# Accession Number:

## ADA459479

# Title:

## On Sampling Methods and Annealing Algorithms

# Descriptive Note:

## Research rept.

# Corporate Author:

## PURDUE UNIV LAFAYETTE IN SCHOOL OF ELECTRICAL ENGINEERING

# Personal Author(s):

# Report Date:

## 1990-12-01

# Pagination or Media Count:

## 15.0

# Abstract:

Discrete Markov random fields MRFs 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, MRFs 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.

# Descriptors:

# Subject Categories:

- Statistics and Probability