Digital geometry algorithms : theoretical foundations and applications to computational imaging PDF
Preview Digital geometry algorithms : theoretical foundations and applications to computational imaging
LectureNotesinComputationalVisionandBiomechanics Editors JoãoManuelR.S.Tavares R.M.NatalJorge Address: FaculdadedeEngenharia UniversidadedoPorto RuaDr.RobertoFrias,s/n 4200-465Porto Portugal [email protected],[email protected] EditorialAdvisoryBoard AlejandroFrangi,UniversityofSheffield,Sheffield,UK ChandrajitBajaj,UniversityofTexasatAustin,Austin,USA EugenioOñate,UniversitatPolitécnicadeCatalunya,Barcelona,Spain FranciscoPerales,BalearicIslandsUniversity,PalmadeMallorca,Spain GerhardA.Holzapfel,RoyalInstituteofTechnology,Stockholm,Sweden J.PauloVilas-Boas,UniversityofPorto,Porto,Portugal JeffreyA.Weiss,UniversityofUtah,SaltLakeCity,USA JohnMiddleton,CardiffUniversity,Cardiff,UK JoseM.GarcíaAznar,UniversityofZaragoza,Zaragoza,Spain PerumalNithiarasu,SwanseaUniversity,Swansea,UK KumarK.Tamma,UniversityofMinnesota,Minneapolis,USA LaurentCohen,UniversitéParisDauphine,Paris,France ManuelDoblaré,UniversidaddeZaragoza,Zaragoza,Spain PatrickJ.Prendergast,UniversityofDublin,Dublin,Ireland RainaldLöhner,GeorgeMasonUniversity,Fairfax,USA RogerKamm,MassachusettsInstituteofTechnology,Cambridge,USA ThomasJ.R.Hughes,UniversityofTexas,Austin,USA YongjieZhang,CarnegieMellonUniversity,Pittsburgh,USA YuboFan,BeihangUniversity,Beijing,China Forfurthervolumes: http://www.springer.com/series/8910 Lecture Notes in Computational Vision and Biomechanics Volume2 Theresearchrelatedtotheanalysisoflivingstructures(Biomechanics)hasbeenasourceofrecentre- searchinseveraldistinctareasofscience,forexample,Mathematics,MechanicalEngineering,Physics, Informatics,MedicineandSport.However,foritssuccessfulachievement,numerousresearchtopics should be considered, such as image processing and analysis, geometric and numerical modelling, biomechanics,experimentalanalysis,mechanobiologyandenhancedvisualization,andtheirapplica- tiontorealcasesmustbedevelopedandmoreinvestigationisneeded.Additionally,enhancedhardware solutionsandlessinvasivedevicesaredemanded. Ontheotherhand,ImageAnalysis(ComputationalVision)isusedfortheextractionofhighlevel informationfromstaticimagesordynamicimagesequences.Examplesofapplicationsinvolvingimage analysiscanbethestudyofmotionofstructuresfromimagesequences,shapereconstructionfrom imagesandmedicaldiagnosis.Asamultidisciplinaryarea,ComputationalVisionconsiderstechniques andmethodsfromotherdisciplines,suchasArtificialIntelligence,SignalProcessing,Mathematics, Physics and Informatics. Despite the many research projects in this area, more robust and efficient methodsofComputationalImagingarestilldemandedinmanyapplicationdomainsinMedicine,and theirvalidationinrealscenariosismatterofurgency. ThesetwoimportantandpredominantbranchesofScienceareincreasinglyconsideredtobestrongly connectedandrelated.Hence,themaingoaloftheLNCV&Bbookseriesconsistsoftheprovisionofa comprehensiveforumfordiscussiononthecurrentstate-of-the-artinthesefieldsbyemphasizingtheir connection.Thebookseriescovers(butisnotlimitedto): • ApplicationsofComputationalVisionand • GridandHighPerformanceComputingfor Biomechanics ComputationalVisionandBiomechanics • BiometricsandBiomedicalPatternAnalysis • Image-basedGeometricModelingandMesh • CellularImagingandCellularMechanics Generation • ClinicalBiomechanics • ImageProcessingandAnalysis • ComputationalBioimagingandVisualization • ImageProcessingandVisualizationin • ComputationalBiologyinBiomedicalImaging Biofluids • DevelopmentofBiomechanicalDevices • ImageUnderstanding • DeviceandTechniqueDevelopmentfor • MaterialModels BiomedicalImaging • Mechanobiology • DigitalGeometryAlgorithmsfor • MedicalImageAnalysis ComputationalVisionandVisualization • MolecularMechanics • ExperimentalBiomechanics • Multi-modalImageSystems • Gait&PostureMechanics • MultiscaleBiosensorsinBiomedicalImaging • MultiscaleAnalysisinBiomechanics • MultiscaleDevicesandBiomemsfor • NeuromuscularBiomechanics BiomedicalImaging • NumericalMethodsforLivingTissues • MusculoskeletalBiomechanics • NumericalSimulation • SportBiomechanics • SoftwareDevelopmentonComputational • VirtualRealityinBiomechanics VisionandBiomechanics • VisionSystems Valentin E. Brimkov (cid:2) Reneta P. Barneva Editors Digital Geometry Algorithms Theoretical Foundations and Applications to Computational Imaging Editors ValentinE.Brimkov RenetaP.Barneva DepartmentofMathematics DepartmentofComputerand BuffaloStateCollege InformationSciences StateUniversityofNewYork StateUniversityofNewYorkatFredonia Buffalo,NY Fredonia,NY USA USA ISSN2212-9391 ISSN2212-9413(electronic) LectureNotesinComputationalVisionandBiomechanics ISBN978-94-007-4173-7 ISBN978-94-007-4174-4(eBook) DOI10.1007/978-94-007-4174-4 SpringerDordrechtHeidelbergNewYorkLondon LibraryofCongressControlNumber:2012939722 ©SpringerScience+BusinessMediaDordrecht2012 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Digitalgeometryisamodernmathematicaldisciplinestudyingthegeometricprop- ertiesofdigitalobjects(usuallymodeledbysetsofpointswithintegercoordinates) andprovidingmethodsforsolvingvariousproblemsdefinedonsuchobjects.Dig- italgeometryisdevelopedwiththeexplicitgoaltoproviderigorousmathematical foundationsandbasicalgorithmsforapplieddisciplinessuchascomputergraphics, medicalimaging,patternrecognition,imageanalysisandprocessing,computervi- sion,imageunderstanding,andbiometrics.Theseareinturnapplicabletoimportant andsocietallysensitiveareaslikemedicine,defense,andsecurity. Although digital geometry has its roots in several classical disciplines (such as graph theory, topology, number theory, and Euclidean and analytic geometry), it was established as an independent subject only in the last few decades. Several researchers have played a pioneering role in setting the foundations of digital ge- ometry. Notable among these is the late Azriel Rosenfeld and his seminal works fromthelate60’sandearly70’softhelastcentury.Someauthorsofchaptersofthe present book are also among the founders of the area or its prominent promoters. Thelasttwodecadesfeatureanincreasingnumberofactivecontributorsthroughout theworld.Anumberofexcellentmonographsandhundredsofresearchpapershave beendevotedtothesubject.Onecanlegitimatelysaythatatpresentdigitalgeom- etry is an independent subject with its own history, vibrant international commu- nity,regularscientificmeetingsandevents,and,mostimportantly,seriousscientific achievements. This contributed book contains thirteen chapters devoted to different (although interrelated)importantproblemsofdigitalgeometry,algorithmsfortheirsolution, and various applications. All authors are well-recognized researchers, as some of themareworldleadersinthefield.Asageneralframework,eachchapterpresents a research topic of considerable importance, provides a review of fundamental re- sultsandalgorithmsfortheconsideredproblems,presentsnewunpublishedresults, aswellasa discussiononrelatedapplications,currentdevelopmentsandperspec- tives.Byitsstructureandcontent,thispublicationdoesnotappeartobeanexhaus- tivesourceofinformationforallbranchesofdigitalgeometry.Rather,thebookis aimed at attracting readers’ attention to central digital geometry tasks and related v vi Preface applications,asdiverseascreatingimage-basedmetrology,proposingnewtoolsfor processing multidimensional images, studying topological transformations for im- ageprocessing,anddevelopingalgorithmsforshapeanalysis. Anadvantageofthechosencontributedbookframeworkisthatallchapterspro- vide enough complete presentations written by leading experts on the considered specific matters. The chapters are self-contained and can be studied in succession dictatedbythereaders’interestsandpreferences. Webelievethatthispublicationwouldbeausefulsourceofinformationforre- searchers