Variational problems and PDEs on implicit surfaces

Conference Paper

A novel framework for solving variational problems and partial differential equations for scalar and vector-valued data defined on surfaces is introduced. The key idea is to implicitly represent the surface as the level set of a higher dimensional function, and solve the surface equations in a fixed Cartesian coordinate system using this new embedding function. The equations are then both intrinsic to the surface and defined in the embedding space. This approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces, as is commonly done in the literature. We describe the framework and present examples in computer graphics and image processing applications, including texture synthesis, flow field visualization, as well as image and vector field intrinsic regularization for data defined on 3D surfaces.

Full Text

Duke Authors

Cited Authors

  • Bertalmió, M; Sapiro, G; Cheng, LT; Osher, S

Published Date

  • January 1, 2001

Published In

  • Proceedings Ieee Workshop on Variational and Level Set Methods in Computer Vision, Vlsm 2001

Start / End Page

  • 186 - 193

International Standard Book Number 10 (ISBN-10)

  • 076951278X

International Standard Book Number 13 (ISBN-13)

  • 9780769512785

Digital Object Identifier (DOI)

  • 10.1109/VLSM.2001.938899

Citation Source

  • Scopus