Discrete geometry for computer imagery : 8th international conference, DGCI ʼ99, Marne-la-Vallée, France, March 17-19, 1999 : proceedings PDF
Preview Discrete geometry for computer imagery : 8th international conference, DGCI ʼ99, Marne-la-Vallée, France, March 17-19, 1999 : proceedings
Lecture Notes in Computer Science 1568 Editedby G.Goos,J. Hartmanisand J.van Leeuwen 3 Berlin Heidelberg NewYork Barcelona HongKong London Milan Paris Singapore Tokyo Gilles Bertrand Michel Couprie Laurent Perroton (Eds.) Discrete Geometry for Computer Imagery 8th International Conference, DGCI’99 Marne-la-Valle´e, France, March 17-19, 1999 Proceedings 1 3 SeriesEditors GerhardGoos,KarlsruheUniversity,Germany JurisHartmanis,CornellUniversity,NY,USA JanvanLeeuwen,UtrechtUniversity,TheNetherlands VolumeEditors GillesBertrand MichelCouprie LaurentPerroton ESIEE 2,Bd.BlaisePascal,B.P.99 F-93162Noisy-Le-GrandCedex,France E-mail:{bertrang,coupriem,perrotol}@esiee.fr Cataloging-in-Publicationdataappliedfor DieDeutscheBibliothek-CIP-Einheitsaufnahme Discretegeometryforcomputerimagery:8thinternationalconference; proceedings/DGCI’99,Marne-la-Valle´e,France,March17-19,1999.Gilles Bertrand...(ed.).-Berlin;Heidelberg;NewYork;Barcelona;HongKong; London;Milan;Paris;Singapore;Tokyo:Springer,1999 (Lecturenotesincomputerscience;Vol.1568) ISBN3-540-65685-5 CRSubjectClassification(1998):I.3.5,I.4,G.2,I.6.8 ISSN0302-9743 ISBN3-540-65685-5Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsare liableforprosecutionundertheGermanCopyrightLaw. (cid:2)c Springer-VerlagBerlinHeidelberg1999 PrintedinGermany Typesetting:Camera-readybyauthor SPIN10702997 06/3142–543210 Printedonacid-freepaper Preface These proceedings contain papers presented at the 8th Discrete Geometry for Computer Imagery conference, held 17-19, March 1999 at ESIEE, Marne-la- Vall´ee. Thedomainsof discretegeometry and computer imagery areclosely related. Discretegeometryprovidesboththeoreticalandalgorithmicmodelsforthepro- cessing, 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 fromnewlaboratoriesandnewresearchers,aswellasthequalityandoriginality of the results have contributed to the success of the conference and are an in- dication of the dynamism of this field. The DGCI has become one of the major conferences related to this topic, including participating researchers and labo- ratories 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. ThesiteofMarne-la-Vall´ee,just20minawayfromParis,isparticularlywell- suited 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-Vall´ee (EPAMARNE), the Universit´e de Marne-la-Vall´ee, the Minist`ere 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 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. Arqu`es IGM, Universit´e Marne-La-Vall´ee, France Y. Bertrand IRCOM-SIC, Poitiers, France G. Borgefors Centre for Image Analysis, SLU, Sweden A. Del Lungo Universita` di Firenze, Italy U. Eckhardt Universita¨t 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, Universit´e 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 VIII Referees Ahronovitz E. Kong T.Y. Arqu`es 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. Franc¸on J. Szekely G. Goldman Y. Tajine M. Jolion J.M. Wang P. 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 ...... 19 G. Borgefors, G. Sanniti di Baja, S. Svensson Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature ........................................ 31 F. Feschet, L. Tougne The Discrete Moments of the Circles ................................. 41 J. Zˇuni´c Planes.......................................................... 51 Graceful Planes and Thin Tunnel-Free Meshes......................... 53 V.E. Brimkov, R.P. Barneva Local Configurations of Digital Hyperplanes........................... 65 Y. G´erard (n,m)-Cubes and Farey Nets for Naive Planes Understanding ............ 77 J. Vittone, J.M. Chassery Surfaces........................................................ 89 A Digital Lighting Function for Strong 26-Surfaces ..................... 91 R. Ayala, E. Dom´ınguez, A.R. Franc´es, A. Quintero Intersection Number of Paths Lying on a Digital Surface and a New Jordan Theorem ......................................... 104 S. Fourey, R. Malgouyres A Topological Method of Surface Representation....................... 118 V. Kovalevsky Presentation of the Fundamental Group in Digital Surfaces.............. 136 R. Malgouyres Multiresolution Representation of Shapes Based on Cell Complexes Leila De Floriani, Paola Magillo and Enrico Puppo Dipartimento di Informatica e Scienze dell’Informazione Universit`a di Genova Via Dodecaneso, 35 – 16146 Genova, ITALY Email: {deflo,magillo,puppo}@disi.unige.it Abstract. Thispaperintroducesadimension-independentmultiresolu- tionmodelofashape,calledtheMulti-Complex(MC),whichisbasedon decompositionintocells.AnMCdescribesashapeasaninitialcellcom- plex approximating it, plus a collection of generic modification patterns tosuchcomplexarrangedaccordingtoapartialorder.Thepartialorder isessentialtoextractvariable-resolutionshapedescriptionsinrealtime. We show how existing multiresolution models reduce to special cases of MCs characterized by specific modification patterns. The MC acts as a unifying framework that is also useful for comparing and evaluating the expressive power of different approaches. 1 Introduction Multiresolution geometric models support representation and processing of spa- tialentitiesatdifferentlevelsofdetail.Suchrepresentationshavegainedrecently much of attention in the literature because of their potential impact on appli- cations, such as terrain modeling in geographic information systems, scientific data visualization, virtual reality, etc. The basis for a multiresolution geometric modelisthedecompositionoftheshapeitdescribesintosimpleelements,called cells. Cellcomplexesareusedasdiscretemodelsofavarietyofshapesintwo,three or higher dimensions. For example, two-dimensional complexes made of polyg- onal cells are used for describing the boundary of solid objects. In particular, two-dimensionalsimplicialcomplexes(trianglemeshes)areusedforrepresenting surfacesincomputergraphics,andforrepresentingterrainsingeographicappli- cations. In solid modeling, three-dimensional complexes are used for describing the interior of an object as well as its boundary. d-Dimensional simplicial com- plexes are used as approximate representations of scalar or vector fields. The accuracy of a cell complex in representing a shape depends on the size, number, and density of its cells: a parameter that we call the resolution of the complex. A high resolution, and thus a high number of cells, is needed to pro- duceaccuratedescriptions.Ontheotherhand,maximumaccuracyisnotalways required in each part of a shape, but a sufficiently high accuracy for the specific application task can be achieved by locally adapting the resolution of a complex indifferentpartsoftheshape,thusreducingprocessingcostsandmemoryspace. G.Bertrand,M.Couprie,L.Perroton(Eds.):DGCI’99,LNCS1568,pp.3–18,1999. (cid:2)c Springer-VerlagBerlinHeidelberg1999
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