Displacement interpolation using Lagrangian mass transport

Nicolas Bonneel*, Michiel Van De Panne, Sylvain Paris, Wolfgang Heidrich

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

Interpolation between pairs of values, typically vectors, is a fundamental operation in many computer graphics applications. In some cases simple linear interpolation yields meaningful results without requiring domain knowledge. However, interpolation between pairs of distributions or pairs of functions often demands more care because features may exhibit translational motion between exemplars. This property is not captured by linear interpolation. This paper develops the use of displacement interpolation for this class of problem, which provides a generic method for interpolating between distributions or functions based on advection instead of blending. The functions can be non-uniformly sampled, high-dimensional, and defined on non-Euclidean manifolds, e.g., spheres and tori. Our method decomposes distributions or functions into sums of radial basis functions (RBFs). We solve a mass transport problem to pair the RBFs and apply partial transport to obtain the interpolated function. We describe practical methods for computing the RBF decomposition and solving the transport problem. We demonstrate the interpolation approach on synthetic examples, BRDFs, color distributions, environment maps, stipple patterns, and value functions.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 SIGGRAPH Asia Conference, SA'11
StatePublished - Dec 1 2011
Event2011 SIGGRAPH Asia Conference, SA'11 - Hong Kong, China
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the 2011 SIGGRAPH Asia Conference, SA'11

Other

Other2011 SIGGRAPH Asia Conference, SA'11
CountryChina
CityHong Kong
Period12/12/1112/15/11

Keywords

  • Displacement interpolation
  • Mass transport

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Software

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