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Mathematical Morphology: 40 Years On Computational Imaging and Vision Managing Editor MAX A. VIERGEVER Utrecht University, Utrecht, The Netherlands Editorial Board GUNILLABORGEFORS,Centre for Image Analysis, SLU, Uppsala, Sweden THOMAS S. HUANG,University of Illinois, Urbana, USA SABURO TSUJI,Wakayama University, Wakayama, Japan Volume 30 Mathematical Morphology: 40 Years On Proceedings of the 7th International Symposium on Mathematical Morphology, April 18-20, 2005 Edited by Christian Ronse LSIIT, UMR 7005 CNRS-ULP, Illkirch, France Laurent Najman A2SI-ESIEE/IGM, UMR 8049 CNRS-UMLV, Noisy-le-Grand, France and Etienne Decencière CMM, École des Mines de Paris, Fontainebleau, France AC.I.P. Catalogue record for this book is available from the Library of Congress. ISBN-10 1-4020-3442-3 (HB) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-10 1-4020-3443-1 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-1-4020-3442-8 (HB) Springer Dordrecht, Berlin, Heidelberg, New York ISBN-13 978-1-4020-3443-5 (e-book) Springer Dordrecht, Berlin, Heidelberg, New York Published by Springer, P.O. Box 17, 3300 AADordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. Thisbookisdedicatedtothe memoryof GeorgesMatheron,who gavethestudyof morphologyitsinitial impetus. Contents Dedication v Foreword xi Preface xiii Acknowledgments xvii PartI Morphologicaloperators BinaryDecisionDiagramsasaNewParadigmforMorphologicalMachines 3 JuniorBarreraandRonaldoFumioHashimoto Imagefilteringusingmorphologicalamoebas 13 RomainLerallut,ÉtienneDecencièreandFernandMeyer NumericalResidues 23 SergeBeucher Efficientpathopeningsandclosings 33 BenAppletonandHuguesTalbot StructuringElementsfollowingtheOpticalFlow 43 NicolasLaveauandChristopheBernard Recursive Interpolation Technique For Binary Images Based on Morphological MedianSets 53 JavierVidal,JoseCrespoandVíctorMaojo PartII Connectedfiltersandreconstruction Second-OrderConnectedAttributeFiltersUsingMax-Trees 65 GeorgiosK.OuzounisandMichaelH.F.Wilkinson TransformationswithReconstructionCriteria: ImageSegmentationandFiltering 75 IvánR.Terol-VillalobosandJorgeD.Mendiola-Santibañez Attribute-SpaceConnectedFilters 85 MichaelH.F.Wilkinson viii MATHEMATICALMORPHOLOGY:40YEARSON Vector-attributeFilters 95 ErikR.Urbach,NiekJ.BoersmaandMichaelH.F.Wilkinson RuminationsonTarjan’sUnion-FindAlgorithmandConnectedOperators 105 ThierryGéraud LabelledReconstructionofBinaryObjects: AVectorPropagationAlgorithm 117 MichaelBuckleyandRyanLagerstrom GrayscaleLevelMulticonnectivity 129 UlissesBraga-Neto Shape-TreeSemilattices 139 RenatoKeshet PartIII Segmentation MorphologicalSegmentationsofColourImages 151 JeanSerra FastImplementationofWaterfallbasedonGraphs 177 BeatrizMarcoteguiandSergeBeucher MosaicsandWatersheds 187 LaurentNajman,MichelCouprieandGillesBertrand Anewdefinitionforthedynamics 197 GillesBertrand Watershed-drivenregion-basedimageretrieval 207 I.Pratikakis,I.Vanhamel,H.Sahli,B.GatosandS.Perantonis Efficientimplementationofthelocallyconstrainedwatershedtransformand seededregiongrowing 217 RichardBeare PartIV Geometryandtopology Optimalshapeandinclusion 229 Jean-MarcChasseryandDavidCoeurjolly RegularMetric: DefinitionandCharacterizationintheDiscretePlane 249 GeraldJeanFrancisBanon Euclideanskeletonsof3Ddatasetsinlineartimebytheintegermedialaxis transform 259 WimH.Hesselink,MennoVisserandJosB.T.M.Roerdink Contents ix DigitizationofNon-regularShapes 269 PeerStelldinger Downsamplingofbinaryimagesusingadaptivecrossingnumbers 279 EtienneDecencièreandMichelBilodeau Grey-weighted,ultrametricandlexicographicdistances 289 FernandMeyer Mathematicalmodelingoftherelationship“between”basedonmorphological operators 299 IsabelleBloch,OlivierColliotandRobertoM.Cesar PartV Partialdifferentialequationsandevolutionarymodels SemidiscreteandDiscreteWell-PosednessofShockFiltering 311 