Probabilistic Information Fusion for Multi-Modal Image Segmentation

Observable evidence from disparate sources are combined coherently and consistently through a hierarchically structured knowledge tree. Prior knowledge of spatial interactions is modeled with Markov Random Fields. A posteriori probabilities of segmentations are maintained incrementally. This paper is a shortened version of [Chou and Brown 87], which contains many more references.* 1. A Probabilistic View of the Segmentation Problem Represent an image as a set of primitive elements S = . ., A segmentation w of the image with respect to a label set is a mapping from S to L. Let represent the label attached to a, in segmentation a. Let 0 be the set of all segmentations. The image segmenta­ tion problem with respect to L can be loosely described as to find the w) that "best fits" the information collected subject to the limitation of the computational resources. This section describes the uses of probability as the representation for vari­ ous kinds of information and the corresponding criteria for finding the "best fit" It is frequently desirable to organise segmentation labels as a hierarchical tree (Figure 1). Each internal node in a tree of labels represents the disjunction of its sons. Each cross-section is a mutually exclusive and exhaustive label set; i.e., a segmen­ tation problem can be denned with respect to a cross-section in a label tree. Using such a tree, we can represent a particular piece of knowledge about the labels at whatever level of abstrac­ tion that is appropriate. We use L to denote a set of mutually exclusive and exhaustive set of labels in a label tree H.