Texture synthesis and compression using Gaussian-Markov random field models

Abstract

The usefulness is illustrated of two-dimensional (2-D) Gaussian-Markov random field (MRF) models for coding of textures. The MRF models used are noncausal; the mean of observation <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> ) at position <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> is written as a linear weighted sum of neighboring observations surrounding <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> in all directions. The method of least squares is used to obtain estimates of the model parameters. The model is then used with periodic boundary conditions to regenerate the original texture. Results obtained indicate that this method could be used to compress textures with low bit rates.