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Interaction entre symbolique et numérique : application à la vision artificielle

Didier Bondyfalat 1, 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : The initial motivations of this work come from the camera calibration in computer vision. We are especially interested in using jointly time measures in the images and formal geometry constraints. We have even enlarged our research to the following theme: "interaction between symbolic and numerical computations". This work is divised into three parts. The first part deals with solving polynomial equations with approximate computation of eigenvalues and eigenvectors. Bath the transformation and the computation are continuous with respect to the coefficients of the equations and can tackle them with approximate coefficients. The second part present an algebraic context in which geometric constraints are easily writen. This formalism enable us to model the calibration of one or several cameras with a map. These calibrations can be performed by using almost only numerical linear systems solving. The third part deals with automated geometry deduction tools and their use to construct 3D articulated models. Numerical optimisation enable to determine the parameters of these articulated models so that their images are in correspondance to the images in the diffrent cameras.
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Contributor : Didier Bondyfalat <>
Submitted on : Thursday, April 5, 2012 - 3:08:13 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:22 PM
Document(s) archivé(s) le : Friday, July 6, 2012 - 2:37:51 AM


  • HAL Id : tel-00685629, version 1



Didier Bondyfalat. Interaction entre symbolique et numérique : application à la vision artificielle. Calcul formel [cs.SC]. Université Nice Sophia Antipolis, 2000. Français. ⟨NNT : 2000NICE5429⟩. ⟨tel-00685629⟩



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