#### Technical Report USC-SIPI-160

“Textured Image Segmentation Based on Multivariate Analysis”

by Ruey-Cheng Cheng

July 1990

A textured image segmentation system is developed systematically based on multivariate analysis. A likelihood ration called Wilks' criterion is proposed as a measure of discriminant information and as a substitute for error analysis.

Feature extraction is based on the scaled Karhunen-Loeve transformation (KLT) which consists of the selected scaled eigenvectors by maximizing the Wilks' criterion, that make the segmentation system work in optimally with minimum classification error. In order to simplify the computational complexity, a feature reduction procedure based on a linear transformation is used to maximize Wilks' criterion in the classification space. The best linear transformation is composed of principal eigenvectors of a generalized eigenvalue problem.

Isolated errors always exist in the initial labeling because of the imperfections of texture modeling. These errors can be removed by applying a spatial constraint since neighboring pixels are likely to be in the same class. A Bayesian segmentation formulation is proposed, then a stochastic relaxation scheme is applied to remove isolated errors and to preserve the boundary positions precisely.

In unsupervised segmentation, the main problem is to determine how many clusters are present. The conventional criterion g2|W| developed from multivariate variance analysis is not reliable for textured image segmentation because the covariance matrices of textures are different. Hypothesis testing requires exact density functions that restricts its applications. Information theoretic criteria, AIC and MDL, are new approaches to estimate the number of Clusters. They are based on the mixture maximum likelihood function and subject to some constraints. These approaches are superior to conventional criterion because mixture maximum likelihood function reflects the nature of the data structure and the goodness of model fitting. Differences of parameter estimation between the K-means algorithms and the maximization of mixture likelihood are also discussed.

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