NDLI: Dirichlet energy for analysis and synthesis of soft maps

Content Provider	ACM Digital Library
Author	Solomon, Justin Butscher, Adrian Guibas, Leonidas
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. 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.
Starting Page	197
Ending Page	206
Page Count	10
File Format	PDF
ISSN	01677055 14678659
DOI	10.1111/cgf.12186
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-07-03
Publisher Place	Goslar
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Computer Networks and Communications

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Dirichlet energy for analysis and synthesis of soft maps