Adaptation of the mathematical apparatus of the Markov chain theory for the probabilistic analysis of recurrent estimation of image inter-frame geometric deformations

Abstract

The paper is devoted to the analysis of the possibilities of using Markov chains for analyzing the accuracy of stochastic gradient relay estimation of image geometric deformations. One of the ways to reduce computational costs is to discretize the domain of studied parameters. This approach allows to choose the dimension of transition probabilities matrix a priori. However, such a matrix has a rather complicated structure. It does not significantly reduce the number of computations. A modification of the transition probabilities matrix is proposed, it’s dimension does not depend on the dimension of estimated parameters vector. In this case, the obtained relations determine a recurrent algorithm for calculating the matrix at the estimation iterations. For the one-step transitions matrix, the calculated expressions for the probabilities of image deformation parameters estimates drift are given.