第5講 特征提取-邊緣 深圳大學(xué) 機(jī)器視覺及應(yīng)用 課件

機(jī)器視覺及應(yīng)用李東lidong@邊緣檢測（Edgedetection）Goal:Identifysuddenchanges(discontinuities)inanimageIntuitively,mostsemanticandshapeinformationfromtheimagecanbeencodedintheedgesMorecompactthanpixels

Ideal:artist’slinedrawing(butartistisalsousingobject-levelknowledge)Whydowecareaboutedges?Extractinformation,recognizeobjectsRecovergeometryandviewpointVanishingpointVanishing

lineVanishingpointVerticalvanishingpoint(atinfinity)OriginofEdgesEdgesarecausedbyavarietyoffactorsdepthdiscontinuitysurfacecolordiscontinuityilluminationdiscontinuitysurfacenormaldiscontinuityCloseupofedgesCloseupofedgesCloseupofedgesCloseupofedgesCharacterizingedgesAnedgeisaplaceofrapidchangeintheimageintensityfunctionimageintensityfunction

(alonghorizontalscanline)firstderivativeedgescorrespondto

extremaofderivative邊緣檢測邊緣是圖像上灰度的不連續(xù)點(diǎn)，或者是灰度變化劇烈處邊緣的數(shù)學(xué)表達(dá)：信號一階微分最大值/兩階微分過零點(diǎn)a：原始信號b：一階微分c：二階微分對于二維圖像f(x,y)，梯度定義為：一階微分是梯度的模：二階微分應(yīng)理解為沿梯度方向的二階方向?qū)?shù)，計(jì)算比較復(fù)雜，一般采用兩階微分算子（拉普拉斯算子）表示，拉普拉斯算子具有各向同性

梯度(gradient)使用梯度(gradient)描述圖像函數(shù)的變化，梯度方向是圖像函數(shù)增長最大的方向

IntensityprofileWithalittleGaussiannoiseGradientEffectsofnoiseConsiderasingleroworcolumnoftheimagePlottingintensityasafunctionofpositiongivesasignalWhereistheedge?EffectsofnoiseDifferencefiltersrespondstronglytonoiseImagenoiseresultsinpixelsthatlookverydifferentfromtheirneighborsGenerally,thelargerthenoisethestrongertheresponseWhatcanwedoaboutit?Solution:smoothfirstTofindedges,lookforpeaksinfgf*gDifferentiationisconvolution,andconvolutionisassociative:

Thissavesusoneoperation:DerivativetheoremofconvolutionfSobel算子Prewitt算子Roberts算子圖像梯度算子的近似Prewitt算子-101-101-101計(jì)算均值，平滑噪聲檢測豎直邊緣-1-1-1000111計(jì)算均值，平滑噪聲檢測水平邊緣Prewitt算子，近似一階微分卷積模版：去噪+增強(qiáng)邊緣Sobel算子-101-202-101計(jì)算均值，平滑噪聲檢測豎直邊緣-1-2-1000121計(jì)算均值，平滑噪聲檢測水平邊緣Sobel算子，近似一階微分去噪+增強(qiáng)邊緣，給四鄰域更大的權(quán)重常見的梯度算子(a):Roberts算子 (b):3x3Prewitt算子(c):Sobel算子 (d):4x4Prewitt算子拉普拉斯算子拉普拉斯算子首先用Gauss函數(shù)對圖像進(jìn)行平滑，抑制噪聲然后對經(jīng)過平滑的圖像使用Laplacian算子利用卷積的性質(zhì)LoG算子等效于：

Gaussian平滑+Laplacian二階微分LaplacianofGaussian(LoG)高斯拉普拉斯LaplacianofGaussianoperator過零點(diǎn)為邊緣的位置在數(shù)字圖像上實(shí)現(xiàn)LoG00-1000-1-2-10-1-216-2-10-1-2-1000-100

Prewitt算子Roberts算子Log算子Soble算子i=imread('miss.bmp');i=i(:,:,1);figure;ro=edge(i,'roberts');imshow(1-ro);figure;pre=edge(i,'prewitt');imshow(1-pre);figure;so=edge(i,'sobel');imshow(1-so);figure;log=edge(i,'log');imshow(1-log);matlab：edgeDerivativeofGaussianfilter*[1-1]=Smoothedderivativeremovesnoise,butblursedge.Alsofindsedgesatdifferent“scales”.1pixel3pixels7pixelsTradeoffbetweensmoothingandlocalizationThegradientmagnitudeislargealongathick“trail”or“ridge,”sohowdoweidentifytheactualedgepoints?Howdowelinktheedgepointstoformcurves?ImplementationissuesDesigninganedgedetectorCriteriaforagoodedgedetector:Gooddetection:theoptimaldetectorshouldfindallrealedges,ignoringnoiseorotherartifactsGoodlocalizationtheedgesdetectedmustbeascloseaspossibletothetrueedgesthedetectormustreturnonepointonlyforeachtrueedgepointCuesofedgedetectionDifferencesincolor,intensity,ortextureacrosstheboundaryContinuityandclosureHigh-levelknowledgeCannyedgedetectorThisisprobablythemostwidelyusededgedetectorincomputervisionTheoreticalmodel:step-edgescorruptedbyadditiveGaussiannoiseCannyhasshownthatthefirstderivativeoftheGaussiancloselyapproximatestheoperatorthatoptimizestheproductofsignal-to-noiseratioandlocalizationJ.Canny,AComputationalApproachToEdgeDetection,IEEETrans.PatternAnalysisandMachineIntelligence,8:679-714,1986.NoteaboutMatlab’sCannydetectorSmallerrorsinimplementationGaussianfunctionnotproperlynormalizedFirstfilterswithaGaussian,thenadifferenceofGaussian(equivalenttofilteringwithalargerGaussianandtakingdifference)Exampleoriginalimage(Lena)DerivativeofGaussianfilterx-directiony-directionComputeGradients(DoG)X-DerivativeofGaussianY-DerivativeofGaussianGradientMagnitudeGetOrientationatEachPixelThresholdatminimumlevelGetorientationtheta=atan2(gy,gx)Non-maximumsuppressionforeachorientationAtq,wehaveamaximumifthevalueislargerthanthoseatbothpandatr.Interpolatetogetthesevalues.BeforeNon-maxSuppressionAfternon-maxsuppressionAssumethemarkedpointisanedgepoint.Thenweconstructthetangenttotheedgecurve(whichisnormaltothegradientatthatpoint)andusethistopredictthenextpoints(hereeitherrors).EdgelinkingHysteresisthresholdingThresholdatlow/highlevelstogetweak/strongedgepixelsDoconnectedcomponents,startingfromstrongedgepixelsHysteresisthresholdingCheckthatmaximumvalueofgradientvalueissufficientlylargedrop-outs?usehysteresisuseahighthresholdtostartedgecurvesandalowthresholdtocontinuethem.FinalCannyEdgesCannyedgedetectorFilterimagewithx,yderivativesofGaussianFindmagnitudeandorientationofgradientNon-maximumsuppression:Thinmulti-pixelwide“ridges”downtosinglepixelwidthThresholdingandlinking(hysteresis):Definetwothresholds