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“Unsupervised Hierarchical Segmentation of Textured Images Based on Homogeneity Testing”
by Zhenyu Wu and Richard Leahy
June 1990
A new unsupervised hierarchical segmentation scheme is presented and is applied to the problem of tissue classification of magnetic resonance (MR) images of the human brain. The images under study are modeled as a mosaic of 'homogeneous' subimages where each subimage is modeled as a first order Gauss-Markov random field (GMRF) with unknown parameters. The segmentation goal is to group the pixels into regions which, under a suitable hypothesis, are homogeneous GMRFs. An analysis of homogeneity testing for GMRF is presented and two tests are proposed: the hierarchical likelihood ratio test and the dispersion test. Useful analytic results are derived for the case of an uncorrelated random field. Based on the homogeneity tests a hierarchical segmentation approach is suggested. The image is represented by a quadtree, and a split and merge procedure is applied to find large homogeneous regions within the image. This is followed by a segmentation refinement step involving connected component labeling and region growing, in which most of the unclassified pixels will be attached to the neighboring regions to which they are most similar. Finally, a constrained maximum likelihood agglomerative clustering procedure is used to reduce the number of segmented regions. The idea here is to allow the algorithm to learn about the image by first clustering the 'easy' pixels while delaying decisions on the 'hard' pixels until more information has been gathered. One difficulty encountered in implementing the algorithm is evaluating the likelihood for irregularly shaped regions. A new highly accurate approximation for the determinant of the covariance matrix based on eigenanalysis is proposed to overcome this problem.