We propose a novel discrete solver for optimizing functional map-based energies, including descriptor preservation and promoting structural properties such as area-preservation, bijectivity Laplacian commutativity among others. Unlike the commonly-used continuous optimization methods, our approach enforces map to be associated with pointwise correspondence hard constraint, which provides strong...

In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape de...

Shape is one of the most important properties of objects. This lecture summarizes the algorithms for shape analysis. Several commonly used simple descriptors are stated first. Then the algorithms are classified into boundary (or external) descriptors and regional (or internal) descriptors based on the boundary tracking only and boundary plus the interior tracking respectively. The characteristi...