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Theses

Schémas de subdivision, analyses multirésolutions non-linéaires. Applications

Abstract : Subdivision schemes were initially introduced for the iterative construction of curves or surfaces starting from control points. It is a basic ingredient in the definition of multiresolution analyses, with applications in approximation and compression of images. In the
construction of curves, surfaces or in image compression, the convergence of the scheme towards a continuous function, the regularity of this function, the stability and the order of the scheme
are crucial properties. Linear schemes presenting an important limitation (they create oscillations in the vicinity of strong gradients which results of blurred zones close to contours in image compression), we have considered non-linear schemes written as a non-linear perturbation of a linear scheme. For this class of non-linear scheme, we have established convergence, regularity, stability theorems. These results have been applied to various non-linear schemes (pre-existing schems or schemes that we have built to answer precise problems).
Next, we have been interested in application of this theory to images compression. The analysis of the 2d multiresolution analysis associated to this class of schemes (stability and application) has been performed.
A second application deals with the construction of finite difference operators adapted to irregular grids, coupling subdivision schemes and finite difference operators.
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https://tel.archives-ouvertes.fr/tel-00326894
Contributor : Karine Dadourian <>
Submitted on : Monday, October 6, 2008 - 12:42:44 PM
Last modification on : Wednesday, October 10, 2018 - 1:26:48 AM
Long-term archiving on: : Thursday, June 3, 2010 - 9:31:25 PM

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Karine Dadourian. Schémas de subdivision, analyses multirésolutions non-linéaires. Applications. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2008. Français. ⟨tel-00326894⟩

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