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 publication

Related Resources

See what’s new.

Article

2023

Learning from and Inspiring Women at Girl Geek X

Dr. Tonya Custis shares how she learned about management and strategy…

Publication

2016

Motion Amplifiers: Sketching Dynamic Illustrations Using the Principles of 2D Animation

We present a sketching tool for crafting animated illustrations that…

Publication

2000

Interacting with smoke and fire in real time

The simulation of fluids is one of the most challenging problems in a…

Project

2021

Software Learning

This learning project investigates advanced techniques for assisting…

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