圖像局部特證及其匹配的詳細(xì)講解課件

圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人高興。野心是使人勤奮的原因，節(jié)制使人枯萎。12、不問收獲，只問耕耘。如同種樹，先有根莖，再有枝葉，爾后花實(shí)，好好勞動(dòng)，不要想太多，那樣只會(huì)使人膽孝懶惰，因?yàn)椴粚?shí)踐，甚至不接觸社會(huì)，難道你是野人。(名言網(wǎng))13、不怕，不悔(雖然只有四個(gè)字，但?？闯Ｐ?。14、我在心里默默地為每一個(gè)人祝福。我愛自己，我用清潔與節(jié)制來珍惜我的身體，我用智慧和知識(shí)充實(shí)我的頭腦。15、這世上的一切都借希望而完成。農(nóng)夫不會(huì)播下一粒玉米，如果他不曾希望它長(zhǎng)成種籽；單身漢不會(huì)娶妻，如果他不曾希望有小孩；商人或手藝人不會(huì)工作，如果他不曾希望因此而有收益。--馬釘路德。圖像局部特證及其匹配的詳細(xì)講解圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人高興。野心是使人勤奮的原因，節(jié)制使人枯萎。12、不問收獲，只問耕耘。如同種樹，先有根莖，再有枝葉，爾后花實(shí)，好好勞動(dòng)，不要想太多，那樣只會(huì)使人膽孝懶惰，因?yàn)椴粚?shí)踐，甚至不接觸社會(huì)，難道你是野人。(名言網(wǎng))13、不怕，不悔(雖然只有四個(gè)字，但?？闯Ｐ隆?4、我在心里默默地為每一個(gè)人祝福。我愛自己，我用清潔與節(jié)制來珍惜我的身體，我用智慧和知識(shí)充實(shí)我的頭腦。15、這世上的一切都借希望而完成。農(nóng)夫不會(huì)播下一粒玉米，如果他不曾希望它長(zhǎng)成種籽；單身漢不會(huì)娶妻，如果他不曾希望有小孩；商人或手藝人不會(huì)工作，如果他不曾希望因此而有收益。--馬釘路德。MatchingwithInvariantFeaturesExample:BuildaPanoramaM.BrownandD.G.Lowe.RecognisingPanoramas.ICCV2003圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人1圖像局部特證及其匹配的詳細(xì)講解課件2圖像局部特證及其匹配的詳細(xì)講解課件3圖像局部特證及其匹配的詳細(xì)講解課件4圖像局部特證及其匹配的詳細(xì)講解課件5MatchingwithFeaturesDetectfeaturepointsinbothimagesFindcorrespondingpairsMatchingwithFeaturesDetectf6MatchingwithFeaturesDetectfeaturepointsinbothimagesFindcorrespondingpairsUsethesepairstoalignimagesMatchingwithFeaturesDetectf7MatchingwithFeaturesProblem1:Detectthesamepointindependentlyinbothimagesnochancetomatch!WeneedarepeatabledetectorMatchingwithFeaturesProblem8MatchingwithFeaturesProblem2:Foreachpointcorrectlyrecognizethecorrespondingone?WeneedareliableanddistinctivedescriptorMatchingwithFeaturesProblem9Moremotivation…Featurepointsareusedalsofor:Imagealignment(homography,fundamentalmatrix)3DreconstructionMotiontrackingObjectrecognitionIndexinganddatabaseretrievalRobotnavigation…otherMoremotivation…Featurepoin10ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector11Anintroductoryexample:HarriscornerdetectorC.Harris,M.Stephens.“ACombinedCornerandEdgeDetector”.1988Anintroductoryexample:Harris12TheBasicIdeaWeshouldeasilyrecognizethepointbylookingthroughasmallwindowShiftingawindowinany

directionshouldgivealargechangeinintensityTheBasicIdeaWeshouldeasily13HarrisDetector:BasicIdea“flat”region:

nochangeinalldirections“edge”:

nochangealongtheedgedirection“corner”:

