On Sampling Methods and Annealing Algorithms
Abstract
Discrete Markov random fields (MRF's) defined on a finite lattice have seen significant application as stochastic models for images [1], [2]. There are two fundamental problems associated with image processing based on such random field models. First, we want to generate realizations of the random fields to determine their suitability as models of our prior knowledge. Second, we want to collect statistics and perform optimizations associated with the random fields to solve model-based estimation problems, e.g., image restoration and segmentation. According to the Hammersley-Clifford Theorem [3], MRF's which are defined on a lattice are in one-to-one correspondence with Gibbs distributions. Starting with [4] there have been various constructions of Markov chains which possess a Gibbs invariant distribution, and whose common characteristic is that their transition probabilities depend only on the ratio of the Gibbs probabilities (and not on the normalization constant). These chains can be used via Monte Carlo simulation for sampling from Gibbs distributions at a fixed temperature, and for finding globally minimum energy states by slowly decreasing the temperature as in the simulated annealing (or stochastic relaxation) method [5], [6]. Certain types of diffusion processes which also have a Gibbs invariant distribution can be used for the same purposes when the random fields are continuous-valued [7], [8].
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1990
- Accession Number
- ADA459479
Entities
People
- Sanjoy K. Mitter
- Saul B. Gelfand
Organizations
- Purdue University