Publication
Earth mover’s distances on discrete surfaces
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.
Download publicationRelated Resources
See what’s new.
2024
Exploring Opportunities for Adopting Generative AI in Automotive Conceptual DesignThis research discusses opportunities for adopting generative AI in…
2024
Autodesk Research Unveils Project Bernini for Generative AI 3D Shape CreationProject Bernini is a research effort focused on developing generative…
2024
Three Ways to Keep Learning from AU All Year LongCheck out how to continue learning from AU 2023 all year long…
1988
Hierarchical Encapsulation and Connection in a Graphical User Interface: a Music Case StudyGraphical representations consisting of nodes and arcs have proven…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us