significantchangeinalldirectionsHarrisDetector:BasicIdea“fl14ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector15HarrisDetector:MathematicsChangeofintensityfortheshift[u,v]:IntensityShiftedintensityWindowfunctionorWindowfunctionw(x,y)=Gaussian1inwindow,0outsideHarrisDetector:MathematicsCh16HarrisDetector:MathematicsForsmallshifts[u,v]wehaveabilinearapproximation:whereMisa22matrixcomputedfromimagederivatives:HarrisDetector:MathematicsFo17HarrisDetector:MathematicsIntensitychangeinshiftingwindow:eigenvalueanalysis1,2–eigenvaluesofMdirectionoftheslowestchangedirectionofthefastestchange(max)-1/2(min)-1/2EllipseE(u,v)=constHarrisDetector:MathematicsIn18HarrisDetector:Mathematics12“Corner”

1and2arelarge,

1~2;

Eincreasesinalldirections1and2aresmall;

Eisalmostconstantinalldirections“Edge”

1>>2“Edge”

2>>1“Flat”regionClassificationofimagepointsusingeigenvaluesofM:HarrisDetector:Mathematics119HarrisDetector:MathematicsMeasureofcornerresponse:(k–empiricalconstant,k=0.04-0.06)HarrisDetector:MathematicsMe20HarrisDetector:Mathematics12“Corner”“Edge”“Edge”“Flat”

RdependsonlyoneigenvaluesofM

Rislargeforacorner

Risnegativewithlargemagnitudeforanedge|R|issmallforaflatregionR>0R<0R<0|R|smallHarrisDetector:Mathematics121HarrisDetectorTheAlgorithm:FindpointswithlargecornerresponsefunctionR(R>threshold)TakethepointsoflocalmaximaofRHarrisDetectorTheAlgorithm:22HarrisDetector:WorkflowHarrisDetector:Workflow23HarrisDetector:WorkflowComputecornerresponseRHarrisDetector:WorkflowCompu24HarrisDetector:WorkflowFindpointswithlargecornerresponse:R>thresholdHarrisDetector:WorkflowFind25HarrisDetector:WorkflowTakeonlythepointsoflocalmaximaofRHarrisDetector:WorkflowTake26HarrisDetector:WorkflowHarrisDetector:Workflow27HarrisDetector:SummaryAverageintensitychangeindirection[u,v]canbeexpressedasabilinearform:

DescribeapointintermsofeigenvaluesofM:

measureofcornerresponse

Agood(corner)pointshouldhavealargeintensitychangeinalldirections,i.e.RshouldbelargepositiveHarrisDetector:SummaryAverag28ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector29HarrisDetector:SomePropertiesRotationinvarianceEllipserotatesbutitsshape(i.e.eigenvalues)remainsthesameCornerresponseRisinvarianttoimagerotationHarrisDetector:SomeProperti30HarrisDetector:SomePropertiesPartialinvariancetoaffineintensitychange

Onlyderivativesareused=>invariancetointensityshiftI

I

+

b

Intensityscale:Ia

IRx

(imagecoordinate)thresholdRx

(imagecoordinate)HarrisDetector:SomeProperti31HarrisDetector:SomePropertiesBut:non-invarianttoimagescale!AllpointswillbeclassifiedasedgesCorner!HarrisDetector:SomeProperti32HarrisDetector:SomePropertiesQualityofHarrisdetectorfordifferentscalechangesRepeatabilityrate:#correspondences

#possiblecorrespondencesC.Schmidet.al.“EvaluationofInterestPointDetectors”.IJCV2000HarrisDetector:SomeProperti33ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector34Wewantto:detectthesameinterestpointsregardlessofimagechangesWewantto:detectthesameint35ModelsofImageChangeGeometryRotationSimilarity(rotation+uniformscale)

Affine(scaledependentondirection)

validfor:orthographiccamera,locallyplanarobjectPhotometryAffineintensitychange(Ia

