SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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A basic diffusion model on Grassmannians for simultaneous Detection, Segmentation and Restoration in Video mini-sequences

J. Finat, E. Cuesta, A. Duran, A. Hurtado and R. Martinez

Noise and aliasing are two very common problems in Image Processing [2]. Both of them are irregularly distributed and very often their local behavior follows different patterns. To minimize adverse effects of noise and aliasing, it is necessary to recover well defined regions without degrading boundaries. First issue concerns to global aspects of image segmentation related to minimization of convex functionals having in account an adaptive behavior in terms of anisotropic diffusion. Second issue involves to the preservation of true edges (very often degraded or missing) in terms of regularization operators. In this work we develop an approach based in the use of grassmannians [1] which involves to a multivector representation of meaningful data (which are represented as points of a grassmannian) and their tracking along a mini-video sequence in terms of shifted means to identify tangent space to the grassmannian in order to have a robust initialization (Lipschitz).

[1] S. Mittal and P. Meer, Conjugate gradient on Grassmann manifolds for robust subspace estimation. Image and Vision Computing, Volume 30, Issues 6 and 7, June 2012, pp. 417 - 427
[2] E. Cuesta and J. Finat Codes, Image Processing by Means of a Linear Integro-differential Equation. Visualization, Imaging, and Image Processing, Paper 91, ACTA Press, Calgary 2003

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