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Summary
cipleisarecommendationtoutilisetheredundancyintheimagedatainaspecific
wayandshouldbeappliedwhenthequalityofthedataislow.
OriginalresultsThemainoriginalresultisthelinedetectordescribedinChap-
ter6.Itisdesignedusingtheevidenceaccumulationprinciple.Asawhole,ithas
nocounterpartsintheliteratureonedgeandlinedetection.Thedetectorisde-
scribedindetailandtested.Thedescriptionshavebeenpublishedintheirmost
partinthepapers[Chm04b,Chm05a,Chm05b].Inthepresentationofthedetec-
toritisstressedthatitisanexampleofapplicationoftheevidenceaccumulation
principleandthatitsdesignisaresultofthepreviouslygatheredexperiencewith
thisprinciple.
Inthedesignofthedetectorseveralelementsknownformtheliteraturehave
beenused.Twoofthemshouldberecalledhere.Bothhavebeendevelopedinthis
bookinnewdirections.
Thefirstoftheelementsusedistheaccumulationintheimagespace,rarely
foundintheaccumulationmethodsandintheHoughtransform,wheretheac-
cumulationismadeprincipallyintheparameterspace.Theaccumulationinthe
imagespaceisoccasionallyusedtofindsomecharacteristicfeaturesoftheobject,
forexample,acentreofacircle.Intheapplicationdescribedheresuchanaccumu-
lationprovidesfordetectingobjectshavingirregularshapesthatareimpossible
ordifficulttoparameterise.Theaccumulationwithouttheshapeparametersof
thedetectedobjectisanoveltyinthedomainoftheaccumulationmethods.The
parameterscharacterisingtheobjectinagivenpixelareusedadditionally(these
arethelocalwidthanddirectionofaline).
Thesecondknownelementusedwasthefuzzificationoftheaccumulatorwhich
improvesthepropertiesofthedetector,inparticular,itsrobustnessagainstthe
noiseintheimage,andalsoitsinvariancewithrespecttolinedirectionandits
abilitytomaintainthelinecontinuity.Theinvestigationsonthechoiceofthe
membershipfunctionusedinthefuzzification,anditsscaleinparticular,have
ledtototheformulationofthenotionofalimitfuzzificationofahistogramand
totherelatednotionofafuzzificationdegree.AccordingtothebestofAuthor?s
knowledge,thereisnoreferencetothesenotionsintheliterature,despiteasignifi-
cantadvancementofthedomainsstrictlyrelatedtothefuzzificationofhistograms,
i.e.,robuststatisticsandkerneldensityestimation.Thesedomainsgobeyondthe
rangeofproblemstreatedinthisbookdevotedmainlytoimageprocessing.The
fuzzificationdegreecanbeusedinasimplewaytofindthescaleofthefuzzi-
fyingfunctionsusedintheanalysisofhistogramsintheaccumulationmethods.
Theoriginalcontribution,yetmodestinrelationtothetwodomainsmentioned,
isthepragmaticrecommendationtoapplyaweakfuzzificationofthehistograms,
i.e.,suchafuzzificationwhichischaracterisedbyasmallvalueifthedegreeof
fuzzification.Theconsiderationsleadingtothisformulationhavebeenrecently
publishedin[Chm06].
AfurtheroriginalresultisthediscoverythattheknownSobeledgedetectoris
aspecialcaseofadetectorbelongingtoafamilyofdetectorsusingthetwo-pixel
neighbourhoodsofapixel,proposedinthisbookwithinanintroductoryexerciseon
theaccumulationmethods.Theelementsofthisfamilyare:themediandetector,
theaccumulationdetectorandtheaveragingdetector.Thislatterdetector,inthe