I+b)ModelsofImageChangeGeometry36ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector37RotationInvariantDetectionHarrisCornerDetectorC.Schmidet.al.“EvaluationofInterestPointDetectors”.IJCV2000RotationInvariantDetectionHa38ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector39ScaleInvariantDetectionConsiderregions(e.g.circles)ofdifferentsizesaroundapointRegionsofcorrespondingsizeswilllookthesameinbothimagesScaleInvariantDetectionConsi40ScaleInvariantDetectionTheproblem:howdowechoosecorrespondingcirclesindependentlyineachimage?ScaleInvariantDetectionThep41ScaleInvariantDetectionSolution:Designafunctionontheregion(circle),whichis“scaleinvariant”(thesameforcorrespondingregions,eveniftheyareatdifferentscales)

Example:averageintensity.Forcorrespondingregions(evenofdifferentsizes)itwillbethesame.scale=1/2Forapointinoneimage,wecanconsideritasafunctionofregionsize(circleradius)

fregionsizeImage1fregionsizeImage2ScaleInvariantDetectionSolut42ScaleInvariantDetectionCommonapproach:scale=1/2fregionsizeImage1fregionsizeImage2TakealocalmaximumofthisfunctionObservation:regionsize,forwhichthemaximumisachieved,shouldbeinvarianttoimagescale.s1s2Important:thisscaleinvariantregionsizeisfoundineachimageindependently!ScaleInvariantDetectionCommo43ScaleInvariantDetectionA“good”functionforscaledetection:

hasonestablesharppeakfregionsizebadfregionsizebadfregionsizeGood!Forusualimages:agoodfunctionwouldbeaonewhichrespondstocontrast(sharplocalintensitychange)ScaleInvariantDetectionA“go44ScaleInvariantDetectionFunctionsfordeterminingscaleKernels:whereGaussianNote:bothkernelsareinvarianttoscaleandrotation(Laplacian)(DifferenceofGaussians)ScaleInvariantDetectionFunct45ScaleInvariantDetectionComparetohumanvision:eye’sresponseShimonUllman,IntroductiontoComputerandHumanVisionCourse,Fall2003ScaleInvariantDetectionCompa46ScaleInvariantDetectorsHarris-Laplacian1

Findlocalmaximumof:Harriscornerdetectorinspace(imagecoordinates)Laplacianinscale1K.Mikolajczyk,C.Schmid.“IndexingBasedonScaleInvariantInterestPoints”.ICCV2001

2D.Lowe.“DistinctiveImageFeaturesfromScale-InvariantKeypoints”.AcceptedtoIJCV2004scalexyHarrisLaplacianSIFT(Lowe)2

Findlocalmaximumof:DifferenceofGaussiansinspaceandscalescalexyDoGDoGScaleInvariantDetectorsHarri47ScaleInvariantDetectorsK.Mikolajczyk,C.Schmid.“IndexingBasedonScaleInvariantInterestPoints”.ICCV2001Experimentalevaluationofdetectors

w.r.t.scalechangeRepeatabilityrate:#correspondences

#possiblecorrespondencesScaleInvariantDetectorsK.Mik48ScaleInvariantDetection:SummaryGiven:

twoimagesofthesamescenewithalargescaledifferencebetweenthemGoal:

findthesameinterestpointsindependentlyineachimageSolution:searchformaximaofsuitablefunctionsinscaleandinspace(overtheimage)Methods:Harris-Laplacian[Mikolajczyk,Schmid]:maximizeLaplacianoverscale,Harris’measureofcornerresponseovertheimageSIFT[Lowe]:maximizeDifferenceofGaussiansoverscaleandspaceScaleInvariantDetection:Sum49ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector50AffineInvariantDetectionAboveweconsidered:

Similaritytransform(rotation+uniformscale)Nowwegoonto:

Affinetransform(rotation+non-uniformscale)AffineInvariantDetectionAbov51AffineInvariantDetectionTakealocalintensityextremumasinitialpointGoalongeveryraystartingfromthispointandstopwhenextremumoffunctionfisreachedT.Tuytelaars,L.V.Gool.“WideBaselineStereoMatchingBasedonLocal,AffinelyInvariantRegions”.BMVC

