  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.
