Bayesian multiscale analysis of images modeled as Gaussian Markov random fields

Abstract

A Bayesian multiscale technique for the detection of statistically significant features in noisy images is proposed. The prior is defined as a stationary intrinsic Gaussian Markov random field on a toroidal graph, which enables efficient computation of the relevant posterior marginals. Hence the method is applicable to large images produced by modern digital cameras. The technique is demonstrated in two examples from medical imaging. We model digital images as intrinsic Gaussian Markov random fields. This Bayesian scale-space method detects significant gradient and curvature. Efficient computation is achieved by defining images on a toroidal graph. The technique is successfully demonstrated in two examples from medical imaging.