Publication
Dirichlet energy for analysis and synthesis of soft maps
Abstract
Soft maps taking points on one surface to probability distributions on another are attractive for representing surface mappings in the presence of symmetry, ambiguity, and combinatorial complexity. Few techniques, however, are available to measure their continuity and other properties. To this end, we introduce a novel Dirichlet energy for soft maps generalizing the classical map Dirichlet energy, which measures distortion by computing how soft maps transport probabilistic mass from one distribution to another. We formulate the computation of the Dirichlet energy in terms of a differential equation and provide a finite elements discretization that enables all of the quantities introduced to be computed efficiently. We demonstrate the effectiveness of our framework for understanding soft maps arising from various sources. Furthermore, we suggest how these energies can be applied to generate continuous soft or point-to-point maps.
Download publicationRelated Resources
See what’s new.
2024
Deep Dive on Project Phoenix in Industry PodcastIndustry podcast features in-depth conversation with David Benjamin…
2011
Post-Deployment Usability: A Survey of Current PracticesDespite the growing research on usability in the pre-development…
2009
Parts of the SUM: A Case Study of Usability Benchmarking Using the SUM MetricWe present real-world lessons learned conducting a usability benchmark…
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