Shape complexes in continuous max-flow segmentation

Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. This paper presents the concept of shape complexes, which combine geodesic star convexity with extendable continuous max-flow solvers. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous work required computationally expensive co-ordinate system warping which are ill-defined and ambiguous in the general case. These shape complexes are validated in a set of synthetic images as well as atrial wall segmentation from contrast-enhanced CT. Shape complexes represent a new, extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems.