On wide-sense Markov random fields and their application to improved texture interpolation

Random field models characterize the correlation between neighboring pixels in an image. Specifically, a wide-sense Markov model is obtained by assuming a separable correlation function for a 2D auto-regressive (AR) model. In this work we analyze the effect of sub-sampling on statistical features of an image such as histogram and the autocorrelation function. We show that the Markovian property is preserved for the 2nd-order case (of the wide-sense model) and use this result to prove that, under mild conditions, the histogram of such images is invariant under sub-sampling. Furthermore, we develop relations between the statistics of the image and its sub-sampled version in terms of moments and noise characteristics. Motivated by these results, we propose a new method for texture interpolation, based on orthogonal decomposition. Experiments with natural texture images demonstrate the advantages of the proposed method over presently available interpolation methods.