This repository contains sources files of my Habilitation à Diriger des Recherches (in French):
"Algorithmique pour l'analyse et la modélisation en géométrie
discrète", David Coeurjolly, Habilitation à diriger des
Recherches, Université Claude Bernard Lyon 1, Décembre 2007.
The Soutenance folder contains the source files of the HDR defense.
The PDF version of the manuscript and defense slides can de downloaded here.
@phdthesis{dcoeurjo_HDR,
month = {dec},
school = {Universit{\'{e}} Claude Bernard Lyon 1},
author = {Coeurjolly, D.},
type = {Habilitation à diriger des Recherches},
title = {Algorithmique pour l{'}analyse et la mod{\'{e}}lisation en g{\'{e}}om{\'{e}}trie discr{\`{e}}te},
year = {2007}
}
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.
Running pdflatex hdr and pdflatex soutenance (with bibtex)
should build the PDF documents.
Creative Commons CC BY-NC-SA 4.0 license, see LICENSE.md
For specific figures, please refer to the manuscript for image credits.