Directeur de Recherche CNRS
Laboratoire LIRIS
Directeur de la Fédération Informatique de Lyon
Université de Lyon, Batiment Nautibus
43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
Tel: (+33) [0]4.72.44.82.40, Fax: (+33) [0]4.72.43.15.36
david.coeurjolly @ liris . cnrs.fr ( PGP)
   

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News

Digital Geometry

Geometry Processing on digital data, High performance volumetric analysis (n-Dimensional Euclidean Distance Transform, Euclidean Medial Axis extraction, Discrete Voronoi Diagram, Discrete Power Diagram, GPU implementation...), Discrete geodesic functions, Fast n-D image transformation using arithmetization process (Quasi-Affine Transforms,...), Discrete estimators (curvature, length, geodesic metrics) on 2D and 3D digital objects, Fundamental aspects in digital geometry (object recognition, digitization schemes,NP-completeness of the minimal medial axis and the minimal digital plane segmentation problems).

Point Sampling Computer Graphics

Spectral analysis of point distributions and variance prediction in Monte-Carlo integration, Tile-based sampling strategies with high quality blue-noise profiles, Computer graphics applications of point distributions (numerical integration, rendering...)

Geometry Processing

Shape processing, variational approaches for surface fairing, mesh denoising, feature extraction, digital surface regularization...

Curriculum Vitae

  • Janvier 2017 - ... Directeur de la Fédération Informatique de Lyon
  • Octobre 2011 - ... Directeur de recherches CNRS
  • Septembre 2011 - Janvier 2015 Responsable équipe m2disco
  • 2009 Médaille de Bronze du CNRS de la section 07
  • 5 Décembre 2007 Habilitation à Diriger des Recherches, Université Claude Bernard Lyon 1, Laboratoire LIRIS, UMR 5205
  • Décembre 2007 Promotion CR1
  • Décembre 2003 - Octobre 2011 Chargé de Recherche CNRS, Laboratoire LIRIS, UMR 5205.
  • Septembre 2003 - Décembre 2003 ATER à l'Institut National des Sciences Appliquées de Lyon (INSA), département Informatique, laboratoire de rattachement LIRIS UMR 5205.
  • Mars 2003 - Juin 2003 Post Doctorat, Laboratoire LIS, Université Joseph Fourier, Grenoble
  • Sept. 2000 - Dec. 2002 Doctorat d'université, Spécialité Informatique, Université Lumière Lyon 2.
  • Sept. 1997 - Sept. 2000 Magistère Informatique et Modélisation, Ecole Normale Supérieure de Lyon et Université Claude Bernard Lyon 1.

Digital Geometry / Computational Geometry / Image Processing (ENS Lyon, M1)

Illustrations come from many sources (previous lectures, personnal tech reports, wikipedia...). Some of them have been provided by colleagues and I'd like to thank them: Jacques-Olivier Lachaud, Tristan Roussillon, Isabelle Sivignon, Olivier Devillers, Nicolas Normand.

If you want to use this material, please let me know. Beside these lectures, 12 sessions of TP (practical works) are available. Most of them are based on DGtal.

Programmation générique sur GPU (UCBL, M1, MIF23, in French)

Other publication profiles: LIRIS, DBLP, Google Scholar

Edited Books and Proceedings

Géométrie discrète et images numériques, D. Coeurjolly, A. Montanvert and J.-M. Chassery, Ouvrage collectif, Traité IC2, Hermès, 416 pages, 2007
Chapters written in this book:
  • Eléments de base, D. Coeurjolly, A. Montanvert, and J.-M. Chassery
  • Distances discrètes, E. Thiel and D. Coeurjolly
  • Représentation par axe médian,D. Attali, D. Coeurjolly and E. Remy
  • Descripteurs de formes et moments géométriques, D. Coeurjolly and A. Montanvert
cover-lncs.jpg Proceedings of the 14th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI 2008), D. Coeurjolly, I. Sivignon, L. Tougne and F. Dupont, Springer, LNCS 2992, 2008.
Pattern Recognition, Special Issue on Discrete Geometry for Computer Imagery (DGCI 2008), I. Sivignon, D. Coeurjolly, L. Tougne, Elsevier, 42(10), Oct. 2009.
Computer and Graphics, Special Issue on Discrete Geometry for Computer Imagery (DGCI 2008), D. Coeurjolly, I. Sivignon and F. Dupont, Elsevier, Feb., 2009.
Discrete Applied Mathematics , Special Issue on Discrete Geometry for Computer Imagery (DGCI 2013), D. Coeurjolly, R. Gonzalez-Diaz, M.-J. Jimenez.

Chapters in Book

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants, J.O. Lachaud, D. Coeurjolly, J. Levallois. in Modern Approaches to Discrete Curvature. Lecture Notes in Mathematics. Springer International Publishing, 2017 (to appear).
Multigrid convergence of discrete geometric estimators, D. Coeurjolly, J.O. Lachaud, T. Roussillon. in Digital Geometry Algorithms. Theoretical Foundations and Applications to Computational Imaging, Lecture Notes in Computational Vision and Biomechanics, V. Brimkov and R. Barneva, vol 2, 395--424 2012.
Separable Distance Transformation and its Applications, D. Coeurjolly, A. Vacavant. in Digital Geometry Algorithms. Theoretical Foundations and Applications to Computational Imaging, Lecture Notes in Computational Vision and Biomechanics, V. Brimkov & R. Barneva, vol 2, 189--214, 2012.
Volumetric Analysis of Digital Objects Using Distance Transformation: Performance Issues and Extensions, D. Coeurjolly, In Applications of Discrete Geometry and Mathematical Morphology, U. Köthe and A. Montanvert and P. Soille, LNCS, vol 7346, 82--92, 2012.
Discrete geometry and projections, David Coeurjolly, Nicolas Normand. in "The Mojette Transform: theory and applications" , Jean-Pierre Guédon, ISTE, Wiley, 2009.

Publications in international journals

(Citation counts are dynamically fetched from google-scholar thanks to Jérémy Levallois's scripts)
Low-Discrepancy Blue Noise Sampling, Abdalla G. M. Ahmed, Hélène Perrier, David Coeurjolly, Victor Ostromoukhov, Jianwei Guo, Dongming Yan, Hui Huang and Oliver Deussen, SIGGRAPH Asia 2016, ACM Transactions on Graphics, 2016.
Citation(s): ..
Piecewise smooth reconstruction of normal vector field on digital data David Coeurjolly, Marion Foare, Pierre Gueth, Jacques-Olivier Lachaud. Computer Graphic Forum, 35(7), 2016 (presented at Pacific Graphics 2016).
Supplementary material.
Citation(s): ..
Scale-space Feature Extraction on Digital Surfaces Jérémy Levallois, David Coeurjolly, Jacques-Olivier Lachaud. Computers and Graphics, Elsevier, pp.12, 2015 (presented at SMI 2015), hal-01149102
Citation(s): ..
Variance Analysis for Monte Carlo Integration A. Pilleboue, G. Singh, D. Coeurjolly, M. Kazhdan and V. Ostromoukhov, SIGGRAPH 2015, ACM Trans. on Graphics, 2015
Project website (article, supp. material, code)
Slides
Citation(s): ..
Fast Tile-Based Adaptive Sampling with User-Specified Fourier Spectra Florent Wachtel, Adrien Pilleboue, David Coeurjolly, Katherine Breeden, Gurprit Singh, Gael Cathelin, Fernando de Goes, Mathieu Desbrun, Victor Ostromoukhov, SIGGRAPH 2014, ACM Trans. on Graphics, 33(4).

