9 - Shape Constraints in Deformable Models

Abstract

Deformable models for medical image segmentation are often enhanced by their use of prior shape information. Some problems are well suited to the constraints that global shape information provides, where the shapes of the organs or structures are very consistent and are well characterized by a specific shape model. Other problems involve structures whose shapes are highly variable or have no consistent shape at all and thus, require more generic constraints. This chapter describes approaches to these two types of segmentation problems illustrating the varying uses of shape information. For the first, it describes integrated approaches in a maximum a posteriori formulation using parametric models with associated probability densities. It also describes level set methods that incorporate powerful generic shape constraints, in particular, a thickness constraint. The chapter also discusses the development of these ideas, current methodology, and future directions. Although the situations requiring global shape models and more generic constraints are different, ultimately, these techniques are likely to benefit from each other. Generic constraints could be incorporated into global shape methods to augment their descriptive power, while global shape models could be incorporated into level set methods to take advantage of their convergence properties. This would allow both global shape and generic properties to be applied, to the degree they are available, resulting in increased robustness and accuracy.