Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Contributions Acquisition Data Simulation Display Modeling processing Plant growth simulation Real time rendering RFPT'03, TOG'03 Light SIG'04, SigT'10, SigP'11, transport Remote sensing I3D'12, TVCG'13 RAMI'07 Fourier analysis of light transport SIG'05,TOG'09,SigP'11,TOG'13,TOG'14 Texture-based visibility SIG'98, TOG'00 Image Image decomposition manipulation SIG'09, CGF'13 Texture analysis AFIG'08 Texture synthesis SIG'02 Computational Geometry instantiation geometry EGSR'00, SgpP'05, TOG'06 Filtering SigP'11 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 7 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Contributions Acquisition Data Simulation Display Modeling processing Plant growth simulation Real time rendering RFPT'03, TOG'03 Light SIG'04, SigT'10, SigP'11, BRDF modeling transport Remote sensing I3D'12, TVCG'13 CGF'12 RAMI'07 Fourier analysis of light transport BRDF acquisition SIG'05,TOG'09,SigP'11,TOG'13,TOG'14 Texture-based visibility SigP'13 SIG'98, TOG'00 Image Image decomposition manipulation SIG'09, CGF'13 Texture analysis AFIG'08 Texture synthesis SIG'02 Computational Geometry instantiation geometry EGSR'00, SgpP'05, TOG'06 Filtering SigP'11 ◮ 11 papers in international journals (10 at TOG/Siggraph) ◮ 8 papers in international conferences (I3D,EG,EGSR) C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 7 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborations/Projects Daimler++ Cornell LIAMA Eden Games++ CIRAD UDeM Noveltis UCL MIT 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 8 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborations/Projects Daimler++ Cornell LIAMA Eden Games++ CIRAD UDeM Noveltis UCL MIT L.Belcour Spectral A.Martinet covariance M.Bagher Instanciation Fourier for RT rendering PE.Landes B.Zupancic Texture BRDF analysis C.Sensing 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 8 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborations/Projects Daimler++ Cornell LIAMA Eden Games++ CIRAD UDeM Noveltis UCL MIT L.Belcour Spectral A.Martinet covariance M.Bagher Instanciation Fourier for RT rendering PE.Landes B.Zupancic Texture BRDF analysis C.Sensing Soleil RealReflect Genac II Garden ALTA (FUI project) (FUI project) (ANR project) (ARC INRIA) (IST European project) 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 8 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborators Research collaborators: P .Dereffye MP .Cani F.Sillion F.Durand J.Thollot N.Holszchuch K.Subr S.Paris J.Kautz K.Bala D.Nowrouz- ezahrai C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 9 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborators Research collaborators: P .Dereffye MP .Cani F.Sillion F.Durand J.Thollot N.Holszchuch K.Subr S.Paris J.Kautz K.Bala D.Nowrouz- ezahrai Past (and current) PhD students: A.Martinet P-E.Landes M.Bagher L.Belcour B.Zupancic C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 9 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Collaborators Research collaborators: P .Dereffye MP .Cani F.Sillion F.Durand J.Thollot N.Holszchuch K.Subr S.Paris J.Kautz K.Bala D.Nowrouz- ezahrai Past (and current) PhD students: A.Martinet P-E.Landes M.Bagher L.Belcour B.Zupancic Assistants, engineers, co-authors: ... D.Courtiol L.Boissieux O.Hoel I.Delore S.Guy K.Smith JC.Roche C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 9 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Outline ◮ Introduction ◮ 2 selected contributions ◮ Automatic instancing ◮ Fourier analysis of light transport ◮ ongoing / future work, and conclusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 10 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Problem statement ◮ origins of the problem: ◮ radiative exchanges in vegetation scenes [Soler, et al. TOG2003] [Soler, Sillion, Blaise, Dereffye. TOG 2003 ] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 11 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Problem statement ◮ origins of the problem: ◮ radiative exchanges in vegetation scenes [Soler, et al. TOG2003] [RAMI challenge website] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 11 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Problem statement ◮ origins of the problem: ◮ radiative exchanges in vegetation scenes [Soler, et al. TOG2003] ◮ compress geometry by instantiation [Martinet, Soler, et al. TOG2006] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 11 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Problem statement ◮ origins of the problem: ◮ radiative exchanges in vegetation scenes [Soler, et al. TOG2003] ◮ compress geometry by instantiation [Martinet, Soler, et al. TOG2006] ◮ in practice most scenes come without structure Raw geometry C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 11 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Instantiation algorithm ◮ Instantiation algorithm ◮ build tiles from polygon soup (See e.g. [Krayevoy’2006, Katz’2005] ) Raw geometry Tiles Hierarchical represention +tiles symmetry + symmetries C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 12 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Instantiation algorithm ◮ Instantiation algorithm ◮ build tiles from polygon soup (See e.g. [Krayevoy’2006, Katz’2005] ) ◮ group hierarchically using: ⋆ a rotation-free similarity distance ⋆ and a symmetry detection algorithm Raw geometry Tiles Hierarchical represention +tiles symmetry + symmetries C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 12 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Instantiation algorithm ◮ Instantiation algorithm ◮ build tiles from polygon soup (See e.g. [Krayevoy’2006, Katz’2005] ) ◮ group hierarchically using: ⋆ a rotation-free similarity distance ⋆ and a symmetry detection algorithm ◮ existing methods (e.g. [Kahzdan’2002]: