turn, these coefficients can be taken as functions of magnitude and direction of the image gradient. Unlike the standard Fuzzy C-means clustering algorithm, which is unstable with respect to image noise and distortions, the proposed GPFCM allows building robust cluster approximations of noisy and corrupted pictures. Algorithm properties are illustrated on real images. Experiments have shown that on the one hand, the algorithm properly represents the homogeneous image regions as separate clusters and, on the other hand, it prevents the merging of different homogeneous areas.