Abstract. We introduce a novel tile based method for adaptive two-dimensional sampling with user-specified spectral properties. Our approach achieves several orders of magnitude speed improvement over current spectrum-controlled sampling methods through a deterministic, hierarchical construction of self-similar, equi-area tiles whose spatial distribution is free of spurious spectral peaks. A lookup table of sample points, computed offline using any existing procedure that optimizes point sets to shape their Fourier spectrum, is then used to populate the tiles. The result is a linear-time, adaptive, and high-quality sampling of arbitrary density functions that conforms to the desired spectral distribution.i
Youtube Video
web site (suppl. material, code, datasets,...).
Citation(s): ...
Multigrid Convergent Principal Curvature Estimators in Digital Geometry D. Coeurjolly and J.-O. Lachaud, J. Levallois, Computer Vision and Image Understanding (CVIU), (accepted for publication), 2014
Citation(s): ...
Digital Flow for Shape Decomposition: Application to 3-D Microtomographic Images of Snow X. Wang, D. Coeurjolly and F. Flin, Pattern Recognition Letters, 2014
Citation(s): ...
Fast and Accurate Approximation of Digital Shape Thickness Distribution in Arbitrary Dimension D. Coeurjolly, Computer Vision and Image Understanding (CVIU), Volume 116, Issue 12, December, pp 1159--1167, 2012
Citation(s): ...
A Generic and Parallel Algorithm for 2D Digital Curve Polygonal Approximation G. Damiand and D. Coeurjolly, Journal of Real-time Imaging Processing (JRTIP), 6(3):145--157, 2011
Citation(s): ...
Separable algorithms for distance transformations on irregular grids A. Vacavant, D. Coeurjolly, L Tougne. Pattern Recognition Letters 32(9):1356-1364 , Elsevier. 2011.
Citation(s): ...
Measure of Straight Lines for Digital Contour Analysis, David Coeurjolly and Isabelle Sivignon, International Journal of Imaging Systems and Technology, 21(1):67-75, 2011. hal-PDF
Citation(s): ...
A Framework for Dynamic Implicit Curve Approximation by an Irregular Discrete Approach, Antoine Vacavant, David Coeurjolly and Laure Tougne Graphical Models, 71(3):113--124, 2009.
Citation(s): ...
Gift-Wrapping based Preimage Computation Algorithm , Yan Gerard, David Coeurjolly, Fabien Feschet, Pattern Recognition, Elsevier, 42:10(2255-2264), 2009. PDF
Citation(s): ...
Minimum Decomposition of a Digital Surface into Digital Plane Segments is NP-Hard , Isabelle Sivignon, David Coeurjolly, Discrete Applied Mathematics, 157(3):558�570, Elsevier, 2008. PDF
Citation(s): ...
Finding a Minimum Medial Axis of a Discrete Shape is NP-hard , David Coeurjolly, Jérôme Hulin, Isabelle Sivignon, Theoretical Computer Science, 206(1-2):72-79, Elsevier, 2008. PDF
Citation(s): ...
Discrete bisector function and Euclidean skeleton in 2D and 3D, M. Couprié, D. Coeurjolly and R. Zrour,Image and Vision Computing, 25(10):1519-1698, Elsevier, 2007 PDF-HAL
Citation(s): ...
Digital Planarity - A Review, V. Brimkov, D. Coeurjolly and R. Klette, Discrete Applied Mathematics, 15(4), pp 468-495,Feb 2007
Research Report (CITR, Auckland).
Citation(s): ...
Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension, D. Coeurjolly and A. Montanvert, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(3):437-448, 2007.
PDF (see the IEEE copyrigth notice in the PDF file).
Citation(s): ...
Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic grids, D. Coeurjolly and L. Zerarga, Computer and Graphics, 30(1),pp. 46-54, 2006. PDF
Citation(s): ...
Generalizations of Angular Radial Transform for 2D and 3D Shape Retrieval, J. Ricard, D. Coeurjolly and A. Baskurt, Pattern Recognition Letters, 26(14),pp. 2174--2186, October, 2005. PDF
Citation(s): ...
On digital plane preimage structure, D. Coeurjolly, I. Sivignon, F. Dupont, F. Feschet and J-M Chassery, Discrete Applied Mathematics, 151(1-3):78-92, 2005. PDF.
Citation(s): ...
An adaptive filtering method to evaluate normal vectors and surface areas of 3D objects: Application to snow images from X-ray tomography, F. Flin, J.-B. Brzoska, B. Lesaffre, C. Coléou, P. Lamboley, D. Coeurjolly, O. Teytaud, G. Vignoles and J.-F. Delesse, IEEE Transactions on Image Processing, 14(5):585-596, 2005
Citation(s): ...
A Comparative Evaluation of Length Estimators of Digital Curves, David Coeurjolly and Reinhard Klette, IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(2):252-258, February 2004
PDF 1.2Mo (see the IEEE copyrigth notice in the PDF file)
Citation(s): ...
2D and 3D Visibility in Discrete Geometry: an Application to Discrete Geodesic Paths, David Coeurjolly, Serge Miguet, Laure Tougne , Pattern Recognition Letters, 25(5):561-570, 2004. PDF
DOI: 10.1016/j.patrec.2003.12.002
Citation(s): ...
An elementary algorithm for digital arc segmentation., David Coeurjolly, Yan Gerard , Jean-Pierre Reveillès and Laure Tougne, Discrete Applied Mathematics, 139(1-3):31-50, 2004. digitalarcrecognition_dam04.pdf

Citation(s): ...

