In this thesis, we address the challenge of computing correspondences between dissimilar shapes. This implies that, although the shapes represent the same class of object, there can be major differences in the geometry, topology, and part composition of the shapes as a whole. Additionally, the dissimilarity can also appear in the form of a shape that possesses additional parts that are not present in another shape. We propose three approaches for handling such shape dissimilarity.
This thesis introduces a new type of meshes called 5-6-7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e., to only have valence-6 vertices. A 5-6-7 mesh is a closed triangle mesh where each vertex has valence 5, 6, or 7. An intriguing question is whether it is always possible to convert an arbitrary mesh into a 5-6-7 mesh.
Geometric silhouettes are arcs on a surface representation that separate front-facing regions from back-facing regions with respect to a given viewpoint. These arcs are in general significantly less complex than the surface itself, and carry a great deal of information describing the surface. In this thesis, we take a plane view of geometric silhouettes, defining them in terms of the tangential planes of the surfaces on which they are defined rather than its local properties. We show that this perspective leads to efficient algorithms as well as a novel characterization of silhouettes based on a silhouette-generating set, or SGS.
Presenter: Paul Stark
Presenter: Niklas Roeber
Presenter: Ken Chidlow