Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis and J. van Leeuwen

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1 Lecture Notes in Computer Science 1568 Edited by G. Goos, J. Hartmanis and J. van Leeuwen

2 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo

3 Gilles Bertrand Michel Couprie Laurent Perroton (Eds.) Discrete Geometry for Computer Imagery 8th International Conference, DGCI 99 Marne-la-Vallée, France, March 17-19, 1999 Proceedings 13

4 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Gilles Bertrand Michel Couprie Laurent Perroton ESIEE 2,Bd.BlaisePascal,B.P.99 F Noisy-Le-Grand Cedex, France Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Discrete geometry for computer imagery : 8th international conference ; proceedings / DGCI 99, Marne-la-Vallée, France, March 17-19, Gilles Bertrand...(ed.).-Berlin;Heidelberg;NewYork;Barcelona;HongKong; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1999 (Lecture notes in computer science ; Vol. 1568) ISBN CR Subject Classification (1998): I.3.5, I.4, G.2, I.6.8 ISSN ISBN Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. c Springer-Verlag Berlin Heidelberg 1999 Printed in Germany Typesetting: Camera-ready by author SPIN / Printed on acid-freepaper

5 Preface These proceedings contain papers presented at the 8th Discrete Geometry for Computer Imagery conference, held 17-19, March 1999 at ESIEE, Marne-la- Vallée. The domains of discrete geometry and computer imagery are closely related. Discrete geometry provides both theoretical and algorithmic models for the processing, analysis and synthesis of images; in return computer imagery, in its variety of applications, constitutes a remarkable experimentational field and is a source of challenging problems. The number of returning participants, the arrival each year of contributions from new laboratories and new researchers, as well as the quality and originality of the results have contributed to the success of the conference and are an indication of the dynamism of this field. The DGCI has become one of the major conferences related to this topic, including participating researchers and laboratories from all over the world. Of the 41 papers received this year, 24 have been selected for presentation and 7 for poster sessions. In addition to these, four invited speakers have contributed to the conference. The site of Marne-la-Vallée, just 20 min away from Paris, is particularly wellsuited to hold the conference. Indeed, as a newly built city, it showcases a great amount of modern creative architecture, whose pure lines and original shapes offer a favorable context for the topic of Geometry. We wish to thank ESIEE for providing the facilities. We also wish to thank for their financial support: PRC-GDR ISIS and AMI from the French CNRS, the city of Marne-la-Vallée (EPAMARNE), the Université de Marne-la-Vallée, the Ministère de la Recherche et de la Technologie, and more generally all the people who helped us organize the conference and made it possible. ESIEE, March 17, 1999 Gilles Bertrand, Michel Couprie, Laurent Perroton

6 VII Conference Co-Chairs G. Bertrand ESIEE, France M. Couprie ESIEE, France L. Perroton ESIEE, France Steering Committee E. Ahronovitz LIRM, Montpellier, France J.M. Chassery TIMC - IMAG Grenoble, France A. Montanvert TIMC - IMAG Grenoble, France M. Nivat LIAFA-Paris VI, France D. Richard LLAIC1, Clermont-Ferrand, France Program Committee D. Arquès IGM, Université Marne-La-Vallée, France Y. Bertrand IRCOM-SIC, Poitiers, France G. Borgefors Centre for Image Analysis, SLU, Sweden A. Del Lungo Università di Firenze, Italy U. Eckhardt Universität Hamburg, Germany C. Fiorio LIRM, Montpellier, France T.Y. Kong CUNY, New-York, USA V. Kovalevsky TF, Berlin, Germany W. Kropatsch TU, Vienna, Austria R. Malgouyres ISMRA, Caen, France S. Miguet ERIC, Université Lyon 2, France G. Sanniti di Baja CNR Napoly, Italy G. Szekely ETH-Zurich, Switzerland M. Tajine ULP, Strasbourg, France P. Wang Northeastern Univ. Boston, USA Organizing Committee and Local Arrangements G. Bertrand ESIEE, France M. Couprie ESIEE, France J. Durand ESIEE, France C. Lohou ESIEE, France L. Perroton ESIEE, France M. Warter ESIEE, France

7 VIII Referees Ahronovitz E. Kong T.Y. Arquès D. Kovalevsky V. Ayala R. Kropatsch W. Bertrand G. Lohou C. Bertrand Y. Malgouyres R. Borgefors G. Miguet S. Chassery J.M. Montanvert A. Couprie M. Nivat M. Del Lungo A. Perroton L. Devillers O. Richard D. Eckhardt U. Ronse C. Fiorio C. Sanniti di Baja G. Françon J. Szekely G. Goldman Y. Tajine M. Jolion J.M. Wang P.

