Showing papers on "Markov random field published in 1981"

Asymptotic Inference for Markov Random Fields on ℤd

Abstract: The purpose of this paper is to generalize results of D.K. PICKARD [1,2,3] on asymptotic inference for the Ising model. Using properties of Gibbs measures on ℤd, we give the canonical exponential structure in which we can study the estimation problem, in the case of vertical sampling. This exponential structure depends on the range of the interaction potential of the underlying Markov random field; we construct, therefore, a test to measure this range: this test is based on the markovian character of the associated Gibbs measure; next we present the properties and the asymptotic laws of the estimators and we compare horizontal to vertical sampling [4]. Certain properties depend on the criticality of the interaction potential [5,6]: consequently, we construct a test of criticality for the interaction potential. Finally, we set the problem of estimation in a random Ising model.

Linear Filtering Models for Terrain Image Segmentation.

Abstract: : A method for modeling images of natural terrain is developed and applied to the segmentation of aerial photographic data. An underlying stochastic structure based on linear filtering concepts provides a means of modeling the terrain in local areas of the image. Superimposed on this is a Markov random field that describes transitions from regions of one terrain type to another. Maximum likelihood and maximum a posteriori estimation is applied to estimate regions of similar terrain. Results of application to digitized aerial photographs of a rural area are presented and discussed. (Author)

Fitting Markov Random Field Models to Images.

Abstract: : We are interested in fitting two-dimensional, Gaussian conditional Markov random field (CMRF) models to images. The given finite image is assumed to be represented on a finite lattice of specific structure, obeying a CMRF model driven by correlated noise. The stochastic model is characterized by a set of unknown parameters. We describe two sets of experimental results. First, by assigning values to parameters in the stationary range, two-dimensional patterns are generated. It appears that quite a variety of patterns can be generated. Next, we consider the problem of estimating the unknown parameters of a given model for an image, and suggest a consistent estimation scheme. We also implement a decision rule to choose an appropriate CMRF model from a class of such competing models. The usefulness of the estimation scheme and the decision rule to choose an appropriate model is illustrated by application to synthetic patterns. Unilateral approximations to CMRF models are also discussed. (Author)