Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension

  • David Shafrir
  • Nir A. Sochen
  • Rachid Deriche
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)


We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly, as functions of the spatial coordinates. We derive the general implicit differential operators, and show how they can be used to generalize previous results concerning the Beltrami flow and other similar flows.

As examples, We show how these results can be used to regularize gray level and color images on manifolds, and to regularize tangent vector fields and direction fields on manifolds.


Intersection Manifold Target Manifold Implicit Constraint Graph Manifold Beltrami Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • David Shafrir
    • 1
  • Nir A. Sochen
    • 1
  • Rachid Deriche
    • 2
  1. 1.University of Tel-AvivRamat-Aviv, Tel-AvivIsrael
  2. 2.Odysee project, INRIA Sophia-AntipolisSophia-AntipolisFrance

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