Analysis of Two-Dimensional Non-Rigid Shapes

Numerical Geometry of Non-Rigid Shapes

Hierarchical Matching of Non-rigid Shapes

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer vision. While rigid alignment can be parameterized using a small number of unknowns representing rotations, reflections and translations, non-rigid alignment does not have this advantage. The majority of the methods addressing this problem boil down to a minimization of a distortion measure. The complex...

Diffusion symmetries of non-rigid shapes

Detection and modeling of self-similarity and symmetry is important in shape recognition, matching, synthesis, and reconstruction. While the detection of rigid shape symmetries is well-established, the study of symmetries in nonrigid shapes is a much less researched problem. A particularly challenging setting is the detection of symmetries in non-rigid shapes affected by topological noise and a...

On elliptic operators and non-rigid shapes

Many shape analysis methods treat the geometry of an object as a metric space captured by the Laplace-Beltrami operator. In this thesis we present an adaptation of a classical operator from quantum mechanics to shape analysis where we suggest to integrate a scalar function through a unified elliptical Hamiltonian operator. We study the addition of a potential function to the Laplacian as a gene...

Retrieval of 3-Dimensional Rigid and Non-Rigid Objects

This dissertation focuses on the problem of 3D object retrieval from large datasets in a near realtime manner. In order to address this task we focus on three major subproblems of the field: (i) pose normalization of rigid 3D models with applications to 3D object retrieval, (ii) non-rigid 3D object description and (iii) search over rigid 3D object datasets based on 2D image queries. Regarding t...