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Variational problems and partial differential equations on implicit surfaces

Publication ,  Journal Article
Bertalmío, M; Cheng, LT; Osher, S; Sapiro, G
Published in: Journal of Computational Physics
December 10, 2001

A novel framework for solving variational problems and partial differential equations for scalar and vector-valued data defined on surfaces is introduced in this paper. The key idea is to implicitly represent the surface as the level set of a higher dimensional function and to 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, and image and vector field intrinsic regularization for data defined on 3D surfaces. © 2001 Elsevier Science.

Duke Scholars

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

December 10, 2001

Volume

174

Issue

2

Start / End Page

759 / 780

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Bertalmío, M., Cheng, L. T., Osher, S., & Sapiro, G. (2001). Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics, 174(2), 759–780. https://doi.org/10.1006/jcph.2001.6937
Bertalmío, M., L. T. Cheng, S. Osher, and G. Sapiro. “Variational problems and partial differential equations on implicit surfaces.” Journal of Computational Physics 174, no. 2 (December 10, 2001): 759–80. https://doi.org/10.1006/jcph.2001.6937.
Bertalmío M, Cheng LT, Osher S, Sapiro G. Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics. 2001 Dec 10;174(2):759–80.
Bertalmío, M., et al. “Variational problems and partial differential equations on implicit surfaces.” Journal of Computational Physics, vol. 174, no. 2, Dec. 2001, pp. 759–80. Scopus, doi:10.1006/jcph.2001.6937.
Bertalmío M, Cheng LT, Osher S, Sapiro G. Variational problems and partial differential equations on implicit surfaces. Journal of Computational Physics. 2001 Dec 10;174(2):759–780.
Journal cover image

Published In

Journal of Computational Physics

DOI

ISSN

0021-9991

Publication Date

December 10, 2001

Volume

174

Issue

2

Start / End Page

759 / 780

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences