Medial branching is usually associated to perturbations of the object bound- ary rather than to its main geometric features. Such instability of the medial surface is a main obstacle for its confident application in shape recognition and description. Medial branches correspond to singularities of the medial surface and, thus, they are problematic for existing morphological and energy-based al- gorithms. In this paper, we use algebraic geometry concepts in an energy-based approach to compute a medial surface presenting a stable branching topology. We also present an efficient GPU-CPU implementation using standard image processing tools. The higher performance of our method in terms of compu- tational cost and medial surface quality is shown on a home-made synthetic database. Finally, we present some results on a medical imaging application for localization of abdominal pathologies.
Hospital de Sant Pau, AlmaITSystems, Universitat Pompeu Fabra, Hospital Clínic