# The total variation denoising problem and Cheeger sets

## Vicent Caselles (Università Pompeu-Fabra, Barcellona)

created by novaga on 02 Apr 2009

8 apr 2009

Abstract.

Seminario di Analisi

Mercoledi' 8 Aprile, ore 16.30, Aula Dini.

Prof. Vicent Caselles (Universita' Pompeu Fabra'', Barcelona)

Titolo: The total variation denoising problem and Cheeger sets

Abstract: We will discuss the ability of the total variation denoising problem to restore discontinuities of the datum. On one hand this is related to the regularity of its solutions. On the other, the explicit solutions of the problem also show that the discontinuities may be smoothed at the points of the datum where the level lines have a high curvature. The study of the explicit solutions leads us to the study of Cheeger sets. Finally we will present some applications of Cheeger sets (with respect to anisotropic perimeters) to image segmentation and image interpolation problems.

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