On texture and image interpolation using Markov models

Markov-type models characterize the correlation among neighboring pixels in an image in many image processing applications. Specifically, a wide-sense Markov model, which is defined in terms of minimum linear mean-square error estimates, is applicable to image restoration, image compression, and texture classification and segmentation. In this work, we address first-order (auto-regressive) wide-sense Markov images with a separable autocorrelation function. We explore the effect of sampling in such images on their statistical features, such as histogram and the autocorrelation function. We show that the first-order wide-sense Markov property is preserved, and use this result to prove that, under mild conditions, the histogram of images that obey this model is invariant under sampling. Furthermore, we develop relations between the statistics of the image and its sampled version, in terms of moments and generating model noise characteristics. Motivated by these results, we propose a new method for texture interpolation, based on an orthogonal decomposition model for textures. In addition, we develop a novel fidelity criterion for texture reconstruction, which is based on the decomposition of an image texture into its deterministic and stochastic components. Experiments with natural texture images, as well as a subjective forced-choice test, demonstrate the advantages of the proposed interpolation method over presently available interpolation methods, both in terms of visual appearance and in terms of our novel fidelity criterion.