Image Segmentation Using Disjunctive Normal Bayesian Shape and Appearance Models

The use of appearance and shape priors in image segmentation is known to improve accuracy; however, existing techniques have several drawbacks. For instance, most active shape and appearance models require landmark points and assume unimodal shape and appearance distributions, and the level set representation does not support construction of local priors. In this paper, we present novel appearance and shape models for image segmentation based on a differentiable implicit parametric shape representation called a disjunctive normal shape model (DNSM). The DNSM is formed by the disjunction of polytopes, which themselves are formed by the conjunctions of half-spaces. The DNSM's parametric nature allows the use of powerful local prior statistics, and its implicit nature removes the need to use landmarks and easily handles topological changes. In a Bayesian inference framework, we model arbitrary shape and appearance distributions using nonparametric density estimations, at any local scale. The proposed local shape prior results in accurate segmentation even when very few training shapes are available, because the method generates a rich set of shape variations by locally combining training samples. We demonstrate the performance of the framework by applying it to both 2-D and 3-D data sets with emphasis on biomedical image segmentation applications.