2000.fpointsalongtherayWewillobtainapproximatelycorrespondingregionsRemark:wesearchforscaleineverydirectionAffineInvariantDetectionTake52AffineInvariantDetectionTheregionsfoundmaynotexactlycorrespond,soweapproximatethemwithellipsesGeometricMoments:Fact:momentsmpquniquelydeterminethefunctionfTakingftobethecharacteristicfunctionofaregion(1inside,0outside),momentsofordersupto2allowtoapproximatetheregionbyanellipseThisellipsewillhavethesamemomentsofordersupto2astheoriginalregionAffineInvariantDetectionThe53AffineInvariantDetectionCovariancematrixofregionpointsdefinesanellipse:(p=[x,y]Tisrelativetothecenterofmass)Ellipses,computedforcorrespondingregions,alsocorrespond!AffineInvariantDetectionCova54AffineInvariantDetectionAlgorithmsummary(detectionofaffineinvariantregion):StartfromalocalintensityextremumpointGoineverydirectionuntilthepointofextremumofsomefunctionfCurveconnectingthepointsistheregionboundaryComputegeometricmomentsofordersupto2forthisregionReplacetheregionwithellipseT.Tuytelaars,L.V.Gool.“WideBaselineStereoMatchingBasedonLocal,AffinelyInvariantRegions”.BMVC

2000.AffineInvariantDetectionAlgo55AffineInvariantDetectionMaximallyStableExtremalRegionsThresholdimageintensities:I>I0Extractconnectedcomponents

(“ExtremalRegions”)Findathresholdwhenanextremal

regionis“MaximallyStable”,

i.e.localminimumoftherelative

growthofitssquareApproximatearegionwith

anellipseJ.Mataset.al.“DistinguishedRegionsforWide-baselineStereo”.ResearchReportofCMP,2001.AffineInvariantDetectionMaxi56AffineInvariantDetection:SummaryUnderaffinetransformation,wedonotknowinadvanceshapesofthecorrespondingregionsEllipsegivenbygeometriccovariancematrixofaregionrobustlyapproximatesthisregionForcorrespondingregionsellipsesalsocorrespondMethods:Searchforextremumalongrays[Tuytelaars,VanGool]:MaximallyStableExtremalRegions[Mataset.al.]AffineInvariantDetection:S57ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector58PointDescriptorsWeknowhowtodetectpointsNextquestion:

Howtomatchthem??Pointdescriptorshouldbe:InvariantDistinctivePointDescriptorsWeknowhowt59ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector60DescriptorsInvarianttoRotationHarriscornerresponsemeasure:

dependsonlyontheeigenvaluesofthematrixMC.Harris,M.Stephens.“ACombinedCornerandEdgeDetector”.1988DescriptorsInvarianttoRotat61DescriptorsInvarianttoRotationImagemomentsinpolarcoordinatesJ.Mataset.al.“RotationalInvariantsforWide-baselineStereo”.ResearchReportofCMP,2003Rotationinpolarcoordinatesistranslationoftheangle:

+0Thistransformationchangesonlythephaseofthemoments,butnotitsmagnitudeRotationinvariantdescriptorconsistsofmagnitudesofmoments:Matchingisdonebycomparingvectors[|mkl|]k,lDescriptorsInvarianttoRotat62DescriptorsInvarianttoRotationFindlocalorientationDominantdirectionofgradientComputeimagederivativesrelativetothisorientation1K.Mikolajczyk,C.Schmid.“IndexingBasedonScaleInvariantInterestPoints”.ICCV2001

2D.Lowe.“DistinctiveImageFeaturesfromScale-InvariantKeypoints”.AcceptedtoIJCV2004DescriptorsInvarianttoRotat63ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector64DescriptorsInvarianttoScaleUsethescaledeterminedbydetectortocomputedescriptorinanormalizedframeForexample:momentsintegratedoveranadaptedwindowderivativesadaptedtoscale:sIxDescriptorsInvarianttoScale65ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector66AffineInvariantDescriptorsAffineinvariantcolormomentsF.Mindruet.al.“RecognizingColorPatternsIrrespectiveofViewpointandIllumination”.CVPR99DifferentcombinationsofthesemomentsarefullyaffineinvariantAlsoinvarianttoaffinetransformationofintensityIa

