AbstractsMathematics

Shape matching is among the most basic research fields in digital geometry processing, with applications ranging from industrial design to three-dimensional medical image analysis. Our focus is restricted to triangle meshes undergoing deformations that can be described by intrinsic isometries, that is, near-isometric changes. In this thesis, we propose a shape matching algorithm comprised by a feature detection and feature matching phase. Specifically, a shape descriptor is introduced, called the vicinity area descriptor, based on the surface area around each vertex bounded by an isoring for a given geodesic radius. We improve the distinctiveness of the local signature by extending it from a scalar to a vector descriptor referring to arbitrary number of areas defined by inner isorings. The most descriptive points are then extracted using non-maximum suppression. By also considering the preservation of geodesic distances among the corresponding pairs of features, we compute a double-order affinity matrix. This combinatorial affinity matrix encodes the pointwise and pairwise relations of features regarding the two meshes. This matrix is then fed to the spectral matching algorithm, a graph matching method, in order to establish correspondences between the two surfaces. Experiments include benchmarks under various conditions regarding internal variables and state-of-the-art methods comparisons. It is showed that the proposed framework is robust over near-isometric deformations and keeps well against modern algorithms.