טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAnastasia Dubrovina Karni
SubjectNon-Rigid Shape Correspondence by Matching Spectral
Features and Global Geodesic Structures
DepartmentDepartment of Electrical Engineering
Supervisor Full Professor Kimmel Ron
Full Thesis textFull thesis text - English Version


Abstract

Finding a correspondence between two non-rigid shapes is one of the cornerstone problems in the field of three-dimensional shape processing. It plays an important role in multiple shape processing and analysis tasks, such as retrieval, morphing and deformation, symmetry and self-similarity detection. In this thesis we propose a framework for marker-less non-rigid shape correspondence, based on matching intrinsic invariant surface descriptors, and the metric structures of the shapes. We formulate the matching task as an optimization problem that can be used with any type of descriptors and metric, and solved using an integer optimization tool. We demonstrate our framework with a specific method for constructing isometry invariant descriptors using the Laplace-Beltrami operator, and with metric given by geodesic distances. We also explore the correspondence ambiguity problem arising when matching intrinsically symmetric shapes using only intrinsic surface properties. We show that when using the proposed invariant surface descriptors, it is possible to construct distinctive sets of surface descriptors for different possible correspondences. When used in a proper minimization problem, those descriptors allow us to explore all possible correspondences between two given shapes. To the best of our knowledge, this is the first attempt to deal with this correspondence ambiguity problem.