Approximation of Conditional Density of Markov Random Field and its Application to Texture Synthesis

Markov random field (MRF) based sampling method is popular for synthesizing natural textures. The main drawback of the synthesis procedure is the large computational complexity involved. In this paper, we propose an approximation of the conditional density description for the reduction of computational complexity required in sampling texture pixels from the conditional density. Assuming, Y isin Lambda, and X isin Lambda^d, we in this work studied the approximation of the conditional density function P(Y|X) as P(Y|thetas^t X), where thetas isin R^d, is a unit vector. We have also shown that the classical gradient based optimization method is not suitable for finding the solution of thetas. We have estimated thetas using genetic algorithm. The perceptual (visual) similarity and neighborhood similarity measures between the textures synthesized using the full conditional description and approximated description, are shown for validating the method developed.