segmentation2 canny edge detectorhough transformlec15邊緣檢測器變換

ImageSegmentation–Edgelinking:

CannyEdgeDetector&HoughTransform

ChongjinZhuSchoolofElectronicEngineering,UESTC2ReviewDetectionofdiscontinuityusing1stderivativeProvidinggradientandmagnitudeZerocrossing(2ndderivativeusingLaplacian)ForedgelocationNogradientinformationSensitivetonoiseSmoothingusingGaussianfilter(LoG)ImageSegmentation-23ImageSegmentation-2Howtodealwithgapsinedges?Howtodealwithnoiseinedges?LinkingpointsbydeterminingwhethertheylieonacurveofaspecificshapeEdgelinking4ImageSegmentation-2AnalyzethecharacteristicsoftheedgepixelsinasmallneighborhoodItsmagnitudeItsdirectionEdgelinking–LocalProcessingE:nonnegativethresholdE=25A:nonnegativeanglethresholdA=150(x0,y0):anedgepoint5Whatismissing?Q1:Isapixelanedgeelementornot?CannyEdgeDetectionQ2:Iftheedgeelementsarenotconnect,howtoestablishtheboundarybetweenregions?HoughTransformImageSegmentation-26CannyEdgeDetectorCannyedgedetectoranswersthefirstquestion.Characteristicsoftheedgedetector:Lowerrorrate--findingalledgesandnothingbutedges.Localizationofedges

–distancebetweenedgesfoundandactualedgesshouldbeminimized.Singleresponse

–nomultipleedgepixelswhenonlyasingleedgeexists.ImageSegmentation-27EdgeFunctioninMatlabI:intensityimage,BW:binaryimageTHRESH:isatwo-elementvectorinwhichthefirstelementisthelowthreshold,andthesecondelementisthehighthreshold.TheCannymethoduses2thresholds,todetectstrongandweakedges,andincludestheweakedgesintheoutputonlyiftheyareconnectedtostrongedges.Thismethodisthereforelesslikelythantheotherstobe"fooled"bynoise,andmorelikelytodetecttrueweakedges.BW=edge(I,'canny')BW=edge(I,'canny',thresh)BW=edge(I,'canny',thresh,sigma)SyntaxsensitivitythresholdssmoothingImageSegmentation-28I=imread(‘Will.jpg’);bw=edge(I,'canny');I=imread(‘Lena.tif’);bw=edge(I,'canny');91011A=edge(I,'canny',[],1);B=edge(I,'canny',[],2);C=edge(I,'canny',[],3);D=edge(I,'canny',[],4);E=[ABCD];imshow(E)sigma12WhyisCannysodominant?Stillwidelyusedafter20years.Theoryisnice(butendresultsame).Detailsgood(magnitudeofgradient).Hysteresisisanimportantheuristic.Codewasdistributed.Perhapsthisisaboutallyoucandowithlinearfiltering.ImageSegmentation-213HoughTransformResultsofedge-detectionmethodsmaycontainsparsepoints,insteadofstraightlinesorcurves.Therefore,needtofitalinetotheedgepoints.Efficientsolution:HoughTransformOriginallyforfindinglinesEasilyvariedtofindothershapesImageSegmentation-214SimpleExampleConsiderapoint(xi,yi)andthegeneralequationofastraightlineinslope-interceptform:Q:Howmanylinesmaypassthrough(xi,yi)?Re-writingtheequationinab-planeHowmanylinesdowegetforafixed(xi,yi)?slopeinterceptImageSegmentation-215Finding(a,b)Nowgivenanotherpoint(xj,yj),howtofindtheparameter(a’,b’)whichdefinesthelinethatcontainsbothpoints?ImageSegmentation-216Finding(a,b)(con’d)Allpointsonthislinehavelinesinparameterspacethatintersectat(a’,b’).

ImageSegmentation-217Whatistheproblem?Howaboutaverticalline?Gradient/slopeisinfiniteNeedanotherparameterizationscheme.Nowconsiderristheshortestdistancefromthelinetotheorigin,andistheangleNewparameterization:ImageSegmentation-218ComputationforHoughTransformChoosingadiscretesetofvaluesofrand.Constructanaccumulatorarray,initializedwith0foreachentry.PicturethisprocessasavotingprocessrminrmaxrImageSegmentation-219ComputationforHoughTransform(con’d)Foreachedgepoint(x,y)intheimage,wecompute foreachIncrementthecounterforthecelloftheresulting(r,)Attheend,the(r,)withhighestcountcorrespondtostrongestlineintheimage.ImageSegmentation-220ImageSegmentation-2Cantoleratenoiseand