This talk will be focused on the characteristics and properties of some Markov random fields (MRFs) that seem well suited to the processing of three-dimensional (3-D) signals.
First, the 3-D segmentation problem using n-ary unilateral MRF models will be addressed. Theoretical properties relating the stationarity to the unilateral factorization of such fields will be presented. Then, we will show how a simple parameterization of such fields can be used to derive a numerically efficient unsupervised 3-D segmentation method.
Second, the 3-D restoration problem will be considered. We will present numerically efficient method, based on a straightforward 3-D extension of "edge-preserving" convex potential MRFs and on the maximization of the joint a posteriori likelihood using the duality principle. In addition, we will show how point spread functions with large support regions can be efficiently accounted for.
In both cases, applications to 3-D medical data will be presented, and the advantages, limitations and open problems will be discussed.
Yves Goussard was born in Paris, France, in 1957. He graduated from Ecole Nationale Superieure de Techniques Avancees in 1980, and he received the Doc. Ing. and Ph.D. degrees from the Universite de Paris-Sud, Orsay, France, in 1983 and 1989, respectively.
From 1983 to 1985, he was a visiting scholar at the Electrical Engineering and Computer Science Department of the University of California, Berkeley. In 1985, he was appointed a Charge de Recherche at CNRS, Gif-sur-Yvetts now an Associate Professor. During the academic year 1990-1991, he was on sabbatical leave at the Department of Electrical Engineering-Systems, University of Southern California, Los Angeles. After some work on nonlinear system identification and modeling, his interests moved toward ill-posed problems in signal and image processing with application to biological systems.
To link to Dr. Goussard's Home Page just click here