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... Introduction
Thischapterprovidesabriefintroductiontothetheoryofmorphologicalsignalprocessingandits
applicationstoimageanalysisandnonlinearfiltering.By“morphologicalsignalprocessing”wemean
abroadandcoherentcollectionoftheoreticalconcepts,mathematicaltoolsforsignalanalysis,non-
linearsignaloperators,designmethodologies,andapplicationssystemsthatarebasedonorrelated
tomathematicalmorphology(MM),aset-andlattice-theoreticmethodologyforimageanalysis.MM
aimsatquantitativelydescribingthegeometricalstructureofimageobjects.Itsmathematicalorigins
stemfromsettheory,latticealgebra,convexanalysis,andintegralandstochasticgeometry.Itwas
initiatedmainlybyMatheron[42]andSerra[58]inthe1960s.Someofitsearlysignaloperationsare
alsofoundintheworkofotherresearcherswhousedcellularautomataandBoolean/thresholdlogic
toanalyzebinaryimagedatainthe1950sand1960s,assurveyedin[49,54].MMhasformalized
theseearlieroperationsandhasalsoaddednumerousnewconceptsandimageoperations.Inthe
1970sitwasextendedtogray-levelimages[22,45,58,62].OriginallyMMwasappliedtoanalyzing
c
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