Publications in international conferences with selection committee

Interactive Curvature Tensor Visualization on Digital Surfaces.. Hélène Perrier, Jérémy Levallois, David Coeurjolly, Jean-Philippe Farrugia, Jean-Claude Iehl, Jacques-Olivier Lachaud, in International Conference on Discrete Geometry for Computer Imagery (DGCI2016), Springer-Verlag, vol 9647, 2016.
2D Parameter-free and Multigrid Convergent Digital Curvature Estimators.. J. Levallois, D. Coeurjolly, J.O. Lachaud, in International Conference on Discrete Geometry for Computer Imagery (DGCI2014), Springer-Verlag, vol 8668, 2014.
2D Subquadratic Separable Distance Transformation for Path-Based Norms. D.Coeurjolly, Dans International Conference on Discrete Geometry for Computer Imagery (DGCI2014), Springer-Verlag, p75--87, vol 8668, 2014.
Slides
Integral based Curvature Estimators in Digital Geometry. D.Coeurjolly, J.-O. Lachaud, J. Levallois, Dans International Conference on Discrete Geometry for Computer Imagery (DGCI2013), Springer-Verlag, vol 7749, p215--227, 2013.
Curvature-Driven Volumetric Segmentation of Binary Shapes: an Application to Snow Microstructure Analysis. X.Wang, L.Gilibert, F.Flin, D.Coeurjolly. Dans International Conference on Pattern Recognition (to appear) 2012.
Texture creation with colorimetric compensation for 3D objects decoration. M. Belperin, B.S Brandel, D. Coeurjolly. Dans Computer Graphics International, Bournemouth, UK. (to appear) 2012.
Decoration of plastic objects using multi view-dependent textures. M. Belperin, B.S Brandel, D. Coeurjolly. Dans SMI, College Station, Texas, USA . (to appear) 2012
Volumetric analysis of digital objects using distance transformation: performance issues and applications, D. Coeurjolly, Workshop on Applications of Digital Geometry and Mathematical Morphology, Istanbul, Turkey, Invited Lecture, 2010.
Fast and Accurate Approximation of the Euclidean Opening Function in Arbitrary Dimension, D. Coeurjolly, 20th International Conference on Pattern Recognition, Istanbul, Turkey, IEEE Computer Society, 2010.
presentation.pdfhal-PDF
Quasi-Affine Transformation in 3-D: Theory and Algorithms , D. Coeurjolly, V. Blot, M.A. Jacob-DaCol, 13th International Workshop on Combinatorial Image Analysis, Mexico, Springer Verlag, LNCS, 2009.
Hierarchical Discrete Medial Axis for Sphere-Tree Construction , A. Broutta, D. Coeurjolly, I. Sivignon, 13th International Workshop on Combinatorial Image Analysis, Mexico, Springer Verlag, LNCS, 2009.
Measure of Straight Lines and its Applications in Digital Geometry , D. Coeurjolly and I. Sivignon, 13th International Workshop on Combinatorial Image Analysis, Mexico,Research Publishing Services, 2009. mesureiwcia09.pdf
First Results on Medial Axis Extraction on Two-Dimensional Irregular Isothetic Grids , A. Vacavant, D. Coeurjolly, 13th International Workshop on Combinatorial Image Analysis, Mexico,Research Publishing Services, 2009.
Quasi-Affine Transformation in Higher Dimension , V. Blot and D. Coeurjolly, 15th IAPR International Workshop on Discrete Geometry for Computer Imagery, Montreal, Springer LNCS,2009.
A Novel Algorithm for Distance Transformation on Irregular Isothetic Grids , A. Vacavant, D. Coeurjolly and L. Tougne, 15th IAPR International Workshop on Discrete Geometry for Computer Imagery, Montreal, Springer LNCS,2009.
Distance Transformation, Reverse Distance Transformation and Discrete Medial Axis on Toric Spaces,D. Coeurjolly. International Conference on Pattern Recognition (ICPR 2008), IEEE Computer Society, Tampa, USA, 2008. PDF]
A Generic and Parallel Algorithm for 2D Image Discrete Contour Reconstruction, G. Damiand, D. Coeurjolly,Proc. of 4th International Symposium on Visual Computing (ISVC), Lecture Notes in Computer Science 5359, pages 792-801, December 2008, Las vegas, Nevada, USA, 2008.
Distance Transformation en Two-Dimensional Irregular Isothetic Grids, A. Vacavant, D. Coeurjolly, L Tougne, 14th International Conference on Discrete Geometry for computer Imagery, Lyon, France, Springer Verlag, LNCS 4992, 2008.
Gift-Wrapping based Preimage Computation Algorithm,Y. Gerard, F Feschet, D. Coeurjolly. 14th International Conference on Discrete Geometry for Computer Imagery, Lyon, France. LNCS 4992. 2008.
Duality and Geometry Straightness, Characterization and Envelope,Jean-Marc Chassery, David Coeurjolly, Isabelle Sivignon, 13th International Conference on Discrete Geometry for computer Imagery, Szeged, Hungary, Springer Verlag, LNCS 4245, p.1�16 2006. Jean-Marc Chassery was an invited speaker
Dynamic Reconstruction of Complex Planar Objects on Irregular Isothetic Grids , Antoine Vacavant,David Coeurjolly et Laure Tougne, International Symposium on Visual Computing (ISVC), Springer LNCS 4292, Nevada, USA, 2006.
