International Journal of Computer Vision

, Volume 50, Issue 3, pp 237–252 | Cite as

Orthonormal Vector Sets Regularization with PDE's and Applications

  • David Tschumperlé
  • Rachid Deriche
Article

Abstract

We are interested in regularizing fields of orthonormal vector sets, using constraint-preserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first develop a general variational framework that solves this regularization problem, thanks to a constrained minimization of φ-functionals. This leads to a set of coupled vector-valued PDE's preserving the orthonormal constraints. Then, we focus on particular applications of this general framework, including the restoration of noisy direction fields, noisy chromaticity color images, estimated camera motions and DT-MRI (Diffusion Tensor MRI) datasets.

partial differential equations (PDE) constrained vector-valued regularization orientation features anisotropic diffusion orthogonal matrices 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • David Tschumperlé
    • 1
  • Rachid Deriche
    • 1
  1. 1.Odyssee Lab, I.N.R.I.ASophia AntipolisFrance

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