Denoising Tensors via Lie Group Flows

  • Y. Gur
  • N. Sochen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3752)


The need to regularize tensor fields arise recently in various applications. We treat in this paper tensors that belong to matrix Lie groups. We formulate the problem of these SO(N) flows in terms of the principal chiral model (PCM) action. This action is defined over a Lie group manifold. By minimizing the PCM action with respect to the group element, we obtain the equations of motion for the group element (or the corresponding connection). Then, by writing the gradient descent equations we obtain the PDE for the Lie group flows. We use these flows to regularize in particular the group of N-dimensional orthogonal matrices with determinant one i.e. SO(N). This type of regularization preserves their properties (i.e., the orthogonality and the determinant). A special numerical scheme that preserves the Lie group structure is used. However, these flows regularize the tensor field isotropically and therefore discontinuities are not preserved. We modify the functional and thereby the gradient descent PDEs in order to obtain an anisotropic tensor field regularization. We demonstrate our formalism with various examples.


Group Manifold Orthogonal Tensor Cayley Mapping Principal Chiral Model Image Processing Problem 
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

  • Y. Gur
    • 1
  • N. Sochen
    • 1
  1. 1.Department of Applied MathematicsTel-Aviv universityRamat-Aviv, Tel-AvivIsrael

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