On texture and image interpolation using Markov models

Shira Nemirovsky and Moshe Porat,
Department of Electrical Engineering, 
Technion - Israel Institute of Technology 
Haifa 32000, Israel


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.

Signal Processing: Image Communication, Vol. 24, pp. 139-157 (2009). 

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