... Press LLCMorphologicalSignalandImage Processing PetrosMaragosGeorgiaInstituteofTechnology 74. 1Introduction 74. 2MorphologicalOperatorsforSetsandSignalsBooleanOperatorsandThresholdLogic•MorphologicalSetOperators•MorphologicalSignalOperatorsandNonlinearConvolutions 74. 3Median,Rank,andStackOperators 74. 4UniversalityofMorphologicalOperators 74. 5MorphologicalOperatorsandLatticeTheory 74. 6SlopeTransforms 74. 7MultiscaleMorphologicalImageAnalysisBinaryMultiscaleMorphologyviaDistanceTransforms•Mul-tiresolutionMorphology 74. 8DifferentialEquationsforContinuous-ScaleMorphology 74. 9ApplicationstoImageProcessingandVisionNoiseSuppression•FeatureExtraction•ShapeRepresentationviaSkeletonTransforms•ShapeThinning•SizeDistributions•Fractals•ImageSegmentation 74. 10ConclusionsAcknowledgmentReferences 74. 1 ... LLCMorphologicalSignalandImage Processing PetrosMaragosGeorgiaInstituteofTechnology 74. 1Introduction 74. 2MorphologicalOperatorsforSetsandSignalsBooleanOperatorsandThresholdLogic•MorphologicalSetOperators•MorphologicalSignalOperatorsandNonlinearConvolutions 74. 3Median,Rank,andStackOperators 74. 4UniversalityofMorphologicalOperators 74. 5MorphologicalOperatorsandLatticeTheory 74. 6SlopeTransforms 74. 7MultiscaleMorphologicalImageAnalysisBinaryMultiscaleMorphologyviaDistanceTransforms•Mul-tiresolutionMorphology 74. 8DifferentialEquationsforContinuous-ScaleMorphology 74. 9ApplicationstoImageProcessingandVisionNoiseSuppression•FeatureExtraction•ShapeRepresentationviaSkeletonTransforms•ShapeThinning•SizeDistributions•Fractals•ImageSegmentation 74. 10ConclusionsAcknowledgmentReferences 74. 1 ... LLCMorphologicalSignalandImage Processing PetrosMaragosGeorgiaInstituteofTechnology 74. 1Introduction 74. 2MorphologicalOperatorsforSetsandSignalsBooleanOperatorsandThresholdLogic•MorphologicalSetOperators•MorphologicalSignalOperatorsandNonlinearConvolutions 74. 3Median,Rank,andStackOperators 74. 4UniversalityofMorphologicalOperators 74. 5MorphologicalOperatorsandLatticeTheory 74. 6SlopeTransforms 74. 7MultiscaleMorphologicalImageAnalysisBinaryMultiscaleMorphologyviaDistanceTransforms•Mul-tiresolutionMorphology 74. 8DifferentialEquationsforContinuous-ScaleMorphology 74. 9ApplicationstoImageProcessingandVisionNoiseSuppression•FeatureExtraction•ShapeRepresentationviaSkeletonTransforms•ShapeThinning•SizeDistributions•Fractals•ImageSegmentation 74. 10ConclusionsAcknowledgmentReferences 74. 1 IntroductionThischapterprovidesabriefintroductiontothetheoryofmorphologicalsignalprocessinganditsapplicationstoimageanalysisandnonlinearfiltering.By“morphologicalsignalprocessing”wemeanabroadandcoherentcollectionoftheoreticalconcepts,mathematicaltoolsforsignalanalysis,non-linearsignaloperators,designmethodologies,andapplicationssystemsthatarebasedonorrelatedtomathematicalmorphology(MM),aset-andlattice-theoreticmethodologyforimageanalysis.MMaimsatquantitativelydescribingthegeometricalstructureofimageobjects.Itsmathematicaloriginsstemfromsettheory,latticealgebra,convexanalysis,andintegralandstochasticgeometry.ItwasinitiatedmainlybyMatheron[42]andSerra[58]inthe1960s.SomeofitsearlysignaloperationsarealsofoundintheworkofotherresearcherswhousedcellularautomataandBoolean/thresholdlogictoanalyzebinaryimagedatainthe1950sand1960s,assurveyedin[49,54].MMhasformalizedtheseearlieroperationsandhasalsoaddednumerousnewconceptsandimageoperations.Inthe1970sitwasextendedtogray-levelimages[22,45,58,62].OriginallyMMwasappliedtoanalyzingc1999byCRCPressLLCdefined)...