Invertible Polygonalization of 3D Planar Digital Curves and Application to Volume Data Reconstruction, Martine Dexet, David Coeurjolly and Eric Andres, International Symposium on Visual Computing (ISVC), Springer LNCS 4292, Nevada, USA, 2006.
Minimal Decomposition of a Digital Surface into Digital Plane Segments is NP-Hard, Isabelle Sivignon and David Coeurjolly 13th International Conference on Discrete Geometry for computer Imagery, Szeged, Hungary, Springer Verlag, LNCS 4245, p.674-68, 2006.
Topological and Geometrical Reconstruction of Complex Objects on Irregular Isothetic Grids, Antoine Vacavant, David Coeurjolly and Laure Tougne 13th International Conference on Discrete Geometry for computer Imagery, Szeged, Hungary, Springer Verlag, LNCS 4245, p.470-481, 2006.
Optimization schemes for the reversible discrete volume polyhedrization using Marching Cubes simplification, David Coeurjolly, Florent Dupont, Laurent Jospin and Isabelle Sivignon, International Conference on Discrete Geometry for computer Imagery, Szeged, Hungary, Springer Verlag, LNCS 4245, p. 413-424, 2006.
Computational aspects of Digital Plane and Hyperplane Recognition, David Coeurjolly and Valentin Brimkov, 11th International Workshop on Combinatorial Image Analysis, 2006. Invited Lecture.
Optimal shape and inclusion: open problems, J.-M. Chassery and D. Coeurjolly, International Symposium on Mathematical Morphology, Computational Imaging and Vision, Springer,p. 229-248, 2005.
Supercover model and digital straight line recognition on irregular isothetic grids, D. Coeurjolly, 12th International Conference on Discrete Geometry for Computer Imagery, Springer-Verlag, LNCS 3429, p. 311-322, 2005
[Presentation PDF]
Generalization of Angular Radial Transform, J. Ricard, D. Coeurjolly, A. Baskurt, IEEE 2004 International Conference on Image Processing, ICIP 2004, Singapore, October 24-27, 2004.
ART Extension for Description, Indexing and Retrieval of 3D Objects, J. Ricard, D. Coeurjolly and A. Baskurt, ICPR 2004, 17th International Conference on Pattern Recognition, Cambridge, United Kingdom, 2004.
Reversible discrete volume polyhedrization using Marching Cubes simplification, David Coeurjolly and Isabelle Sivignon, SPIE Vision Geometry XII, 5300(1-11), 2004.
[Presentation PDF]
Digital straight line recognition on heterogeneous grids, David Coeurjolly and Laure Tougne, SPIE Vision Geometry XII, 5300(108-116), 2004.
[Presentation PDF]
d-Dimensional Reverse Euclidean Distance Transformation and Euclidean Medial Axis Extraction in Optimal Time, David Coeurjolly, Discrete Geometry for Computer Imagery, Springer, LNCS 2886, 2003.
Estimation of curvature along curves with application to fibres in 3D images of paper, David Coeurjolly and Stina Svensson, Scandinavian Conference on Image Analysis, 2003, Springer-Verlag, LNCS 2749, pages 247�254 2003.
Digital Plane Preimage Structure, D. Coeurjolly, I. Sivignon, F. Dupont, F. Feschet and J.-M. Chassery, International Workshop on Combinatorial Image Analysis, Elsevier,ENDM, 2003
Multigrid Convergence and Surface Area Estimation, D. Coeurjolly, F. Flin, O. Teytaud and L. Tougne, Theoretical Foundations of Computer Vision �Geometry, Morphology, and Computational Imaging�, Springer, LNCS, 2616, pages 101�119, 2003
From digital plane Segmentation to Polyhedral representation, I. Sivignon and D. Coeurjolly, Theoretical Foundations of Computer Vision Springer�Geometry, Morphology, and Computational Imaging�, Springer Verlag LNCS, 2616, pages 356�367, 2003
A Comparative Evaluation of Length Estimators, David Coeurjolly, Reinhard Klette, Internaltional Conference on Pattern Recognition, ICPR 2002, IEEE Computer Science, Quebec
Visibility in Discrete Geometry: an application to discrete geodesic paths., David Coeurjolly, Discrete Geometry for Computer Imagery, 10th International Conference, DGCI 2002, LNCS Springer 2301:326�327, Bordeaux - France
An elementary algorithm for digital arc segmentation., David Coeurjolly, Yan Gerard, Jean-Pierre Reveill�s and Laure Tougne, International Workshop on Combinatorial Image Analysis, 2001, volume 46, Electronic Notes in Theoretical Computer Science, Elsevier Science Publishers, Temple University, Philadelphia, Pennsylvania, U.S.A.
Segmentation and Length Estimation of 3D Discrete Curves, David Coeurjolly, Isabelle Debled-Rennesson and Olivier Teytaud, Digital and Image Geometry, LNCS Springer 2243:295-313, 2001.
Discrete Curvature based on Osculating Circles Estimation, David Coeurjolly, Serge Miguet, Laure Tougne, 4th International Workshop on Visual Form 2001, Capri, Italy, Springer Lecture Notes in Computer Science 2059, pages 303-312.