brute force) Raw geometry Tiles Hierarchical represention +tiles symmetry + symmetries C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 12 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Instantiation algorithm ◮ Instantiation algorithm ◮ build tiles from polygon soup (See e.g. [Krayevoy’2006, Katz’2005] ) ◮ group hierarchically using: ⋆ a rotation-free similarity distance ⋆ and a symmetry detection algorithm ◮ existing methods (e.g. [Kahzdan’2002]: brute force) ◮ we used spherical harmonics! Raw geometry Tiles Hierarchical represention +tiles symmetry + symmetries C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 12 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation � M 2 p ( ω ) = � s × ω � 2 p ds (Generalized moment) s ∈S C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 13 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation � M 2 p ( ω ) = � s × ω � 2 p ds (Generalized moment) s ∈S – For all p , all symmetries of S are symmetries of M 2 p C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 13 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation � M 2 p ( ω ) = � s × ω � 2 p ds (Generalized moment) s ∈S – For all p , all symmetries of S are symmetries of M 2 p – If ω is a symmetry axis of S , then ∇M 2 p ( ω ) = 0 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 13 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation � M 2 p ( ω ) = � s × ω � 2 p ds (Generalized moment) s ∈S – For all p , all symmetries of S are symmetries of M 2 p – If ω is a symmetry axis of S , then ∇M 2 p ( ω ) = 0 – M 2 p has a finite spherical harmonics decomposition ! C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 13 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics � c m M 2 p ( ω ) y m = l ( ω ) d ω l Ω C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics � c m = S l � s � 2 p y m 2 l ( s ) ds l p s ∈S C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically M 2 p = � c m l y m l l , m C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically ∇M 2 p = � c m l ∇ y m l l , m C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically ◮ look for the zeroes, this gives the axes of the symmetries C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically ◮ look for the zeroes, this gives the axes of the symmetries ◮ for each axis, align M 2 p with this axis using SH rotation. C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically ◮ look for the zeroes, this gives the axes of the symmetries ◮ for each axis, align M 2 p with this axis using SH rotation. C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Symmetry computation (2/2) Symmetry detection algorithm: ◮ decompose M 2 p into spherical harmonics ◮ compute ∇M 2 p for all p analytically ◮ look for the zeroes, this gives the axes of the symmetries ◮ for each axis, align M 2 p with this axis using SH rotation. ◮ compute the symmetry angle/sign C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 14 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Similarity distance m ( c m l ) 2 ◮ compute the L2 square norm � ◮ concatenate for all p C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 15 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Similarity distance m ( c m l ) 2 ◮ compute the L2 square norm � ◮ concatenate for all p C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 15 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Results [A.Martinet, C.Soler,... ACM TOG 2006 ] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 16 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Outline ◮ Introduction ◮ 2 selected contributions ◮ Automatic instancing ◮ Fourier analysis of light transport ◮ ongoing / future work, and conclusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 17 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor � L ( p ) = C ( x , p ) dx x ∈P C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor � L ( p ) = C ( x , p ) dx x ∈P N C ( x , p ) L ( p ) ≈ 1 � N P ( x ) i = 1 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor ◮ many variants! (MLT, Photon Mapping, BDPT, ...) � L ( p ) = C ( x , p ) dx x ∈P N C ( x , p ) L ( p ) ≈ 1 � N P ( x ) i = 1 C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 18 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor ◮ many variants! (MLT, Photon Mapping, BDPT, ...) C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 19 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor ◮ many variants! (MLT, Photon Mapping, BDPT, ...) C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 19 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor ◮ many variants! (MLT, Photon Mapping, BDPT, ...) ◮ eventually the image can be very smooth. C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 19 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Monte-Carlo Light Transport ◮ collect light bouncing in a scene toward a captor ◮ many variants! (MLT, Photon Mapping, BDPT, ...) ◮ eventually the image can be very smooth. Can we predict in advance–and leverage–image smoothness? C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 19 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Let’s use Fourier analysis! ◮ the local Fourier spectrum in the image tells us a lot! C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 20 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Let’s use Fourier analysis! ◮ the local Fourier spectrum in the image tells us a lot! ◮ image-space sampling densities (2D spatial component, image) [Soler, Subr, et al. TOG’2009] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 20 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Let’s use Fourier analysis! ◮ the local Fourier spectrum in the image tells us a lot! ◮ image-space sampling densities (2D spatial component, image) ◮ light-space variance (2D angular component, scene) [Soler, Subr, et