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Textural signature, Bayesian estimation of the Markov random field parameters

The work on the Bayesian estimation of Markov fields in the FLIERS project has been a step towards the full exploitation of the Markov field as a model of texture. Since aerial and satellite images may contain clearly visible textural segments and also smoothly changing textures, and in general, no a priori information the tessellation of an image is available, simultaneously unsupervised estimation of both the textural homogeneity and the parameters was necessary. Markov field parameters were recognized as a potential set of textural signature, but their estimation was a problem. A separation of the problems of segmentation and parameterization was not wanted. By posing the problem as a Bayesian estimation problem, i.e. by writing the joint posterior probability density of a tessellation and parameters on condition of the data and then estimating the posterior mean of the field parameters, both problems were solved simultaneously.
The advantage of the Bayesian formulation lies in the posterior density: it gives the complete statistical description of the result and can be used to derive metrics on uncertainties like sample size effects and noise. The parameters can be used, for example, for a hierarchical model or as in our as an input to a classifier. The parameterization is under certain general conditions consistent from one image to another. This provides the opportunity to screen textural changes in a series of images taken from one target - landscape, cell cultivation, ice. The task was completed by writing a software program which estimates the Markov parameters using the Markov Chain Monte Carlo algorithm. The parameter values with their uncertainty estimates are then computable as an input to a classifier.

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