... 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].OriginallyMMwasappliedtoanalyzingc1999byCRCPressLLCis ... successfully model several image processing problems, several nonlinear PDE -based approaches have been developed. Among them,some PDEs have been recently developed to model multiscale morphological ... time. The final result would be f2= f ⊕ g. Such slope filters are usefulfor envelope estimation [37].74.7 Multiscale Morphological Image AnalysisMultiscale signal analysis has recently emerged...