Habilitation à Diriger des Recherches (HDR)

Titre : Algorithmique pour l'analyse et la modélisation en géométrie discrète

Jury :

  • Mme. Borgefors Gunilla Rapporteur Professeur, CBA, Uppsala Universitet, Suède
  • M. Braquelaire Achille Rapporteur Professeur, LaBRI, Université Bordeaux 1
  • M. Maître Henri Rapporteur Professeur, TSI, ENST, Paris
  • Mme Montanvert Annick Examinateur Professeur, GIPSA-Lab, Univ. Pierre Mendès-France, Grenoble
  • M. Devillers Olivier Examinateur Directeur de Recherches, INRIA, Sophia-Antipolis
  • M. Péroche Bernard Examinateur Professeur, LIRIS, Université Lyon 1

Documents :

PhD Thesis

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

Télécharger le manuscrit :

Transparents de ma soutenance

Résumé : Cette thèse se situe dans le cadre de la géométrie discrète qui constitue l'une des grandes familles de méthodes dédiées � l'analyse automatisée des formes dans les images numériques 2D et 3D. Tous les systèmes d'acquisition d'images fournissent des données organisées sur une grille régulière, appelées données discrètes. Les méthodes que nous nous proposons d'explorer et d'�tendre conservent aux données ce caractère discret, par opposition aux techniques qui construisent préalablement un modèle continu approximant les objets à analyser. Nous nous intéressons plus particulièrement à l'étude des courbes et des surfaces discrètes. Dans un premier temps, nous analysons les objets de base que sont les droites, les plans et les cercles discrets. Nous présentons des algorithmes qui permettent de les caractériser et proposons des extensions à ces méthodes. Ensuite, nous étudions des métriques sur les objets discrets comme la transformation en distance euclidienne ou la notion de géodésique discrète. Une approche basée sur la visibilité dans les domaines discrets est introduite. La troisième partie est consacrée à la définition et à l'évaluation d'estimateurs de mesures euclidiennes telles que la longueur, la courbure ou l'aire. Des résultats de convergence de ces estimateurs sont établis. Enfin, nous présentons les applications dans lesquelles ces recherches ont été utilisées~: classification automatisée d'objets archéologiques et analyse des micro-structures d'échantillon de neige.

