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Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization

  • C. Chefd’hotel
  • D. Tschumperlé
  • R. Deriche
  • O. Faugeras
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2350)

Abstract

Nonlinear partial differential equations (PDE) are now widely used to regularize images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a geometric framework to design PDE flows acting on constrained datasets. We focus our interest on flows of matrix-valued functions undergoing orthogonal and spectral constraints. The corresponding evolution PDE’s are found by minimization of cost functionals, and depend on the natural metrics of the underlying constrained manifolds (viewed as Lie groups or homogeneous spaces). Suitable numerical schemes that fit the constraints are also presented. We illustrate this theoretical framework through a recent and challenging problem in medical imaging: the regularization of diffusion tensor volumes (DTMRI).

Keywords

Tangent Space Homogeneous Space Tensor Orientation Constraint Preserve Image Inpainting 
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 2002

Authors and Affiliations

  • C. Chefd’hotel
    • 1
  • D. Tschumperlé
    • 1
  • R. Deriche
    • 1
  • O. Faugeras
    • 1
  1. 1.INRIASophia-AntipolisFrance

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