I+bAffineInvariantDescriptorsAf67AffineInvariantDescriptorsFindaffinenormalizedframeJ.Mataset.al.“RotationalInvariantsforWide-baselineStereo”.ResearchReportofCMP,2003AA1A2rotationComputerotationalinvariantdescriptorinthisnormalizedframeAffineInvariantDescriptorsFi68SIFT–ScaleInvariantFeatureTransform1Empiricallyfound2toshowverygoodperformance,invarianttoimagerotation,scale,intensitychange,andtomoderateaffinetransformations1D.Lowe.“DistinctiveImageFeaturesfromScale-InvariantKeypoints”.AcceptedtoIJCV2004

2K.Mikolajczyk,C.Schmid.“APerformanceEvaluationofLocalDescriptors”.CVPR2003Scale=2.5

Rotation=450SIFT–ScaleInvariantFeature69SIFT–ScaleInvariantFeatureTransformDescriptoroverview:Determinescale(bymaximizingDoGinscaleandinspace),

localorientationasthedominantgradientdirection.

Usethisscaleandorientationtomakeallfurthercomputationsinvarianttoscaleandrotation.Computegradientorientationhistogramsofseveralsmallwindows(128valuesforeachpoint)NormalizethedescriptortomakeitinvarianttointensitychangeD.Lowe.“DistinctiveImageFeaturesfromScale-InvariantKeypoints”.AcceptedtoIJCV2004SIFT–ScaleInvariantFeature70AffineInvariantTextureDescriptorSegmenttheimageintoregionsofdifferenttextures(byanon-invariantmethod)ComputematrixM(thesameasin

Harrisdetector)overtheseregions

ThismatrixdefinestheellipseF.Schaffalitzky,A.Zisserman.“ViewpointInvariantTextureMatchingandWideBaselineStereo”.ICCV2003RegionsdescribedbytheseellipsesareinvariantunderaffinetransformationsFindaffinenormalizedframeComputerotationinvariantdescriptorAffineInvariantTextureDescr71InvariancetoIntensityChangeDetectorsmostlyinvarianttoaffine(linear)changeinimageintensity,becausewearesearchingformaximaDescriptorsSomearebasedonderivatives=>invarianttointensityshiftSomearenormalizedtotolerateintensityscaleGenericmethod:pre-normalizeintensityofaregion(eliminateshiftandscale)InvariancetoIntensityChange72TalkResumeStable(repeatable)featurepointscanbedetectedregardlessofimagechangesScale:searchforcorrectscaleasmaximumofappropriatefunctionAffine:approximateregionswithellipses(thisoperationisaffineinvariant)InvariantanddistinctivedescriptorscanbecomputedInvariantmomentsNormalizingwithrespecttoscaleandaffinetransformationTalkResumeStable(repeatable)73HappyEnd!HappyEnd!74HarrisDetector:ScaleRmin=0Rmin=1500HarrisDetector:ScaleRmin=0R75

