Image Representation and Processing Using Autoregressive Random Fields with Multiple Roots of Characteristic Equations

Abstract

An analytical review of mathematical models of images was performed, and their main advantages and disadvantages were noted. It is proposed to use Random Fields (RF) generated by AutoRegressive (AR) models with multiple roots of characteristic equations for describing images with a smooth change in brightness. Results of the study of the proposed models probabilistic properties are presented. The results obtained for Random Sequences (RS) are generalized to multidimensional RF. The filtering efficiency of simulated images is investigated. Analytical expressions are obtained for the relative variance of the filtering error of the arbitrary dimension and multiplicities RF against the background of white noise. Algorithm for identifying the parameters and the multiplicity of the model using the Yule–Walker equations is proposed. The possibilities and efficiency of application of the developed algorithms on real images are considered.