טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentArbel Nadav Yehonata
SubjectPartial Correspondence of 3D Shapes using Properties of the
Nearest-Neighbor Field
DepartmentDepartment of Electrical Engineering
Supervisors Professor Ayellet Tal
Professor Lihi Zelnik-Manor


Abstract

This work proposes an algorithm for finding sparse vertex to vertex correspondences between shapes in three dimensions. The method is designed to address three challenging cases: large non rigid deformations, partiality of the shapes, and topological noise.

At the core of the method lies a novel, yet simple, similarity measure that analyzes statistical properties of the nearest-neighbor field, which is a mapping of vertices in a local shape descriptor space from the source surface to their nearest neighbors on the target shape. This information is shown to be powerful, compared to minimizing some function of distances. In particular, our proposed similarity function analyzes the diversity of the nearest-neighbor field and its preservation of distances.

Our algorithm leverages the proposed similarity measure with respect to smaller sub surfaces at multiple sizes, in order to obtain a sparse, yet coherent set of vertex to vertex correspondences. The latter can then be turned into dense correspondences using existing methods.

We provide an extensive empirical evaluation of our algorithm on existing common shape correspondence benchmarks. We show that our method outperforms existing state-of-the-art methods. In particular, the results on partial matching benchmarks shows that our method outperforms the best existing techniques, both quantitatively and qualitatively by a significant margin.