Bayesian estimation for multiscale image segmentation

We present a solution to the problem of intensity image segmentation using Bayesian estimation in a multiscale set up. Our approach regards the number of regions, the data partition and the parameter vectors that describe the probability densities of the regions as unknowns. We compute their MAP estimates jointly by maximizing their joint posterior probability density given the data. Since the estimation of the number of regions is also included into the Bayesian formulation we have a fully automatic or unsupervised method of segmenting images. An important aspect of our formulation is to consider the data partition as a variable to be estimated. We provide a descent algorithm that starts with an arbitrary initial segmentation of the image when the number of regions is known and iteratively computes the MAP estimates of the data partition and the associated parameter vectors of the probability densities. Our method can incorporate any additional information about a region while assigning its probability density. It can also utilize any available training samples that arise from di erent regions.