1、最靈繁的人也看不見自己的背脊。——非洲

2、最困難的事情就是認(rèn)識(shí)自己?！ＥD

3、有勇氣承擔(dān)命運(yùn)這才是英雄好漢?！谌?/p>

4、與肝膽人共事，無字句處讀書?！芏鱽?/p>

5、閱讀使人充實(shí)，會(huì)談使人敏捷，寫作使人精確。——培根

1、最靈繁的人也看不見自己的背脊。——非洲

2、最困76圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人高興。野心是使人勤奮的原因，節(jié)制使人枯萎。12、不問收獲，只問耕耘。如同種樹，先有根莖，再有枝葉，爾后花實(shí)，好好勞動(dòng)，不要想太多，那樣只會(huì)使人膽孝懶惰，因?yàn)椴粚?shí)踐，甚至不接觸社會(huì)，難道你是野人。(名言網(wǎng))13、不怕，不悔(雖然只有四個(gè)字，但常看常新。14、我在心里默默地為每一個(gè)人祝福。我愛自己，我用清潔與節(jié)制來珍惜我的身體，我用智慧和知識(shí)充實(shí)我的頭腦。15、這世上的一切都借希望而完成。農(nóng)夫不會(huì)播下一粒玉米，如果他不曾希望它長(zhǎng)成種籽；單身漢不會(huì)娶妻，如果他不曾希望有小孩；商人或手藝人不會(huì)工作，如果他不曾希望因此而有收益。--馬釘路德。圖像局部特證及其匹配的詳細(xì)講解圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人高興。野心是使人勤奮的原因，節(jié)制使人枯萎。12、不問收獲，只問耕耘。如同種樹，先有根莖，再有枝葉，爾后花實(shí)，好好勞動(dòng)，不要想太多，那樣只會(huì)使人膽孝懶惰，因?yàn)椴粚?shí)踐，甚至不接觸社會(huì)，難道你是野人。(名言網(wǎng))13、不怕，不悔(雖然只有四個(gè)字，但?？闯Ｐ?。14、我在心里默默地為每一個(gè)人祝福。我愛自己，我用清潔與節(jié)制來珍惜我的身體，我用智慧和知識(shí)充實(shí)我的頭腦。15、這世上的一切都借希望而完成。農(nóng)夫不會(huì)播下一粒玉米，如果他不曾希望它長(zhǎng)成種籽；單身漢不會(huì)娶妻，如果他不曾希望有小孩；商人或手藝人不會(huì)工作，如果他不曾希望因此而有收益。--馬釘路德。MatchingwithInvariantFeaturesExample:BuildaPanoramaM.BrownandD.G.Lowe.RecognisingPanoramas.ICCV2003圖像局部特證及其匹配的詳細(xì)講解11、獲得的成功越大，就越令人77圖像局部特證及其匹配的詳細(xì)講解課件78圖像局部特證及其匹配的詳細(xì)講解課件79圖像局部特證及其匹配的詳細(xì)講解課件80圖像局部特證及其匹配的詳細(xì)講解課件81MatchingwithFeaturesDetectfeaturepointsinbothimagesFindcorrespondingpairsMatchingwithFeaturesDetectf82MatchingwithFeaturesDetectfeaturepointsinbothimagesFindcorrespondingpairsUsethesepairstoalignimagesMatchingwithFeaturesDetectf83MatchingwithFeaturesProblem1:Detectthesamepointindependentlyinbothimagesnochancetomatch!WeneedarepeatabledetectorMatchingwithFeaturesProblem84MatchingwithFeaturesProblem2:Foreachpointcorrectlyrecognizethecorrespondingone?WeneedareliableanddistinctivedescriptorMatchingwithFeaturesProblem85Moremotivation…Featurepointsareusedalsofor:Imagealignment(homography,fundamentalmatrix)3DreconstructionMotiontrackingObjectrecognitionIndexinganddatabaseretrievalRobotnavigation…otherMoremotivation…Featurepoin86ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector87Anintroductoryexample:HarriscornerdetectorC.Harris,M.Stephens.“ACombinedCornerandEdgeDetector”.1988Anintroductoryexample:Harris88TheBasicIdeaWeshouldeasilyrecognizethepointbylookingthroughasmallwindowShiftingawindowinany

directionshouldgivealargechangeinintensityTheBasicIdeaWeshouldeasily89HarrisDetector:BasicIdea“flat”region:

nochangeinalldirections“edge”:

nochangealongtheedgedirection“corner”:

significantchangeinalldirectionsHarrisDetector:BasicIdea“fl90ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector91HarrisDetector:MathematicsChangeofintensityfortheshift[u,v]:IntensityShiftedintensityWindowfunctionorWindowfunctionw(x,y)=Gaussian1inwindow,0outsideHarrisDetector:MathematicsCh92HarrisDetector:MathematicsForsmallshifts[u,v]wehaveabilinearapproximation:whereMisa22matrixcomputedfromimagederivatives:HarrisDetector:MathematicsFo93HarrisDetector:MathematicsIntensitychangeinshiftingwindow:eigenvalueanalysis1,2–eigenvaluesofMdirectionoftheslowestchangedirectionofthefastestchange(max)-1/2(min)-1/2EllipseE(u,v)=constHarrisDetector:MathematicsIn94HarrisDetector:Mathematics12“Corner”

1and2arelarge,

1~2;

Eincreasesinalldirections1and2aresmall;

Eisalmostconstantinalldirections“Edge”

1>>2“Edge”

