LJKDeterministic Models and Algorithms: EDPMOISE Seminar

On Thursday December 15 2011 at 11h00 in Salle 1  Tour IRMA

Seminary of Mr Maher MOAKHER (Ecole Nationale d'IngĂ©nieurs de Tunis)

The geometry of the space of symmetric positivedefinite matrices and its applications in smoothing positivedefinite tensor fields

Summary

We start by presenting the differential geometry of the space of symmetric positivedefinite matrices. We give explicit forms of the metric tensor, Christoffel symbols, differential operators and geodesics on this Riemannian manifold. We then use the harmonic map and minimal immersion theories to construct three flows that drive a noisy field of symmetric positivedefinite data into a smooth one. The harmonic map flow is equivalent to the heat flow or isotropic linear diffusion which smooths data everywhere. A modification of the harmonic flow leads to a PeronaMalik 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.
