Reversible Harmonic Maps between Discrete Surfaces

Abstract

Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can sometimes be computed between nearly isometric meshes, the more general case of meshes with diverse geometries remains challenging. We propose a novel approach for direct map computation between triangle meshes without mapping to an intermediate domain, which optimizes for the harmonicity and reversibility of the forward and backward maps. Our method is general both in the information it can receive as input, e.g., point landmarks, a dense map, or a functional map, and in the diversity of the geometries to which it can be applied. We demonstrate that our maps exhibit lower conformal distortion than the state of the art, while succeeding in correctly mapping key features of the input shapes.

Document Details

Document Type
Pub Defense Publication
Publication Date
Mar 29, 2019
Source ID
10.1145/3202660

Entities

People

  • Danielle Ezuz
  • Justin Solomon
  • Mirela Ben-chen

Organizations

  • Army Research Office
  • Israel Science Foundation
  • Massachusetts Institute of Technology
  • National Science Foundation
  • Svend Beck Peter Holm og Vagn Jacobsens Almene Fond
  • Technion – Israel Institute of Technology

Tags

Fields of Study

  • Computer science

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Geodesy
  • Systems Analysis and Design