Information in Markov random fields and image redundancy

Abstract

The rate of information transmission of a transmitter-receiver couple was defined by C.E. Shannon in his Information Theory. We use this concept in Computer Vision to define models of image redundancy. Houzelle et Giraudon applied information theory to a simple model considering an image as a set of isolated pixels. We introduce a Markov Random Field model to take into account the spatial neighbourhood of a pixel. We show that we have to determine some parameters of the MRF in order to obtain sufficient statistics from common satellite images, and we propose a measure based on a generalized Ising model. Another model which also takes into account a pixel's spatial context is then proposed. It considers the correspondence between grey level vectors of cliques. We introduce a distance in the grey level space to solve the problem of insufficient statistics. Finally, results for the proposed definitions are presented for some synthetic and a large variety of SPOT XS1, XS2 and XS3 image triples and are compared to the classical correlation coefficient measure.