Variational Shape Representation for Modeling, Elastic Registration and Segmentation

Shapes describe objects in terms of information invariant to scale, translation and rotation. Depending of the data source, shapes may be represented by object contours or representation/transformations that sustain the objects characteristics, such as the signed distance function. Biomedical objects have inherent plasticity due to movement and changes over time. Elastic registration is a fundamental image analysis step for tracking anatomical structures, diseases, progress of treatment and in image-guided interventions. Variational level set methods (LSM) represent objects’ contours through an implicit function that enables tracking the objects’ topologies. This chapter provides an overview of variational shape modeling as applied to the registration and segmentation problems. The chapter evaluates similarity/dissimilarity measures and common energy functional representations used in elastic shape registration. Common numerical methods to solve the optimization involved are studied. In addition, the chapter discusses clinical applications for which shape-based models enable robust performance with respect to occlusion and other image degradation.