Real-time robust estimation of vanishing points through nonlinear optimization

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1、RobustestimationofvanishingpointsMarcosNieto-mnd@gti.ssr.upm.esLuisSalgado-L.Salgado@gti.ssr.upm.esGrupodeTratamientodeImágenesOutlineòIntroduction●Vanishingpoints●ImagefeaturesòRelatedwork–ErrorfunctionòProposederrorfunction●Errormaps●Convergenceevaluationò

2、MLESAC●RANSAC●Variants●TrackingextensionòResultsIntroduction–Vanishingpoints“Pointsintheimageplanecorrespondingto3Dspacedirections”“Pointintheimageplanewhereparallellinesinthe3Dspaceseemtoconverge”Introduction–ApplicationsPlanerectificationVideocompassMosaic

3、ingIntroduction–Imagefeatures“Gradient-pixels”“Edge-points”…Introduction–Imagefeatures“Linesegments”Introduction–LinesegmentsRandomsamplingandMean-ShiftforNon-InputimageStraight-edgesmaximalsuppresionOrientation-basedgrowingalgorithmResult(Bresenham)Introduc

4、tion–Howto…StilleasyQuiteeasyNointersectionpointin2D!Andnow?òFormally,anerrorfunctionmustbedefinedbetweenthevanishingpointandtheimagefeaturesòE.g.…2Dpoint-linedistanceintheimageòWhataboutparallellines?CalibratecoordinatesòAnestimationmethodshallprovidetheval

5、uesofthevanishingpointcoordinatesthatminimizesthetotalerroròE.g.…LeastsquaresòArobustapproachisneededtoselectsub-setsofimagefeaturesmeetingacommonvanishingpointtodetectmultiplevanishingpointsinthepresenceofclutterRelatedwork–ErrorfunctionòImage-planesolution

6、●BadperformanceforfarorinfinitevanishingpointsErrorfunctionEstimationmethodPoint-linedistanceLeastsquares(SVD)Relatedwork–ErrorfunctionòProjective-planesolutions●Handleinfinitevanishingpoints●Requirecameracalibrationmatrixforexactcorrespondencebetweenimagepo

7、intsand3DdirectionsErrorfunctionEstimationmethod“Calibrated”point-lineLeastsquares(SVD)distanceRelatedwork–UnitspherePoint-linedistanceLine-linedistanceRelatedwork–UnitsphereVanishinglinesFinitevanishingpointInfinitevanishingpointRelatedwork–ErrorfunctionòPr

8、ojective-planesolutionsErrorfunctionEstimationmethod●WithoutneedofcalibrationSumofend-pointtolineLevenberg-Marquardt●Specificforlinesegmentsdistances(non-linearoptimization)Relatedwork–Errorfunc