8 Table of Contents Discrete Objects and Shapes... 1 Invited Paper: Multiresolution Representation of Shapes Based on Cell Complexes... 3 L. De Floriani, P. Magillo, E. Puppo Decomposing Digital 3D Shapes Using a Multiresolution Structure G. Borgefors, G. Sanniti di Baja, S. Svensson Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature F. Feschet, L. Tougne The Discrete Moments of the Circles J. Žunić Planes Graceful Planes and Thin Tunnel-Free Meshes V.E. Brimkov, R.P. Barneva Local Configurations of Digital Hyperplanes Y. Gérard (n,m)-cubes and Farey Nets for Naive Planes Understanding J. Vittone, J.M. Chassery Surfaces A Digital Lighting Function for Strong 26-Surfaces R. Ayala, E. Domínguez, A.R. Francés, A. Quintero Intersection Number of Paths Lying on a Digital Surface and a New Jordan Theorem S. Fourey, R. Malgouyres A Topological Method of Surface Representation V. Kovalevsky Presentation of the Fundamental Group in Digital Surfaces R. Malgouyres

9 X Table of Contents Reconstruction Invited Paper: Reconstruction in Different Classes of 2D Discrete Sets A. Kuba Curve Reconstruction in Arbitrary Dimension and the Traveling Salesman Problem J. Giesen Shape-from-Silhouette/Stereo and Its Application to 3-D Digitizer Y. Matsumoto, K. Fujimura, T. Kitamura Topology Invited Paper: Set Connections and Discrete Filtering J. Serra Topological Operators on the Topological Graph of Frontiers E. Ahronovitz, C. Fiorio, S. Glaize New Notions for Discrete Topology G. Bertrand A Model for Digital Topology G. Bertrand, M. Couprie Borders Map: A Topological Representation for nd Image Analysis Y. Bertrand, C. Fiorio, Y. Pennaneach A Discrete Homotopic Deformable Model Dealing with Objects with Varying Local Dimension Y. Cointepas, I. Bloch, L. Garnero Distance and Object Recognition Unraveling the Thrill of Metric Image Spaces P. Eklund, F. Georgsson Measuring Resemblance of Complex Patterns M. Hagedoorn, R. Veltkamp Tree Representation for Image Matching and Object Recognition J. Mattes, M. Richard, J. Demongeot Thinning Ultra-Fast Skeleton Based on an Isotropic Fully Parallel Algorithm A. Manzanera, T.M. Bernard, F. Prêteux, B. Longuet Directional 3D Thinning Using 8 Subiterations K. Palágyi, A. Kuba

10 Table of Contents XI Order Independent Homotopic Thinning V. Ranwez, P. Soille Discretization Invited Paper: Computable Partial Solids and Voxels Sets A. Lieutier Convex Hull of Grid Points Below a Line or a Convex Curve H. Balza-Gomez, J.M. Moreau, D. Michelucci Rounding Voronoi Diagram O. Devillers, P.M. Gandoin Digitization of Bézier Curves and Patches Using Discrete Geometry O. Figueiredo, J.P. Reveillès, R.D. Hersch Hausdorff Discretization and Its Comparison to Other Discretization Schemes M. Tajine, D. Wagner, C. Ronse Visualization The Discrete Tube: A Spatial Acceleration Technique for Efficient Diffraction Computation L. Aveneau, E. Andres, M. Mériaux Polyhedrization of the Boundary of a Voxel Object J. Françon, L. Papier Discrete Ray-Casting I.Salam,P.Nehlig,E.Andres 3D Discrete Normal Vectors P. Tellier, I. Debled-Rennesson Author Index...459