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Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces

Abstract : The context of the work presented in this thesis is the digital geometry. This research area is devoted to the automatic analysis of objects in digital images in dimension 2 and 3. All acquisition devices provide data organized on regular grids, called digital data. The algorithms that are explored and extended keep the discrete aspect of the data, in opposition to techniques based on an approximation process of a continuous model. More precisely, we are interested in the study of digital curves and surfaces. First of all, we consider basic digital objects such as digital straight lines, planes and circles. We present algorithms that allow to characterize such objects and we propose some extensions of these methods. Then, we study some metrics on the digital objects such as the Euclidean distance transform and the notion of digital geodesic. An approach based on the visibility property in digital domains is presented. In the third part, we define and evaluate estimators of the Euclidean measurements such as the length, the curvature or the area. Some results on the convergence of these estimators are presented. Finally, we illustrate some applications in which these researches have been used for: archaeological object automatic classification and snow sample micro-structure analysis.
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Contributor : David Coeurjolly Connect in order to contact the contributor
Submitted on : Monday, August 20, 2007 - 11:25:57 AM
Last modification on : Saturday, September 24, 2022 - 12:04:06 PM
Long-term archiving on: : Friday, April 9, 2010 - 12:58:44 AM


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License


  • HAL Id : tel-00167370, version 1



David Coeurjolly. Algorithmique et géométrie discrète pour la caractérisation des courbes et des surfaces. Interface homme-machine [cs.HC]. Université Lumière - Lyon II, 2002. Français. ⟨NNT : ⟩. ⟨tel-00167370⟩



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