Seminar Details
2008-01-29 (14.00) : A Riemannian Framework for the Regularization of Symmetric Positive-Definite Tensor Fields
At Euler building
Organized by Mathematical Engineering
Speaker :
Maher MOAKHER
( Ecole Nationale d'Ingenieurs de Tunis
)
Abstract :
In this talk we present a Riemannian framework for the smoothing of data that are constrained to live in the space of symmetric
positive-definite matrices. We start by giving the differential geometry of this space. We then use the harmonic map and minimal
immersion theories to construct three flows that drive a noisy field of symmetric positive-definite data into a smooth one.
The harmonic map flow is the equivalent of the heat flow or isotropic linear diffusion which smooths data everywhere.
A modification of the harmonic flow leads to a Perona-Malik like flow which is a selective smoother that preserves edges.
The minimal immersion flow gives rise to a nonlinear system of coupled diffusion equations with anisotropic diffusivity.
Some preliminary numerical results are presented for synthetic diffusion tensor MRI data.