Statistical models for MRF image restoration and segmentation

Yuh-Chin Chang, Purdue University

Abstract

Statistical models, and the resulting algorithms, for image processing depend on the goals, segmentation versus restoration, of the processing. For restoration, we propose models that are recursive non-symmetric half plane Markov processes driven by Cauchy-distributed residuals and the corresponding Bayesian recursive filters provide improved performance, especially at edges in the image. For segmentation based on intensity we propose two classes of model, multi-resolution Gibbs Markov Random Fields (MRF) and Hidden Markov Mesh Random Fields (HMMRF). Symbolic calculations of the behavior of multi-resolution Gibbs MRF in a mean-field approximation are presented as an aid to parameter identification and Iterated Conditional Mode segmentations using these models are demonstrated. Two estimation approaches based on HMMRF are considered. The first method is a recursive sub-optimal maximum a posteriori approach based on a D x D look ahead region and we demonstrate that a fourth order region provides the best performance in terms of visual perception. The second method is expectation-maximization computation of the maximum likelihood estimate which we are able to generalize to include adaptive estimation of the state transition probabilities. For segmentation based on texture we circumvent the difficulty of providing a texture model by taking a pattern recognition approach and apply clustering to multi-resolution feature vectors. The feature vectors are pre-selected test statistics of partitions at the fine resolution. The segmentation of textures is then equivalent to the classification of clusters in the created feature space. The resulting algorithm is highly efficient and robust to differences in the characteristics of the image.

Degree

Ph.D.

Advisors

Doerschuk, Purdue University.

Subject Area

Electrical engineering

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