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FINITE NEIGHBORHOOD INDUCED RANDOM FIELDS: A MODEL FOR IMAGES (PATTERN, TEXTURE)
Abstract
Probabilistic image representation models find application in the problem of image registration. A model is developed on which computation of the probability of registration could be tractable without making any unrealistic assumptions regarding correlation properties of images. A small number of parameters of the proposed model help simplify computations although the model cannot represent images of great complexity. This image model, finite-neighborhood-induced-random-field, (fnirf), is a causal random field on discrete space and discrete state. Fnirfs are defined by a two dimensional stochastic process (similar to a wave propagation) which is a generalization of homogeneous Markov chains. The key parameter of fnirfs is its neighborhood. Geometrical transformations are discussed to identify essential similarities among different processes. The entire sets of these fnirfs is partitioned into 'essentially similar' fnirfs using an equivalence relation induced by those geometrical transformations. Further, a collection of representative fnirfs, one from each equivalence class, is identified. Every member of this collection has the same neighborhood and they only differ in a numerical parameter called the transition probability. The ergodicity property of fnirfs is studied in detail. Two sets of sufficient conditions for ergodicity are developed. Besides the demonstration of the existence of a unique stationary state of the random field our interest lies in computing it (at least approximately). It is shown that the initial distribution of the stationary process (if it is ergodic) can be approximated by a one-dimensional Markov chain up to any desired accuracy. Finally, a very general but not in-depth analysis is done regarding the correlation characteristics of the images represented by fnirfs.
Subject Area
Computer science
Recommended Citation
MEHTA, SHASHANK KANTILAL, "FINITE NEIGHBORHOOD INDUCED RANDOM FIELDS: A MODEL FOR IMAGES (PATTERN, TEXTURE)" (1985). ETD collection for University of Nebraska-Lincoln. AAI8602933.
https://digitalcommons.unl.edu/dissertations/AAI8602933