Geometric flows for shape analysis

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This research program will concentrate on two recent developments in the field of shape analysis. The first has to do with an outward flow by which the boundary of an object is recovered from a medial manifold. Very recent results in mathematics show that it is possible to recover the differential geometry of a bounding surface from appropriate calculations on its corresponding medial manifold. Furthermore, my group's work on hamilton-jacobi skeletons, and in particular our average-outward flux based formulation, has been shown to be a special case of a more general medial integral. In fact, it is now possible in theory to obtain integrals of measurable functions on surfaces or volumes directly in terms of their medial integral counterparts. I will focus on translating these theoretical results to a computational setting, grounded in my own expertise in the development of algorithms for obtaining and manipulating medial representations.