Chi-hsin Wu

Tree approximations to Markov random fields

Methods for approximately computing the marginal probability mass functions and means of a Markov random field (MRF) by approximating the lattice by a tree are described. Applied to the a posteriori MRF these methods solve Bayesian spatial pattern classification and image restoration problems. The methods are described, several theoretical results concerning fixed-point problems are proven, and four numerical examples are presented, including comparison with optimal estimators and the iterated conditional mode estimator and including two agricultural optical remote sensing problems. >

Texture-based segmentation using Markov random field models and approximate Bayesian estimators based on trees

We describe segmentation based on textures using the label and image model of D. Gemanet al., “Boundary Detection by Constrained Optimization,”IEEE Trans. Pattern Analysis and Machine Intelligence, 12(7):609–628, July 1990. We replace their maximuma posteriori estimation criterion with a Bayesian estimator that minimizes the sum of the pixel misclassification probabilities. The new estimation goal allows the use of a different computational algorithm, which is deterministic rather than random, based on approximating lattices by trees. An example demonstrating an accurate segmentation of a collage of Brodatz textures is included.

Texture-based segmentation using Markov random field models

We describe segmentation based on textures using the label and image model of D. Geman et al. We replace their maximum a posteriori estimation criteria with a Bayesian estimator that minimizes the sum of the pixel misclassification probabilities. The new estimation goal allows the use of a different computational algorithm based on approximating lattices by trees. An example demonstrating an accurate segmentation of a collage of Brodatz textures is included.

Deterministic parallel computation of Bayesian deblurring using cluster approximations

A family of approximations to Bayesian estimators based on Markov random fields models of images and mean squared error reconstruction criteria is described. The computation of the estimator requires the solution of a multivariable fixed point problem for which existence, uniqueness, and convergent algorithm results are stated. These algorithms preserve the structure of the grey levels. Two simple examples are given which show excellent performance.<<ETX>>

Application of the cluster approximation for the simultaneous restoration and segmentation of tomographic images

We describe a Bayesian restoration and segmentation algorithm based on a pixel-line Markov random field and using an efficient approximation based on locality of interactions. A medical tomography example is given.

Spatial pattern classification for optical agricultural remote sensing

We describe a new method for computing approximations to the marginal probability mass function of the random variables in a Markov random field (MRF). When applied to the a posteriori MRF, this yields approximations to the conditional marginal probability mass function, which is the key quantity in a Bayesian classifier. We apply these ideas to an optical agricultural remote sensing problem where they outperform the pixel-by-pixel ML classifier by 38%.

Cluster approximations for statistical image processing

A disadvantage of using discrete-state Markov random field models of images is that optimal estimators for reconstruction problems require excessive and typically random amounts of computation. In one approach the key task is the computation of the conditional mean of the field given the data or equivalently the unconditional mean of the a posteriori field. In this paper we describe a hierarchy of deterministic parallelizable methods for such computations.