In this paper, we propose a more robust kernelized algorithm incorporating Gibbs spatial constraints for fuzzy segmentation of magnetic resonance imaging (MRI) data. The proposed method is implemented by incorporating a fuzzy Gibbs spatial compensation term in the objective function of kernelized fuzzy C-means algorithm. The spatial compensation term, modeled by Gibbs Random Field (GRF), is actually a normalized kernel- induced measure for the correlation of pixel neighborhoods, and very similar to Gaussian radial basis function (GRBF) kernel, which is usually used to measure the distances between the image data and the prototypes of clusters. The GRBF based kernel and the GRF based spatial constraints can bias the segmentation towards a better piecewise homogeneous classification. In this sense, the Gibbs compensation term can be considered as a coarser measurement for the correlation of neighboring pixels while GRBF kernel acts as a fine measurement for intensity information. The experiments on synthetic images, digital phantoms and real clinical MRI data show the proposed method is more robust and usually a better alternative than other algorithms.
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