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ECCV
2002
Springer

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

14 years 5 months ago
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
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 matrixvalued 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).
Christophe Chefd'Hotel, David Tschumperlé,
Added 16 Oct 2009
Updated 16 Oct 2009
Type Conference
Year 2002
Where ECCV
Authors Christophe Chefd'Hotel, David Tschumperlé, Olivier D. Faugeras, Rachid Deriche
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