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FourierSlicePhotography RenNgStanfordUniversity ConventionalPhotograph LightFieldPhotography Capturethelightfieldinsidethecamerabody Hand HeldLightFieldCamera Mediumformatdigitalcamera Camerain use 16megapixelsensor Microlensarray LightFieldinaSingleExposure LightFieldinaSingleExposure LightFieldInsidetheCameraBody DigitalRefocusing DigitalRefocusing QuestionsAboutDigitalRefocusing Whatisthecomputationalcomplexity Arethereefficientalgorithms Whatarethelimitsonrefocusing Howfarcanwemovethefocalplane Overview FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusing PreviousWork IntegralphotographyLippmann1908 Ives1930Lotsofvariants especiallyin3DTVOkoshi1976 Javidi Okano2002ClosestvariantisplenopticcameraAdelson Wang1992FourieranalysisoflightfieldsChaietal 2000RefocusingfromlightfieldsIsaksenetal 2000 Stewartetal 2003 FourierSlicePhotographyTheorem IntheFourierdomain aphotographisa2Dsliceinthe4Dlightfield Photographsfocusedatdifferentdepthscorrespondto2Dslicesatdifferenttrajectories DigitalRefocusingbyRay Tracing Lens Sensor u x DigitalRefocusingbyRay Tracing Lens Sensor u Imaginaryfilm x DigitalRefocusingbyRay Tracing Lens Sensor u x Imaginaryfilm DigitalRefocusingbyRay Tracing Lens Sensor u Imaginaryfilm x DigitalRefocusingbyRay Tracing Lens Sensor u x Imaginaryfilm RefocusingasIntegralProjection Lens Sensor u x Imaginaryfilm RefocusingasIntegralProjection Lens Sensor u x Imaginaryfilm RefocusingasIntegralProjection Lens Sensor u x Imaginaryfilm RefocusingasIntegralProjection Lens Sensor u x Imaginaryfilm ClassicalFourierSliceTheorem 2DFourierTransform 1DFourierTransform 2DFourierTransform ClassicalFourierSliceTheorem 1DFourierTransform ClassicalFourierSliceTheorem 2DFourierTransform 1DFourierTransform FourierDomain ClassicalFourierSliceTheorem SpatialDomain SpatialDomain ClassicalFourierSliceTheorem FourierDomain FourierSlicePhotographyTheorem IntegralProjection Slicing FourierDomain SpatialDomain FourierSlicePhotographyTheorem 4DFourierTransform IntegralProjection Slicing FourierSlicePhotographyTheorem 4DFourierTransform 2DFourierTransform IntegralProjection Slicing FourierSlicePhotographyTheorem 4DFourierTransform 2DFourierTransform IntegralProjection Slicing FourierSlicePhotographyTheorem 4DFourierTransform 2DFourierTransform IntegralProjection Slicing PhotographicImagingEquations Spatial DomainIntegralProjection Fourier DomainSlicing PhotographicImagingEquations Spatial DomainIntegralProjection Fourier DomainSlicing PhotographicImagingEquations Spatial DomainIntegralProjection Fourier DomainSlicing TheoremLimitations FilmparalleltolensEverydaycamera notviewcameraAperturefullyopenClosingaperturerequiresspatialmask Overview FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusing ExistingRefocusingAlgorithms ExistingrefocusingalgorithmsareexpensiveO N4 wherelightfieldhasNsamplesineachdimensionAllarevariantsonintegralprojectionIsaksenetal 2000Vaishetal 2004Levoyetal 2004Ngetal 2005 RefocusinginSpatialDomain 4DFourierTransform 2DFourierTransform IntegralProjection Slicing RefocusinginFourierDomain 4DFourierTransform Inverse2DFourierTransform IntegralProjection Slicing RefocusinginFourierDomain 4DFourierTransform Inverse2DFourierTransform IntegralProjection Slicing AsymptoticPerformance Fourier domainslicingalgorithmPre process O N4logN Refocusing O N2logN Spatial domainintegrationalgorithmRefocusing O N4 ResamplingFilterChoice Trianglefilter quadrilinear Kaiser Besselfilter width2 5 Goldstandard spatialintegration Overview FourierSlicePhotographyTheoremFourierRefocusingAlgorithmTheoreticalLimitsofRefocusing ProblemStatement AssumealightfieldcamerawithAnf AlensNxNpixelsundereachmicrolensIfwecomputerefocusedphotographsfromtheselightfields overwhatrangecanwemovethefocalplane AnalyticalassumptionAssumeband limitedlightfields Band LimitedAnalysis Band LimitedAnalysis Lightfieldshotwithcamera Band widthofmeasuredlightfield Band LimitedAnalysis Band LimitedAnalysis Band LimitedAnalysis PhotographicImagingEquations Spatial DomainIntegralProjection Fourier DomainSlicing ResultsofBand LimitedAnalysis AssumealightfieldcamerawithAnf AlensNxNpixelsundereachmicrolensFromitslightfieldswecanRefocusexactlywithindepthoffieldofanf A N lensInourprototypecameraLensisf 412x12pixelsundereachmicrolensTheoreticallyrefocuswithindepthoffieldofanf 48lens LightFieldPhotoGallery StanfordQuad Rodin sBurghersofCalais PalaceofFineArts SanFrancisco PalaceofFineArts SanFrancisco WaitingtoRace StartoftheRace SummaryofMainContributions FormaltheoremaboutrelationshipbetweenlightfieldsandphotographsComputationalapplicationgivesasymptoticallyfastrefocusingalgorithmTheoreticalapplicationgivesanalyticsolutionforlimitsofrefocusing FutureWork Applygeneralsignal processingtechniquesCross fertilizationwithmedicalimaging ThanksandAcknowledgments CollaboratorsoncameratechreportMarcLevoy MathieuBr dif GeneDuval MarkHorowitzandPatHanrahanReadersandlistenersRaviRamamoorthi BrianCurle
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