Functional Maps Representation On Product Manifolds
Abstract
We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 21, 2019
- Source ID
- 10.1111/cgf.13598
Entities
People
- A. M. Bronstein
- Emanuele Rodolà
- J. Solomon
- M. M. Bronstein
- Z. Lähner
Organizations
- Army Research Office
- FP7 Ideas: European Research Council
- Imperial College London
- Intel Corporation
- Massachusetts Institute of Technology
- National Science Foundation
- Sapienza University of Rome
- Technical University of Munich
- Technion – Israel Institute of Technology