A Framework for Constructing Probability Distributions on the Space of Image Segmentations

The goal of traditional probabilistic approaches to image segmentation has been to derive a single, optimal segmentation, given statistical models for the image formation process. In this paper, we describe a new probabilistic approach to segmentation, in which the goal is to derive a set of plausible segmentation hypotheses and their corresponding probabilities. Because the space of possible image segmentations is too large to represent explicitly, we present a representation scheme that allows the implicit representation of large sets of segmentation hypotheses that have low probability. We then derive a probabilistic mechanism for applying Bayesian, model-based evidence to guide the construction of this representation. One key to our approach is a general Bayesian method for determining the posterior probability that the union of regions is homogeneous , given that the individual regions are homogeneous. This method does not rely on estimation, and properly treats the issues involved when sample sets are small and estimation performance degrades. We present experimental results for both real and synthetic range data, obtained from objects composed of piecewise planar and implicit quadric patches.