UMD CMSC 828V - A 
Frequency 
Analysis 
o f
Light
 Transport


Unformatted text preview:

A"Frequency"Analysis"of"Light"Transport"Frédo&Durand,&Nicolas&Holzschuch,&Cyril&Soler,&Eric&Chan&&&François&Sillion&Images and Material provided by Frédo Durand and the paper SIGGRAPH 2005Light"Transport"• Light"travels"from"the"source"and"is"filtered"and"reflected."• Example:"• The"goal"of"this"work"is"to"study"this"in"the"frequency"domain"Why"frequency"domain?"• Because"something"in"the"image"is…"– Sharp"– Blurred"• Sharp"(HIGH"frequencies)"– DisconMnuity,"Edges"• Blurred"(LOW"frequencies)"– SoP"Shadows,"indirect"illuminaMon,"Depth"of"Field""Light"Field"ParameterizaMon"Central"ray"local""light""field"space:"x"angle:"v"or"θ"Area"Light"Ray"space"v"(angle)"x"(space)"Area"Light"Fourier"space"Ωv"(angle)"Ωx"(space)"The"Flow"of"Light"Transport"• Transport"in"free"space"• Occlusion"• BRDF"The"Flow"of"Light"Transport"• The"effects"can"be"modeled"in"frequency"domain."• They"involve"– Shearing)– Convolu/on"in"spaMal"domain"– Mul/plica/on"in"the"frequency"domain"Transport"in"Free"Space"• Shear:"x’"="x"‐"v"d"Ray"space"v"(angle)"x"(space)"Ray"space"v"(angle)"x"(space)"dvd"vxx’"Fourier"space"Ωv"(angle)"Ωx"(space)"Occlusion"• Planar"occluders"• MulMplicaMon"for"SpaMal"• ConvoluMon"in"Frequency"Fourier"space"Blocker"spectrum"Blocker"funcMon"Transport"again"Blockers Light source ReceiverBRDF"• BRDF"(integraMon)"is"convoluMon"in"spaMal"domain"(recall"from"Spherical"Harmonics"LighMng)"xBRDF"• Convolu<on"in"spaMal"domain"is"Mul<plica<on"in"frequency"domain."Ωv"(angle)"Ωx"(space)"Ωv"(angle)"Ωx"(space)"BRDF"spectrum"Curvature"• Treat"the"curved"surface"as"a"plane"• Rotate"the"light"direcMons""(i.e."Shearing)"• So"it’s"also"shearing"in"frequency"domain"AdapMve"Sampling"Example"Curvature"&"BRDF""Blocker"distance"Results"(Uniform"20k"Sampling)"AdapMve"20k"Sampling"Sample"Pa]ern"AdapMve"Wavelet"Rendering"Ryan"S."Overbeck"Craig"Donner"Ravi"Ramamoorthi"Images and Material provided by Ryan S. Overbeck and the SIGGRAPH Asia 2009 paperOverview"• AdapMve"super"sampling"• Sampling"in"the"image"space"mul<scale&wavelet"domain"• The"sampling"rate"on"different"scales"of"wavelets"adapts"to"the"details"of"the"image""Wavelets"• Wavelets"are"mulMscale"basis"funcMons"• Scale"Coefficients"• Wavelet"Coefficients"€ Sk,ij= B • Φk,ijWk,ij= B • Ψk,ijWavelet"ReconstrucMon"• A"is"reconstructed"by""S"(Scaling"Coefficients)"• D"is"reconstructed"by"W"(Wavelet"Coefficients)""Sampling"on"a"Budget"1. Coarsely"sample"the"image"(4"for"each"pixel)"2. Wavelet"transform"the"samples"3. Compute"the"prioriMes"for"S"4. "Importance"sampling"Iterate until there is no budget samplesCompute"Priority"of"Scale"Coefficients"• Priority"• More"samples"to"the"scale"with"large"variance"• Global"features"–"More"samples"at"coarse"• Local"features"–"More"samples"at"fine"€ P(Sk,ij) =σ2(Sk,ij) − Wk,ij2CompuMng"the"Variance"• The"variance"scale"coefficients"is"computed"by"projecMng"the"variance"of"the"image"to"the"scaling"basis""€ σ2(Sk,ij) =σ2(B) • Φ2k,ijReconstrucMon"• Use"variance"informaMon"for"smoothing""(The"std"dev"of"W"for"this"Mme)"• Filter"low"magnitude"coefficients"(ie."Noise)"Input Variance Image OutputResults"Wavelet 32 MC 56 MC 512 MDAS 16 (Slow)Conclusions"• Light"transport"can"be"analyzed"in"the"frequency"domain"efficiently"– Transport"="Shearing"(SpaMal"or"Frequency)"– Occlusion"="MulMplicaMon"in"SpaMal"Domain"– BRDF"="MulMplicaMon"in"Frequency"Domain"– Curved"Surface"can"be"treated"as"planes"with"rotated"lights"Conclusion"• AdapMve"Wavelet"Rendering"– Importance"sampling"according"to"the"variance"of"the"wavelet"domain"scale"coefficients"(Find"the"right"scale"for"sampling)"–


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UMD CMSC 828V - A 
Frequency 
Analysis 
o f
Light
 Transport


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Frequency 
Analysis 
o f
Light
 Transport

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Frequency 
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Light
 Transport
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Frequency 
Analysis 
o f
Light
 Transport
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