in digital geometry as well as for practitioners in related applied disci- plines. It can also be used as a supplementary material or a text for graduate or upperlevelundergraduatecourses. Wewouldliketothankallthosewhomadethispublicationpossible.Wearein- debtedtoJoãoManuelR.S.TavaresandRenatoManuelNatalJorge,editorsofthe Springer’s series “Lecture Notes in Computational Vision and Biomechanics,” for invitingustoorganizeandeditavolumeoftheseries.WearethankfultoSpringer’s Office and particularly to Ms. Nathalie Jacobs, Senior Publishing Editor, and Dr. D.Merkle,EditorialDirector,forreviewingourproposalandgivingustheoppor- tunity to publish this work with Springer, as well as for the pleasant cooperation throughoutthe editorialprocess. Lastly and most importantly,our thanks go to all authorswhocontributedexcellentchapterstothisbook. FredoniaandBuffalo,NY,USA ValentinE.Brimkov RenetaP.Barneva Contents PartI General 1 DigitalGeometryinImage-BasedMetrology. . . . . . . . . . . . . . 3 AlfredM.Bruckstein 2 Provably Robust Simplification of Component Trees of MultidimensionalImages . . . . . . . . . . . . . . . . . . . . . . . . 27 GaborT.Herman,T.YungKong,andLucasM.Oliveira PartII Topology,Transformations 3 DiscreteTopologicalTransformationsforImageProcessing . . . . . 73 MichelCouprieandGillesBertrand 4 ModelingandManipulatingCellComplexesinTwo,Threeand HigherDimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 LidijaCˇomic´ andLeilaDeFloriani 5 Binarization of Gray-Level Images Based on Skeleton Region Growing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 XiangBai,QuannanLi,TianyangMa,WenyuLiu,and LonginJanLatecki 6 TopologyPreservingParallel3DThinningAlgorithms . . . . . . . . 165 KálmánPalágyi,GáborNémeth,andPéterKardos 7 SeparableDistanceTransformationandItsApplications . . . . . . . 189 DavidCoeurjollyandAntoineVacavant 8 SeparabilityandTightEnclosureofPointSets. . . . . . . . . . . . . 215 PeterVeelaert vii viii Contents PartIII ImageandShapeAnalysis 9 DigitalStraightness,Circularity,andTheirApplicationstoImage Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 ParthaBhowmickandBhargabB.Bhattacharya 10 ShapeAnalysiswithGeometricPrimitives . . . . . . . . . . . . . . . 301 FabienFeschet 11 ShapefromSilhouettesinDiscreteSpace . . . . . . . . . . . . . . . . 323 AtsushiImiyaandKosukeSato 12 CombinatorialMapsfor2Dand3DImageSegmentation. . . . . . . 359 GuillaumeDamiandandAlexandreDupas 13 MultigridConvergenceofDiscreteGeometricEstimators . . . . . . 395 DavidCoeurjolly,Jacques-OlivierLachaud,andTristanRoussillon Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 Contributors XiangBai HuazhongUniversityofScienceandTechnology,Wuhan,China Gilles Bertrand Laboratoire d’Informatique Gaspard-Monge, Équipe A3SI, Uni- versitéParis-Est,ESIEEParis,Marne-la-Vallée,France Bhargab B. Bhattacharya Advanced Computing and Microelectronics Unit, In- dianStatisticalInstitute,Kolkata,India ParthaBhowmick DepartmentofComputerScienceandEngineering,IndianIn- stituteofTechnology,Kharagpur,India AlfredM.Bruckstein OllendorffProfessorofScience,ComputerScienceDepart- ment,Technion,IIT,Haifa,Israel David Coeurjolly LIRIS, UMR CNRS 5205, Université de Lyon, Villeurbanne, France Lidija Cˇomic´ Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia Michel Couprie Laboratoire d’Informatique Gaspard-Monge, Équipe A3SI, Uni- versitéParis-Est,ESIEEParis,Marne-la-Vallée,France GuillaumeDamiand LIRIS,UMR5205,UniversitédeLyon,CNRS,Lyon,France LeilaDeFloriani DepartmentofComputerScience,UniversityofGenoa,Genoa, Italy AlexandreDupas Unit698,Inserm,Paris,France FabienFeschet IGCNC-EA2782,ClermontUniversité,Universitéd’Auvergne, Clermont-Ferrand,France GaborT.Herman ComputerSciencePh.D.Program,GraduateCenter,CityUni- versityofNewYork,NewYork,NY,USA ix
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