Shape Complexes in Continuous Max-Flow Hierarchical Multi-Labeling Problems

Although topological considerations amongst multiple labels have been previously investigated in the context of continuous max-flow image segmentation, similar investigations have yet to be made about shape considerations in a general and extendable manner. This paper presents shape complexes for segmentation, which capture more complex shapes by combining multiple labels and super-labels constrained by geodesic star convexity. Shape complexes combine geodesic star convexity constraints with hierarchical label organization, which together allow for more complex shapes to be represented. This framework avoids the use of co-ordinate system warping techniques to convert shape constraints into topological constraints, which may be ambiguous or ill-defined for certain segmentation problems.