Title : Algorithmic and digital geometry for curve and surface characterization

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.

Supervised students

  • Thomas Caissard (2015-... with Tristan Roussillon and Jacques-Olivier Lachaud, ANR Project COMEDIC).
  • Hélène Perrier (2014-... with Victor Ostromoukhov): Point Sampling and Monte-Carlo Integration in Computer Graphics.
  • Matthieu Heitz (2016-... with Nicolas Bonneel): ANR ROOT, inverse problems in optimal transportation.

Former Students

  • Adrien Pilleboue (2015-2016, with Victor Ostromoukhov): Analyse spatiale et spectrale des motifs d'échantillonnage pour l'intégration Monte-Carlo
  • Jérémy Levallois: (2012-2015) with Jacques-Olivier Lachaud (ANR Project digitalSnow)
  • Xi Wang: (2010-2014), with Frederic Flin, CEN-MeteoFrance
  • Maxime Belperin: (2011-2013) with Sylvain Brandel (PhD started in 2009)
  • Alain Broutta: Discrete Hierarchical Medial Axis (2008-2011)
  • Antoine Vacavant: Digital Geometry and the Irregular Isothetic Model (2005/2008)
  • Julien Ricard: 2D/3D Shape Indexing and Retrieval (2002/2005)

HDR/PhD Committees

  • Henri Der Sarkissian (rapporteur) : Tomographie et géométrie discrètes avec la transformée Mojette, juin 2015
  • Julien André (examinateur) : Conception de réflecteurs pour des applications photométriques, mars 2015
  • Phuc Ngo (rapporteur) : Transformations rigides discrètes sur des images digitales 2D : analyses combinatoire et topologique, octobre 2013.
  • Nicolas Normand (HDR, rapporteur) : Projections et distances discrètes, novembre 2012
  • Frédéric Rieux (rapporteur) : Processus de Diffusion Discret Opérateur Laplacien appliqué à l'étude de surfaces, Août 2012
  • Raphaelle Chaine (HDR, examinateur) : Triangulations pertinentes pour les formes 3D, décembre 2011
  • Marc Rodriguez (rapporteur) : Redimensionnement adaptatif et reconnaissance de primitives discrètes, décembre 2011
  • Roland Levillain (rapporteur) : Octobre 2011
  • Mouhammad Said (rapporteur) : Géométrie multi-résolution des objets discrets bruités, LAMA, Université de Grenoble, Décembre 2010.
  • Thanh Phuong Nguyen (examinateur) : Etude des courbes discrète : applications en analyse d'images, LORIA, Université Nancy 1, Octobre 2010.
  • Shekhar Suresh Chandra (rapporteur) : Circulant theory of the Radon transform, Monash University, Australia, 2010*
  • Christophe Lohou (HDR, rapporteur) :
  • Emilie Charrier (examinateur) : Simplification polyédrique optimale pour le rendu, ESIEE-PARIS, Université Paris-Est, Décembre 2009.
  • Michel Loeb (rapporteur) : Modèles géométriques et mesures d'ensembles de cercles contraints, CPE, Université Jean Monnet, Saint-Etienne, Décembre 2008.
  • Robin Strand (opponent = rapporteur) : Distance Functions and Image Processing on Point- Lattices, CBA, Uppsala, Suède, Novembre 2008
  • François de Vielleville (examinateur) : Analyse de parties linéaires des objets discrets pour l'extraction de caractéristiques géométriques, LaBRI, Bordeaux, juillet 2007.
  • Martine Dexet (examinateur) : Architecture d'un modeleur géométrique à base topologique d'objets discrets et méthodes de reconstruction en dimensions 2 et 3, SIC Poitiers, décembre 2006.