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FourierSlicePhotography
RenNgStanfordUniversityConventionalPhotographLightFieldPhotographyCapturethelightfieldinsidethecamerabodyHand-HeldLightFieldCameraMediumformatdigitalcameraCamerain-use16megapixelsensorMicrolensarrayLightFieldinaSingleExposureLightFieldinaSingleExposureLightFieldInsidetheCameraBodyDigitalRefocusingDigitalRefocusingQuestionsAboutDigitalRefocusing
Whatisthecomputationalcomplexity?
Arethereefficientalgorithms?Whatarethelimitsonrefocusing?
Howfarcanwemovethefocalplane?Overview
FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusingPreviousWorkIntegralphotographyLippmann1908,Ives1930Lotsofvariants,especiallyin3DTV
Okoshi1976,Javidi&Okano2002Closestvariantisplenopticcamera
Adelson&Wang1992FourieranalysisoflightfieldsChaietal.2000RefocusingfromlightfieldsIsaksenetal.2000,Stewartetal.2003FourierSlicePhotographyTheoremIntheFourierdomain,aphotographisa
2Dsliceinthe4Dlightfield.
Photographsfocusedatdifferentdepthscorrespondto2Dslicesatdifferenttrajectories.DigitalRefocusingbyRay-TracingLensSensoruxDigitalRefocusingbyRay-TracingLensSensoruImaginaryfilmxDigitalRefocusingbyRay-TracingLensSensoruxImaginaryfilmDigitalRefocusingbyRay-TracingLensSensoruImaginaryfilmxDigitalRefocusingbyRay-TracingLensSensoruxImaginaryfilmRefocusingasIntegralProjectionLensSensoruxImaginaryfilmxuRefocusingasIntegralProjectionLensSensoruxImaginaryfilmxuRefocusingasIntegralProjectionLensSensoruxxuImaginaryfilmRefocusingasIntegralProjectionLensSensoruxxuImaginaryfilmClassicalFourierSliceTheorem2DFourier
Transform1DFourier
TransformIntegral
Projection
Slicing2DFourier
TransformClassicalFourierSliceTheorem1DFourier
TransformIntegral
Projection
SlicingClassicalFourierSliceTheorem2DFourier
Transform1DFourier
TransformIntegral
Projection
SlicingFourierDomainClassicalFourierSliceTheoremIntegral
Projection
SlicingSpatialDomainSpatialDomainClassicalFourierSliceTheoremIntegral
Projection
SlicingFourierDomainFourierSlicePhotographyTheoremIntegral
Projection
SlicingFourierDomainSpatialDomainFourierSlicePhotographyTheorem4DFourier
TransformIntegral
Projection
SlicingFourierSlicePhotographyTheorem4DFourier
Transform2DFourier
TransformIntegral
Projection
SlicingFourierSlicePhotographyTheorem4DFourier
Transform2DFourier
TransformIntegral
Projection
SlicingFourierSlicePhotographyTheorem4DFourier
Transform2DFourier
TransformIntegral
Projection
SlicingPhotographicImagingEquationsSpatial-DomainIntegralProjectionFourier-DomainSlicingPhotographicImagingEquationsSpatial-DomainIntegralProjectionFourier-DomainSlicingPhotographicImagingEquationsSpatial-DomainIntegralProjectionFourier-DomainSlicingTheoremLimitationsFilmparalleltolensEverydaycamera,notviewcameraAperturefullyopenClosingaperturerequiresspatialmaskOverview
FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusingExistingRefocusingAlgorithmsExistingrefocusingalgorithmsareexpensiveO(N4) wherelightfieldhas
NsamplesineachdimensionAllarevariantsonintegralprojectionIsaksen etal. 2000Vaish etal. 2004Levoy etal. 2004Ng etal. 2005RefocusinginSpatialDomain4DFourier
Transform2DFourier
TransformIntegral
Projection
SlicingRefocusinginFourierDomain4DFourier
TransformInverse
2DFourier
TransformIntegral
Projection
SlicingRefocusinginFourierDomain4DFourier
TransformInverse
2DFourier
TransformIntegral
Projection
SlicingAsymptoticPerformanceFourier-domainslicingalgorithmPre-process:O(N4logN)Refocusing:O(N2logN)Spatial-domainintegrationalgorithmRefocusing:O(N4)ResamplingFilterChoiceTrianglefilter(quadrilinear)Kaiser-Besselfilter
(width2.5)Goldstandard(spatialintegration)Overview
FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusingProblemStatementAssumealightfieldcamerawithAnf/AlensNxNpixelsundereachmicrolensIfwecomputerefocusedphotographs
fromtheselightfields,overwhatrange
canwemovethefocalplane?AnalyticalassumptionAssumeband-limitedlightfieldsBand-LimitedAnalysisBand-LimitedAnalysisLightfieldshot
withcameraBand-widthof
measuredlightfieldBand-LimitedAnalysisBand-LimitedAnalysisBand-LimitedAnalysisPhotographicImagingEquationsSpatial-DomainIntegralProjectionFourier-DomainSlicingResultsofBand-LimitedAnalysisAssumealightfieldcamerawithAnf/AlensNxNpixelsundereachmicrolensFromitslightfieldswecanRefocusexactlywithin
depthoffieldofanf/(AN)lensInourprototypecameraLensisf/412x12pixelsundereachmicrolensTheoreticallyrefocuswithin
depthoffieldofanf/48lensLightFieldPhotoGalleryStanfordQuadRodin’sBurghersofCalaisPalaceofFineArts,SanFranciscoPalaceofFineArts,SanFranciscoWaitingtoRaceStartoftheRaceSummaryofMainContributions
Formaltheoremaboutrelationship
betweenlightfieldsandphotographsComputationalapplicationgivesasymptoticallyfastrefocusingalgorithmTheoreticalapplicationgives
analyticsolutionfor
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