Bayesian Image Segmentation Using Wavelet-Based Priors

Abstract

This paper introduces a formulation which allows using wavelet-based priors for image segmentation. This formulation can be used in supervised, unsupervised, or semi-supervised modes, and with any probabilistic observation model (intensity, multispectral, texture). Our main goal is to exploit the well-known ability of wavelet-based priors to model piece-wise smoothness (which underlies state-of-the-art methods for denoising, coding, and restoration) and the availability of fast algorithms for wavelet-based processing. The main obstacle to using wavelet-based priors for segmentation is that they're aimed at representing real values, rather than discrete labels, as needed for segmentation. This difficulty is sidestepped by the introduction of real-valued hidden fields, to which the labels are probabilistically related. These hidden fields, being unconstrained and real-valued, can be given any type of spatial prior, such as one based on wavelets. Under this model, Bayesian MAP segmentation is carried out by a (generalized) EM algorithm. Experiments on synthetic and real data testify for the adequacy of the approach.