2>>1“Flat”regionClassificationofimagepointsusingeigenvaluesofM:HarrisDetector:Mathematics195HarrisDetector:MathematicsMeasureofcornerresponse:(k–empiricalconstant,k=0.04-0.06)HarrisDetector:MathematicsMe96HarrisDetector:Mathematics12“Corner”“Edge”“Edge”“Flat”

RdependsonlyoneigenvaluesofM

Rislargeforacorner

Risnegativewithlargemagnitudeforanedge|R|issmallforaflatregionR>0R<0R<0|R|smallHarrisDetector:Mathematics197HarrisDetectorTheAlgorithm:FindpointswithlargecornerresponsefunctionR(R>threshold)TakethepointsoflocalmaximaofRHarrisDetectorTheAlgorithm:98HarrisDetector:WorkflowHarrisDetector:Workflow99HarrisDetector:WorkflowComputecornerresponseRHarrisDetector:WorkflowCompu100HarrisDetector:WorkflowFindpointswithlargecornerresponse:R>thresholdHarrisDetector:WorkflowFind101HarrisDetector:WorkflowTakeonlythepointsoflocalmaximaofRHarrisDetector:WorkflowTake102HarrisDetector:WorkflowHarrisDetector:Workflow103HarrisDetector:SummaryAverageintensitychangeindirection[u,v]canbeexpressedasabilinearform:

DescribeapointintermsofeigenvaluesofM:

measureofcornerresponse

Agood(corner)pointshouldhavealargeintensitychangeinalldirections,i.e.RshouldbelargepositiveHarrisDetector:SummaryAverag104ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector105HarrisDetector:SomePropertiesRotationinvarianceEllipserotatesbutitsshape(i.e.eigenvalues)remainsthesameCornerresponseRisinvarianttoimagerotationHarrisDetector:SomeProperti106HarrisDetector:SomePropertiesPartialinvariancetoaffineintensitychange

Onlyderivativesareused=>invariancetointensityshiftI

I

+

b

Intensityscale:Ia

IRx

(imagecoordinate)thresholdRx

(imagecoordinate)HarrisDetector:SomeProperti107HarrisDetector:SomePropertiesBut:non-invarianttoimagescale!AllpointswillbeclassifiedasedgesCorner!HarrisDetector:SomeProperti108HarrisDetector:SomePropertiesQualityofHarrisdetectorfordifferentscalechangesRepeatabilityrate:#correspondences

#possiblecorrespondencesC.Schmidet.al.“EvaluationofInterestPointDetectors”.IJCV2000HarrisDetector:SomeProperti109ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector110Wewantto:detectthesameinterestpointsregardlessofimagechangesWewantto:detectthesameint111ModelsofImageChangeGeometryRotationSimilarity(rotation+uniformscale)

Affine(scaledependentondirection)

validfor:orthographiccamera,locallyplanarobjectPhotometryAffineintensitychange(Ia

I+b)ModelsofImageChangeGeometry112ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector113RotationInvariantDetectionHarrisCornerDetectorC.Schmidet.al.“EvaluationofInterestPointDetectors”.IJCV2000RotationInvariantDetectionHa114ContentsHarrisCornerDetectorDescriptionAnalysisDetectorsRotationinvariantScaleinvariantAffineinvariantDescriptorsRotationinvariantScaleinvariantAffineinvariantContentsHarrisCornerDetector115ScaleInvariantDetectionConsiderregions(e.g.circles)ofdifferentsizesaroundapointRegionsofcorrespondingsizeswilllookthesameinbothimagesScaleInvariantDetectionConsi116ScaleInvariantDetectionTheproblem:howdowechoosecorrespondingcirclesindependentlyineachimage?ScaleInvariantDetectionThep117ScaleInvariantDetectionSolution:Designafunctionontheregion(circle),whichis“scaleinvariant”(thesameforcorrespondingregions,eveniftheyareatdifferentscales)

Example:averageintensity.Forcorrespondingregions(evenofdifferentsizes)itwillbethesame.scale=1/2Forapointinoneimage,wecanconsideritasafunctionofregionsize(circleradius)

fregionsizeImage1fre