Earth mover's distances on discrete surfaces
Abstract
We introduce a novel method for computing the earth mover's distance (EMD) between probability distributions on a discrete surface. Rather than using a large linear program with a quadratic number of variables, we apply the theory of optimal transportation and pass to a dual differential formulation with linear scaling. After discretization using finite elements (FEM) and development of an accompanying optimization method, we apply our new EMD to problems in graphics and geometry processing. In particular, we uncover a class of smooth distances on a surface transitioning from a purely spectral distance to the geodesic distance between points; these distances also can be extended to the volume inside and outside the surface. A number of additional applications of our machinery to geometry problems in graphics are presented.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 27, 2014
- Source ID
- 10.1145/2601097.2601175
Entities
People
- Adrian Butscher
- Justin Solomon
- Leonidas J. Guibas
- Raif Rustamov
Organizations
- Hertz Foundation
- Max Planck Institute for Informatics
- National Science Foundation
- Office of Naval Research
- Stanford University