Handbook of Computer Vision Algorithms in Image Al

HandbookofComputerVisionAlgorithmsinImageAlgebraGerhardX.RitterJosephN.WilsonCenterforComputerVisionandVisualizationUniversityofFloridaPrefaceTheaimofthisbookistoacquaintengineers,scientists,andstudentswiththebasicconceptsofimagealgebraanditsuseintheconciserepresentationofcomputervisionalgorithms.Inordertoachievethisgoalweprovideabriefsurveyofcommonlyusedcomputervisionalgorithmsthatwebelieverepresentsacoreofknowledgethatallcomputervisionpractitionersshouldhave.Thissurveyisnotmeanttobeanencyclopedicsummaryofcomputervisiontechniquesasitisimpossibletodojusticetothescopeanddepthoftherapidlyexpandingfieldofcomputervision.ThearrangementofthebookissuchthatitcanserveasareferenceforcomputervisionalgorithmdevelopersingeneralaswellasforalgorithmdevelopersusingtheimagealgebraC++objectlibrary,iac++.1Thetechniquesandalgorithmspresentedinagivenchapterfollowaprogressionofincreasingabstractness.Eachtechniqueisintroducedbywayofabriefdiscussionofitspurposeandmethodology.Sincetheintentofthistextistotrainthepractitionerinformulatinghisalgorithmsandideasinthesuccinctmathematicallanguageprovidedbyimagealgebra,anefforthasbeenmadetoprovidetheprecisemathematicalformulationofeachmethodology.Thus,wesuspectthatpracticingengineersandscientistswillfindthispresentationsomewhatmorepracticalandperhapsabitlessesotericthanthosefoundinresearchpublicationsorvarioustextbooksparaphrasingthesepublications.Chapter1providesashortintroductiontofieldofimagealgebra.Chapters2–11aredevotedtoparticulartechniquescommonlyusedincomputervisionalgorithmdevelopment,rangingfromearlyprocessingtechniquestosuchhigherleveltopicsasimagedescriptorsandartificialneuralnetworks.Althoughthechaptersontechniquesaremostnaturallystudiedinsuccession,theyarenottightlyinterdependentandcanbestudiedaccordingtothereader’sparticularinterest.IntheAppendixwepresentiac++computerprogramsofsomeofthetechniquessurveyedinthisbook.Theseprogramsreflecttheimagealgebrapseudocodepresentedinthechaptersandserveasexamplesofhowimagealgebrapseudocodecanbeconvertedintoefficientcomputerprograms.1Theiac++librarysupportstheuseofimagealgebraintheC++programminglanguageandisavailableforanonymousftpfromfirstprogrammanager,Ms.KarenNorris,andmostespeciallyDr.PatrickCoffieldwhopersuadedustoturnatechnicalreportoncomputervisionalgorithmsinimagealgebraintothisbook.LastbutnotleastwewouldliketothankDr.RobertLyjackofERIMforhisfriendshipandenthusiasticsupportduringtheformativestagesofimagealgebra.ivNotationThetablespresentedhereprovideabriefexplantationofthenotationusedthroughoutthisdocument.ThereaderisreferredtoRitter[1]foracomprehensivetreatisecoveringthemathematicsofimagealgebra.LogicSymbolExplanationimplies.Ifistrue,thenistrue.ifandonlyif,whichmeansthatandarelogicallyequivalent.iffifandonlyifnotthereexiststheredoesnotexistforeachs.t.suchthatSetsTheoreticNotationandOperationsSymbolExplanationUppercasecharactersrepresentarbitrarysets.Lowercasecharactersrepresentelementsofanarbitraryset.Bold,uppercasecharactersareusedtorepresentpointsets.Bold,lowercasecharactersareusedtorepresentpoints,i.e.,elementsofpointsets.Theset.Thesetofintegers,positiveintegers,andnegativeintegers.Theset.Theset.Theset.Thesetofrealnumbers,positiverealnumbers,negativerealnumbers,andpositiverealnumbersincluding0.vSymbolExplanationThesetofcomplexnumbers.Anarbitrarysetofvalues.Thesetunionedwith.Thesetunionedwith.Thesetunionedwith.Theemptyset(thesetthathasnoelements).Thepowersetof(thesetofallsubsetsof).isanelementofisnotanelementofisasubsetofUnionLetbeafamilyofsetsindexedbyanindexingset.IntersectionLetbeafamilyofsetsindexedbyanindexingset.CartesianproductTheCartesianproductofcopiesof,i.e.,.viSymbolExplanationSetdifferenceLetandbesubsetsofsomeuniversalset,.Complement,whereistheuniversalsetthatcontains.Thecardinalityoftheset.Afunctionthatrandomlyselectsanelementfromtheset.PointandPointSetOperationsSymbolExplanationIf,thenIf,thenIf,thenIf,th