分割算法的英文讲稿Word文件下载.docx
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分割算法的英文讲稿Word文件下载.docx
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INTRODUCTIONTOFUNDAMENTALSOFEDGEDETECTION
Edgedetectionreferstotheprocessofidentifyingandlocatingsharpdiscontinuitiesinanimage.Thediscontinuitiesareabruptchangesinpixelintensitywhichcharacterizeboundariesofobjectsinascene.Classicalmethodsofedgedetectioninvolveconvolvingtheimagewithanoperator(a2-Dfilter),whichisconstructedtobesensitivetolargegradientsintheimagewhilereturningvaluesofzeroinuniformregions.Thereisanextremelylargenumberofedgedetectionoperatorsavailable,eachdesignedtobesensitivetocertaintypesofedges.Variablesinvolvedintheselectionofanedgedetectionoperatorinclude:
∙Edgeorientation:
Thegeometryoftheoperatordeterminesacharacteristicdirectioninwhichitismostsensitivetoedges.Operatorscanbeoptimizedtolookforhorizontal,vertical,ordiagonaledges.
∙Noiseenvironment:
Edgedetectionisdifficultinnoisyimages,sinceboththenoiseandtheedgescontainhigh-frequencycontent.Attemptstoreducethenoiseresultinblurredanddistortededges.Operatorsusedonnoisyimagesaretypicallylargerinscope,sotheycanaverageenoughdatatodiscountlocalizednoisypixels.Thisresultsinlessaccuratelocalizationofthedetectededges.
∙Edgestructure:
Notalledgesinvolveastepchangeinintensity.Effectssuchasrefractionorpoorfocuscanresultinobjectswithboundariesdefinedbyagradualchangeinintensity.Theoperatorneedstobechosentoberesponsivetosuchagradualchangeinthosecases.Newerwavelet-basedtechniquesactuallycharacterizethenatureofthetransitionforeachedgeinordertodistinguish,forexample,edgesassociatedwithhairfromedgesassociatedwithaface.
Therearemanywaystoperformedgedetection.However,themajorityofdifferentmethodsmaybegroupedintotwocategories:
∙Gradient:
Thegradientmethoddetectstheedgesbylookingforthemaximumandminimuminthefirstderivativeoftheimage.
∙Laplacian:
TheLaplacianmethodsearchesforzerocrossingsinthesecondderivativeoftheimagetofindedges.Anedgehastheone-dimensionalshapeofarampandcalculatingthederivativeoftheimagecanhighlightitslocation.Supposewehavethefollowingsignal,withanedgeshownbythejumpinintensitybelow:
Supposewehavethefollowingsignal,withanedgeshownbythejumpinintensitybelow:
Ifwetakethegradientofthissignal(which,inonedimension,isjustthefirstderivativewithrespecttot)wegetthefollowing:
Clearly,thederivativeshowsamaximumlocatedatthecenteroftheedgeintheoriginalsignal.Thismethodoflocatinganedgeischaracteristicofthe“gradientfilter”familyofedgedetectionfiltersandincludestheSobelmethod.Apixellocationisdeclaredanedgelocationifthevalueofthegradientexceedssomethreshold.Asmentionedbefore,edgeswillhavehigherpixelintensityvaluesthanthosesurroundingit.Soonceathresholdisset,youcancomparethegradientvaluetothethresholdvalueanddetectanedgewheneverthethresholdisexceeded.Furthermore,whenthefirstderivativeisatamaximum,thesecondderivativeiszero.Asaresult,anotheralternativetofindingthelocationofanedgeistolocatethezerosinthesecondderivative.ThismethodisknownastheLaplacianandthesecondderivativeofthesignalisshownbelow:
EDGEDETECTIONTECHNIQUES
SobelOperator
Theoperatorconsistsofapairof3×
3convolutionkernelsasshowninFigure1.Onekernelissimplytheotherrotatedby90°
.
Thesekernelsaredesignedtorespondmaximallytoedgesrunningverticallyandhorizontallyrelativetothepixelgrid,onekernelforeachofthetwoperpendicularorientations.Thekernelscanbeappliedseparatelytotheinputimage,toproduceseparatemeasurementsofthegradientcomponentineachorientation(calltheseGxandGy).Thesecanthenbecombinedtogethertofindtheabsolutemagnitudeofthegradientateachpointandtheorientationofthatgradient.Thegradientmagnitudeisgivenby:
Typically,anapproximatemagnitudeiscomputedusing:
whichismuchfastertocompute.
Theangleoforientationoftheedge(relativetothepixelgrid)givingrisetothespatialgradientisgivenby:
Robert’scrossoperator:
The
RobertsCrossoperatorperformsasimple,quicktocompute,2-Dspatialgradientmeasurementonanimage.Pixelvaluesateachpointintheoutputrepresenttheestimatedabsolutemagnitudeofthespatialgradientoftheinputimageatthatpoint.
Theoperatorconsistsofapairof2×
2convolutionkernelsasshowninFigure.Onekernelissimplytheotherrotatedby90°
.ThisisverysimilartotheSobeloperator.
