Institut de Mathématiques de Toulouse

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12e séminaire SPOT

par Delphine Dallariva - publié le , mis à jour le

SPOT 12 - Séminaire Pluridisciplinaire d’Optimisation de Toulouse
Lundi 4 novembre 2013

Lieu : UT1, Salle MF323 (3ème étage, bât. F) conjoint au séminaire MAD

http://projects.laas.fr/spot/

14h : Otmar Scherzer (Computational Science Center, University of Vienna)
Optical Flow Revisited

Variational optical flow is a method for analyzing movements in images. It is widely used in Computer Vision, surveillance, and image analysis. It is possible to reformulate optical flow as a denoising problem. In this paper we give an overview on variational denoising methods and extend them to optical flow models, which results in variational optimization problems for vector valued data. Optical flow is traditionally computed from a sequence of flat images. Finally, we extend the concept of optical flow in a dynamic non-Euclidean setting and introduce variational motion estimation for images that are defined on an (evolving) surfaces. Moreover, we are presenting some examples of biological imaging for cell movement analysis. This is joint work with Lukas Lang and Clemens Kirisits (Univ. of Vienna)

15h : Markus Grasmair (Norwegian Univ. Sci. Tech. Trondheim)
The Multi-resolution Norm for Non-parametric Regression and Inverse Problems

We study the application of the multi-resolution norm, which measures the maximal size of scaled local means of a function, in the problems of non-parametric regression and deconvolution. Our main result is the derivation of convergence rates for Tikhonov regularization, where we use the multi-resolution norm as the similarity term and a homogeneous Sobolev norm for the regularization term. The results are based on an asymptotic estimate for the norm of samples of a Gaussian random variable as the sample size tends to infinity, and an interpolation inequality for the multi-resolution norm and Sobolev norms. This is a joint work with Housen Li and Axel Munk (University of Goettingen).