Diffusion of General Data on Non-Flat Manifolds via Harmonic Maps Theory: The Direction Diffusion Case

  title={Diffusion of General Data on Non-Flat Manifolds via Harmonic Maps Theory: The Direction Diffusion Case},
  author={Bei Tang and Guillermo Sapiro and Vicent Caselles},
  journal={International Journal of Computer Vision},
In a number of disciplines, directional data provides a fundamental source of information. A novel framework for isotropic and anisotropic diffusion of directions is presented in this paper. The framework can be applied both to denoise directional data and to obtain multiscale representations of it. The basic idea is to apply and extend results from the theory of harmonic maps, and in particular, harmonic maps in liquid crystals. This theory deals with the regularization of vectorial data… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 39 references

Image selective smoothing and edge detection by nonlinear diffusion

  • L. Alvarez, P. L. Lions, J. M. Morel
  • 1992
Highly Influential
7 Excerpts

Variational restoration of non-flat image

  • T. Chan, J. Shen
  • 2000
Highly Influential
4 Excerpts

Singularities of harmonic maps

  • R. M. Hardt
  • 1997
Highly Influential
5 Excerpts

Uniqueness for the harmonic map flow in two di

  • A. 19761–790. Freire
  • 1995
Highly Influential
4 Excerpts

Minimizing p-harmonic maps into spheres

  • J. M. Coron, R. Gulliver
  • 1989
Highly Influential
5 Excerpts

Density of smooth functions between two manifolds in Sobolev spaces

  • F. Bethuel, X. Zheng
  • 1988
Highly Influential
6 Excerpts

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