al. TOG’2009] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 20 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Let’s use Fourier analysis! ◮ the local Fourier spectrum in the image tells us a lot! ◮ image-space sampling densities (2D spatial component, image) ◮ light-space variance (2D angular component, scene) ◮ image-space reconstruction filters (4D/5D spectrum, scene) [Belcour, Soler, et al. TOG’2011] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 20 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Let’s use Fourier analysis! ◮ the local Fourier spectrum in the image tells us a lot! ◮ image-space sampling densities (2D spatial component, image) ◮ light-space variance (2D angular component, scene) ◮ image-space reconstruction filters (4D/5D spectrum, scene) ◮ density estimation kernels (2D spatial component, scene) [Belcour, Soler. Siggraph’2012 poster] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 20 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space Convolution Occlusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space Convolution Occlusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space Space travel Shear Convolution Occlusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space Space travel Shear Convolution Occlusion Reflectance Angular product C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events Primal space Fourier space b Space travel Shear Convolution Occlusion Reflectance Angular product C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events ◮ we need a good representation for this Primal space Fourier space b Space travel Shear Convolution Occlusion Reflectance Angular product C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events ◮ we need a good representation for this Primal space Fourier space Spectral covariance (4x4 matrix!) b Space travel Shear Convolution Occlusion Reflectance Angular product C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion So, can we predict the local image spectrum?? ◮ spectra are additive! ◮ add up spectra of local light fields along light paths ◮ ...and analyze the effect of the various events ◮ we need a good representation for this Primal space Fourier space Spectral covariance (4x4 matrix!) b Left-right product Space travel Shear Convolution Sum of matrices Occlusion Reflectance Angular product Product + p-inverse C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 21 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Scattering and Absorption [TOG’2013] ◮ Fourier analysis: ◮ absorption increases bandwidth ◮ scattering reduces bandwidth � − 1 Σ ′ = Σ + A Σ ′ = � Σ − 1 + S C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 22 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Scattering and Absorption [TOG’2013] ◮ Fourier analysis: ◮ absorption increases bandwidth ◮ scattering reduces bandwidth ◮ Derived prediction formulas for ◮ 3D frequency spectrum of the fluence ◮ reconstruction kernels for progressive photon beams [To be presented at Sig’2014] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 22 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Selected contributions ◮ Introduction ◮ 2 selected contributions ◮ Ongoing/Future work, and Conclusion C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 23 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Ongoing work: spherical filtering ◮ idea: efficient filtering using isotropic function bases C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 24 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Ongoing work: spherical filtering ◮ idea: efficient filtering using isotropic function bases ◮ lots of possible applications: ◮ rendering measured materials in real time [Brush alum. MERL database] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 24 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Ongoing work: spherical filtering ◮ idea: efficient filtering using isotropic function bases ◮ lots of possible applications: ◮ rendering measured materials in real time ◮ anti-aliasing sub-pixel curvature C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 24 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Ongoing work: spherical filtering ◮ idea: efficient filtering using isotropic function bases ◮ lots of possible applications: ◮ rendering measured materials in real time ◮ anti-aliasing sub-pixel curvature ◮ efficient reconstruction for 4D BRDFs ◮ lightfield illumination [Purple satin. MERL database] C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 24 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Ongoing work: Compressed Material Acquisition ◮ Idea: Use compressive sensing for BRDF acquisition ◮ BRDFs are very sparse signals ◮ according to E.Candès work, a few photographs should be sufficient to recover a BRDF ◮ 1 PhD student working on it (Benoit Zupancic) C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 25 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Future work: Dimensional analysis of light transport ◮ reflectance, visibility, scattering,... − → are all linear operators in light field space ◮ eigen analysis will probably provide: ◮ optimal representation bases (made of harmonic functions!) ◮ new computation methods C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 26 / 28
Introduction Automatic instancing (2006) Fourier Analysis of Light Transport (2005-2014) Conclusion Future work: Dimensional analysis of light transport ◮ reflectance, visibility, scattering,... − → are all linear operators in light field space ◮ eigen analysis will probably provide: ◮ optimal representation bases (made of harmonic functions!) ◮ new computation methods Λ 0 Λ 1 α Λ 0 + TL e Best Ambient Illum. Plausible rendering C.Soler (INRIA) Models and Analyses for Image Synthesis June 24, 2014 26 / 28
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