Algorithms for selecting parameters of combination of acyclic adjacency graphs in the problem of texture image processing

Nowadays the great interest of researchers in the problem of processing the interrelated data arrays including images is retained. In the classical theory of machine learning objects for recognition are examined independently. In the modern theory of machine learning, the problem of image processing is often viewed as a problem in the field of graph models. Image pixels constitute a unique array of interrelated elements. The interrelations between array elements are represented by an adjacency graph. The problem of image processing is often solved by minimizing Gibbs energy [2,3,6,7] associated with corresponding arbitrary adjacency graphs. The crucial disadvantage of Gibbs approach is that it requires empirical specifying of appropriate energy functions on cliques. This requirement is not always easily done. In the present work, we propose a simpler, but not less effective model, which is an expansion of the Markov chain theory indeed. In this model, the array of interrelated elements is represented in the form of a two-component Markov random field of hidden classes and their observed features. In linearly ordered arrays, the adjacency graph is a chain. This allows us to organize an efficient processing of data arrays based on popular approaches such as the dynamic programming or the Markov chain theory. The linear Markov models controlling changes of hidden classes of recognized objects are proved to be extremely efficient [4]. However, for arbitrary adjacency graphs with cycles the segmentation problem is more complicated. In particular, the adjacency graph for raster images is a lattice that contains cycles and is not an acyclic one. In this case, the using of Markov models leads to time-consuming algorithms and the processing problem belongs to the NP class [2]. In this work, our approach to image processing is based on the idea of replacing the arbitrary adjacency graphs by tree-like (acyclic in general) ones and linearly combining of acyclic Markov models in order to get the best quality of restoration of hidden classes. For acyclic adjacency graphs, the one-sided model of a Markov random field in the form of a Markov chain was previously proposed and the effective recognition algorithm [4] that is performed with three passes along the acyclic graph was developed. In this model, the problem of processing of the interrelated data arrays is solved as a problem of the supervised learning and recognition. The main idea is that results of independent learning are coordinated with each other through the graph model. The crucial advantage of this model among other things is that it allows us to restore numerically a posteriori distributions of hidden classes of a Markov random field. Properties of the one-sided model of a Markov random field can be configured using a Markov matrix of