Markov chain Monte Carlo in Image Analysis
Markov chain Monte Carlo in image analysis,
by Peter Green (Bristol, UK).
Chapter 21 (pp. 381--399) of
Markov chain Monte Carlo in Practice, W. Gilks, S. Richardson and
D. J. Spiegelhalter, eds. Chapman and Hall, London (1996).
Digital images now routinely convey information in
most branches of science and technology. The Bayesian approach to the
analysis of such information was pioneered by Grenander (1983), Geman
and Geman (1984), and Besag (1986), and both fundamental research and
practical implementations have been pursued energetically ever since.
In broad terms, the Bayesian approach treats the recorded raw image as
numerical data, generated by a statistical model, involving both a
stochastic component (to accommodate the effects of noise due to the
environment and imperfect sensing) and a systematic component (to
describe the true scene under view). Using Bayes' theorem, the
corresponding likelihood is combined with a prior distribution on
the true scene description to allow inference about the scene on
the basis of the recorded image.
This informal and simplistic summary in fact embraces extraordinary
variety, both in the style of modelling and in the type of application
-- from say, removal of noise and blur in electron microscopy to the
recognition of objects in robotic vision. There is little common
ground in this wide spectrum about which to generalise, but one feature
that does stand out in any general view of image analysis literature is
the prominent role played by Markov chain Monte Carlo (MCMC) as a means
of calculation with image models.
The purpose of this article is to discuss general reasons for this
prominence of MCMC, to give an overview of a variety of image models
and the use made of MCMC methods in dealing with them, to describe two
applications in more detail, and to review some of the methodological
innovations in MCMC stimulated by the needs of image
analysis, that may prove important in other types of application.
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