Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. (English) Zbl 0573.62030

Geman, Stuart; Geman, Donald

IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741 (1984).

Some methods for image restoration resulting by observing analogies between images and statistical lattice based systems are discussed. Their goal is to restore degraded images by means of a Bayesian approach introducing a statistical model based on the Gibbs distribution.
The problem of maximizing the conditional distribution of the image \(X=(F,L)\) (F stands for the matrix of observable pixel intensities while L is a matrix of unobservable edge elements), given data \(G=\underline g\), i.e. \(P(X=\underline x| G=\underline g)\) is solved with the aid of stochastic relaxation.

Reviewer: W.Pedrycz

MSC:

62F15	Bayesian inference
68T10	Pattern recognition, speech recognition

Keywords:

line process; MAP estimate; Markov random field; scene modeling; spatial degradation; image restoration; statistical lattice based systems; Gibbs distribution; maximizing the conditional distribution; stochastic relaxation