what is the range of surface reconstructions from a gradient field

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1、WhatistheRangeofSurfaceReconstructionsfromaGradientField?AmitAgrawal1,RameshRaskar2,andRamaChellappa11CenterforAutomationResearch,UniversityofMarylandCollegePark,MD,USA20742{aagrawal,rama}@cfar.umd.edu2MitsubishiElectricResearchLabs(MERL)201Broadway,Cambridge,MA,USA02139{raskar}@merl.comAbst

2、ract.Weproposeageneralizedequationtorepresentacontinuumofsur-facereconstructionsolutionsofagivennon-integrablegradientfield.WeshowthatcommonapproachessuchasPoissonsolverandFrankot-Chellappaalgo-rithmarespecialcasesofthisgeneralizedequation.ForaN×Npixelgrid,the2subspaceofallintegrablegradientfi

3、eldsisofdimensionN−1.Ourframe-workcanbeappliedtoderivearangeofmeaningfulsurfacereconstructionsfromthishighdimensionalspace.Thekeyobservationisthattherangeofsolutionsisrelatedtothedegreeofanisotropyinapplyingweightstothegradientsintheinte-grationprocess.Whilecommonapproachesuseisotropicweight

4、s,weshowthatbyusingaprogressionofspatiallyvaryinganisotropicweights,wecanachievesignificantimprovementinreconstructions.Wepropose(a)α-surfacesusingbi-naryweights,wheretheparameterαallowstradeoffbetweensmoothnessandro-bustness,(b)M-estimatorsandedgepreservingregularizationusingcontinuousweight

5、sand(c)Diffusionusingaffinetransformationofgradients.Weprovideresultsonphotometricstereo,comparewithpreviousapproachesandshowthatanisotropictreatmentdiscountsnoisewhilerecoveringsalientfeaturesinrecon-structions.1IntroductionReconstructionfromgradientfieldsisimportantinseveralapplicationssucha

6、spho-tometricstereo(PS)andshapefromshading(SfS)[1],meshsmoothing,retinex[2],highdynamicrangecompression[3],phaseunwrapping,imageediting,mattingandfusion[4].Ingradientbasedalgorithms,thegradientfieldofimagesismanipulatedtoachievethedesiredgoalandthefinalimageisobtainedbya2Dintegrationofthema-ni

7、pulatedgradientfield.InPS/SfS,surfacenormals/gradientsareobtainedfirstandthedesiredsurfaceisobtainedbyintegratingthegradientfield.Thegradientfieldofasur-faceshouldhavezerocurloritshouldbeintegrable.Theintegralalonganyclosedloop(path)shouldbeequaltozero