Thesekernelsaredesignedtorespondmaximallytoedgesrunningat45°
tothepixelgrid,onekernelforeachofthetwoperpendicularorientations.Thekernelscanbeappliedseparatelytotheinputimage,toproduceseparatemeasurementsofthegradientcomponentineachorientation(calltheseGxandGy).Thesecanthenbecombinedtogethertofindtheabsolutemagnitudeofthegradientateachpointandtheorientationofthatgradient.Thegradientmagnitudeisgivenby:
althoughtypically,anapproximatemagnitudeiscomputedusing:
Theangleoforientationoftheedgegivingrisetothespatialgradient(relativetothepixelgridorientation)isgivenby:
Prewitt’soperator:
PrewittoperatorissimilartotheSobeloperatorandisusedfordetectingverticalandhorizontaledgesinimages.
LaplacianofGaussian:
TheLaplacianisa2-Disotropicmeasureofthe2ndspatialderivativeofanimage.TheLaplacianofanimagehighlightsregionsofrapidintensitychangeandisthereforeoftenusedfor
edgedetection.TheLaplacianisoftenappliedtoanimagethathasfirstbeensmoothedwithsomethingapproximatingaGaussianSmoothingfilterinordertoreduceitssensitivitytonoise.Theoperatornormallytakesasinglegraylevelimageasinputandproducesanothergraylevelimageasoutput.
TheLaplacianL(x,y)ofanimagewithpixelintensityvaluesI(x,y)isgivenby:
Sincetheinputimageisrepresentedasasetofdiscretepixels,wehavetofindadiscreteconvolutionkernelthatcanapproximatethesecondderivativesinthedefinitionoftheLaplacian.ThreecommonlyusedsmallkernelsareshowninFigure1.
Figure1ThreecommonlyuseddiscreteapproximationstotheLaplacianfilter.
Becausethesekernelsareapproximatingasecondderivativemeasurementontheimage,theyareverysensitivetonoise.Tocounterthis,theimageisoftenGaussianSmoothedbeforeapplyingtheLaplacianfilter.Thispre-processingstepreducesthehighfrequencynoisecomponentspriortothedifferentiationstep.
Infact,sincetheconvolutionoperationisassociative,wecanconvolvetheGaussiansmoothingfilterwiththeLaplacianfilterfirstofall,andthenconvolvethishybridfilterwiththeimagetoachievetherequiredresult.Doingthingsthiswayhastwoadvantages:
∙SinceboththeGaussianandtheLaplaciankernelsareusuallymuchsmallerthantheimage,thismethodusuallyrequiresfarfewerarithmeticoperations.
∙TheLoG(`LaplacianofGaussian'
)kernelcanbeprecalculatedinadvancesoonlyoneconvolutionneedstobeperformedatrun-timeontheimage.
The2-DLoGfunctioncenteredonzeroandwithGaussianstandarddeviation
hastheform:
andisshowninFigure2.
Figure3DiscreteapproximationtoLoGfunctionwithGaussian
=1.4
NotethatastheGaussianismadeincreasinglynarrow,theLoGkernelbecomesthesameasthesimpleLaplaciankernelsshowninFigure1.ThisisbecausesmoothingwithaverynarrowGaussian(
<
0.5pixels)onadiscretegridhasnoeffect.Henceonadiscretegrid,thesimpleLaplaciancanbeseenasalimitingcaseoftheLoGfornarrowGaussians.
Canny’sEdgeDetectionAlgorithm
TheCannyedgedetectionalgorithmisknowntomanyastheoptimaledgedetector.Canny'
sintentionsweretoenhancethemanyedgedetectorsalreadyoutatthetimehestartedhiswork.Hewasverysuccessfulinachievinghisgoalandhisideasandmethodscanbefoundinhispaper,"
AComputationalApproachtoEdgeDetection"
.Inhispaper,hefollowedalistofcriteriatoimprovecurrentmethodsofedgedetection.Thefirstandmostobviousislowerrorrate.ItisimportantthatedgesoccurringinimagesshouldnotbemissedandthattherebeNOresponsestonon-edges.Thesecondcriterionisthattheedgepointsbewelllocalized.Inotherwords,thedistancebetweentheedgepixelsasfoundbythedetectorandtheactualedgeistobeataminimum.Athirdcriterionistohaveonlyoneresponsetoasingleedge.Thiswasimplementedbecausethefirst2werenotsubstantialenoughtocompletelyeliminatethepossibilityofmultipleresponsestoanedge.
Basedonthesecriteria,thecannyedgedetectorfirstsmoothestheimagetoeliminateandnoise.Itthenfindstheimagegradienttohighlightregionswithhighspatialderivatives.Thealgorithmthentracksalongtheseregionsandsuppressesanypixelthatisnotatthemaximum(nonmaximumsuppression).Thegradientarrayisnowfurtherreducedbyhysteresis.Hysteresisisusedtotrackalongtheremainingpixelsthathavenotbeensuppressed.Hysteresisusestwothresholdsandifthemagnitudeisbelowthefirstthreshold,itissettozero(madeanonedge).Ifthemagnitudeisabovethehighthreshold,itismadeanedge.Andifthemagnitudeisbetweenthe2thresholds,thenitissettozerounlessthereisapathfromthispixeltoapixelwithagradientaboveT2.
St
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