Theses Defense

Ph.D. Thesis Defense: Matching Dissimilar Shapes -- Oliver van Kaick

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.

M.Sc. Thesis Defense: 5-6-7 Meshes - Nima Aghdaii

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.

M.Sc. Thesis Defense: Edge Aware Anisotropic Diffusion for 3D Scalar Data - Zahid Hossain

We present a novel anisotropic diffusion model targeted for 3D scalar
field data. Our model preserves material boundaries as well as fine tubular structures while noise is smoothed out. One of the major novelties is the use of the directional second derivative to define material boundaries instead of the gradient magnitude for thresholding. This results in a diffusion model that has much lower sensitivity to the diffusion parameter and smoothes material boundaries consistently compared to gradient magnitude based techniques. We analyze the stability and convergence of the proposed diffusion and demonstrate its denoising capabilities for both analytic and real data. We also discuss applications in the context of volume rendering.

Ph.D. Thesis Defense: A Plane View of Geometric Silhouettes - Matthew Olson


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.