Considering multiple surface hypotheses in a Bayesian hierarchy

In this paper, we present a probabilistic approach to segmentation which maintains a set of competing, plausible segmentation hypotheses. This is in contrast to previous approaches, in which probabilistic methods are used to converge to a single segmentation. The benefit of our approach is that belief values associated with segmentation hypotheses can be used to guide the recognition process, and, the recognition process can, in turn, exert influence on the belief values associated with segmentation hypotheses in the network. In this way, segmentation and recognition can be coupled together to achieve a combination of expectation driven segmentation and data-driven recognition. Our algorithms are based on the formalism of Bayesian belief networks. By storing segmentation hypotheses in a tree structured network, we are able to limit the storage demands associated with maintaining the competing hypotheses. We have also introduced an implicit representation for segmentation hypotheses (without this implicit representation, we would be forced to enumerate the power set of region groupings). Likelihood measures are used both to control the expansion of the hypothesis tree and to evaluate belief in hypotheses. Local likelihood measures are used during an expansion phase, in which leaf nodes are refined into more specific hypotheses. Global likelihood measures are applied during an evaluation phase. The global likelihood measures are derived by fitting quadric surfaces to the range data. By using this expand and evaluate approach guided by a measure of entropy defined on the leaves of the tree, we are able to limit the application of costly numerical fitting algorithms to a small number of nodes in the tree.