MartinWelkandJoachimWeickert AVariationalFormulationofPDE’sforDilationsandLevelings 321 PetrosMaragos StochasticShapeOptimisation 333 CostinAlinCaciu,EtienneDecencièreandDominiqueJeulin Onthelocalconnectivitynumberofstationaryrandomclosedsets 343 EvgueniSpodarevandVolkerSchmidt PartVI Texture,colourandmultivaluedimages Intersizecorrelationofggrainoccurrencesintexturesanditsapplicationto textureregeneration 357 AkiraAsano,YasushiKobayashiandChieMuraki TextureSegmentationUsingAreaMorphologyLocalGranulometries 367 NeilD.FletcherandAdrianN.Evans Illumination-invariantMorphologicalTextureClassification 377 AllanHanbury,UmasankarKandaswamyandDonaldA.Adjeroh Unifiedmorpphologicalcolorprocessingframeworkinalum/sat/hue representation 387 JesúsAngulo Iterativeareaseededregiongrowingformultichannelimagesimplification 397 DominikBrunnerandPierreSoille MorphologyforHigher-DimensionalTensorDataviaLoewnerOrdering 407 B.Burgeth,N.Papenberg,A.Bruhn,M.Welk,C.Feddern,andJ.Weickert x MATHEMATICALMORPHOLOGY:40YEARSON PartVII Applicationsinimagingsciences UsinggWatershedandMultimodalDataforVesselSegmentation: Application totheSuperiorSagittalSinus 419 N.Passat,C.Ronse,J.Baruthio,J.-P.ArmspachandJ.Foucher Usinggggggreyyscalehit-or-misstransformforsegmentingtheportalnetworkof theliver 429 BenoîtNaegel,ChristianRonseandLucSoler BloodCellSegggmentationUsingMinimumAreaWatershedandCircleRadon Transformations 441 F.BorayTek,AndrewG.DempsterandIzzetKale Quantifyingmeanshapeandvariabilityoffootprintsusingmeansets 455 J.Domingo,B.Nacher,E.deVes,E.Alcantara,E.Diaz,G.AyalaandA.Page ExploitingandEvolvingRnMathematicalMorphologyFeatureSpaces 465 VitorinoRamosandPedroPina MorphologicalSegmentationAppliedTo3DSeismicData 475 TimothéeFaucon,EtienneDecencièreandCédricMagneron Index 485 AuthorIndex 489 Foreword Mathematical Morphology (MM) was born in 1964 through the collabo- ration of Georges Matheron and Jean Serra, who established its basic con- cepts and tools, coined the name in 1966, and set up in 1968 the “Centre de Morphologie Mathématique” on the Fontainebleau site of the Paris School of Mines. MMgainedawiderecognitionafterthepublicationofthethreebooks“Ran- dom Sets and Integral Geometry” by G. Matheron (1975), “Image Analysis and Mathematical Morphology” by J. Serra (1982), and “Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances” edited by J. Serra (1988). It has now spread worldwide, with active research teams in several countries. Thisledtotheorganizationofaspecificinternationalforumforpre- sentingthemostrecentadvancesinthefield: theInternationalSymposiumon MathematicalMorphology(ISMM).ItsfirstsixvenueswereheldinBarcelona (1993), Fontainebleau (1994), Atlanta (1996), Amsterdam (1998), Palo Alto (2000)andSydney(2002). In May 2003, on the occasion of a MM day workshop of the GDR ISIS (a Frenchnationalactionlinkingmanylaboratoriesandresearchersinimagepro- cessing)oftheCNRS,heldinParis,itwasproposedtoorganizethe7thISMM in2005inParis,andtomakeitacelebrationofthe40yearsofMM.Wewere pleased by the warm welcome that this proposal met among our colleagues fromallcountries,sowewentaheadandplannedthemeetingtotakeplacein April2005inParis, justafterDGCI’05(the12thInternationalConferenceon Discrete Geometry for Computer Imagery) in Poitiers. We were lucky to be abletomakeuseoftheroomsinthehistoricalbuildingsoftheParisSchoolof Mines. Wereceived62submissions,fromwhich41wereacceptedfororalpresen- tation,afterbeingreviewedbyatleasttwoindependentreferees. Acceptedpa- persoriginatefrom14countries: Australia,Austria,Brazil,France,Germany, Greece, Israel, Italy, Japan, Mexico, Netherlands, Portugal, Spain and United Kingdom. Severalcamefrom“new”researchersorteams,thatis,whohadnot presentedpapersatpreviousISMM’s. Wearealsohonouredbythepresenceof 3 eminent guest speakers: Jean Serra himself, Jean-Marc Chassery, leader of

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