Real-time Shading with Filtered Importance Sampling Mark Colbert University of Central Florida Jaroslav Křivánek Czech Technical University in Prague

Motivation Dynamic BRDF and lighting Applications Material design Gaming Production pipeline friendly Single GPU shader No precomputation Minimal code base Solution that can be put into a game engine or Renderman

Demo

Our Approach BRDF proportional sampling Environment map filtering

Related Work A Unified Approach to Prefiltered Environment Maps [ Kautz et al. 2000 ] Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions [ McAllister et al. 2002 ] Efficient Reflectance and Visibility Approximations for Environment Map Rendering [ Green et al. 2007 ] Interactive Illumination with Coherent Shadow Maps [ Ritschel et al. 2007 ] Kautz et al. - Providing a good review of prefiltering techniques McAllister et al. – Demonstrates SBRDFs on GPU novel MIP-map Green et al. – Prefilter Gaussians for glossy materials (EG) Ritschel et al. – Importance sampling on GPU for visiblity (EGSR)

Illumination Integral Ignores visibility [ Kozlowski and Kautz 2007 ] Computationally expensive Explain in terms of the equation components Li Incoming Radiance (Environment Map) f Material Function (BRDF)  Angle between normal and incoming direction

Importance Sampling Choose a few random samples Select according to the BRDF PDF – guides

Importance Sampling Result 40 samples per pixel

Random Numbers on the GPU Relatively expensive Random numbers per pixel (computation) Random number textures (memory/indirection) Quasi-random sequence Good sample distribution (no clumping) Use same sequence for each pixel

Same Sequence Result 40 samples per pixel

Filtered Importance Sampling Filter environment map between samples over hemisphere Samples distributed by the BRDF Support approximately equivalent to: Add omega being proportional to this thing N Number of samples p Probability density function

Filtering Use MIP-maps Level proportional to log of filter size Spherical Harmonics diffuse component [Ramamoorthi and Hanrahan 2001]

Implementation Auto-generated MIP-map Dual paraboloids Single GPU Shader Sum together filtered samples

Results Sphere – Grace Probe Stochastic No Filtering Our Result Reference

Results Bunny – Ennis Probe Stochastic No Filtering Our Result Reference

Approximations Constant BRDF across filter Isotropic filter shape Tri-linear filtering

RMS Error Phong Reflection - Ennis Light Probe n=10 n=100 n=1000 TODO: Get from MATLAB Maybe show reference image? Make sure to mention the RMS error as a function of n n=1000

Performance 512x512 Sphere No portion of the algorithm is ran on the CPU From 7800 to 8800 SLI: 8.4x faster @ 40 spp From 7800 to 8800 : 5.75x faster @ 40 spp

Conclusions Real-time glossy surface reflections Signal Processing Theory Practical Affords new interfaces For more information: GPU Gems 3 Download the code now! graphics.cs.ucf.edu/gpusampling/

Questions

Additional Slides

Performance From 7800 to 8800 SLI: 8.4x faster From 7800 to 8800 : 5.75x faster

Which distribution? Product of lighting and BRDF Lighting BRDF Requires bookkeeping Too expensive Lighting BRDF Sample-Importance Resample (SIR) Lighting – already know BRDF is higher frequency, so….

Which distribution? Product of lighting and BRDF Lighting BRDF Too many samples for glossy surfaces BRDF Sample-Importance Resample (SIR) Lighting – already know BRDF is higher frequency, so….

Which distribution? Product of lighting and BRDF Lighting BRDF Computationally efficient Sample-Importance Resample (SIR) Lighting – already know BRDF is higher frequency, so….

Environment Mapping Dual Paraboloid Error Support Region Use because cube maps cause seams artifacts when using MIP-maps Support Region

Environment Mapping Cube Maps Low distortion Accelerated by GPU Decimation/reconstruction filters non-spherical Introduces Seams Decimation/reconstruction is non-spherical (i.e. per face) causing filter region to

Environment Mapping Latitude/Longitude Too much distortion at poles Makes rate of change from spherical to image vary greatly as a distance from the pole

Measured BRDF Data Fast primitive distribution for illustration [ Secord et al. 2002 ] Efficient BRDF importance sampling using a factored representation [ Lawrence et al. 2004 ] Probability Trees [ McCool and Harwood 1997 ]

PDF-Proportional Samples Importance Sampling Random Samples on Unit Square PDF-Proportional Samples on Hemisphere 1 PDF Mapping TODO: Add animation Random values on unit square 1

Pseudocode float4 FilteredIS(float3 viewing : TEXCOORD1 uniform sampler2D env) : COLOR { float4 c = 0;   // sample loop for (int k=0; k < N; k++) { float2 xi = quasi_random_seq(k); float3 u = sample_material(xi); float pdf = p(u, viewing); float lod = compute_lod(u, pdf); float3 L = tex2Dlod(env,float4(u, lod)); c += L*f(u,viewing)/pdf; } return c/N;

Filter Support Ideal Isotropic approximation Assume sample points are perfectly stratified Implies area of 1 sample = 1 / N Use Jacobian approximation for warping function (Inverted PDF) Support region of sample  1 / p(i, o) N TODO: Convert text to equations Mention: Ideal = Support region between each sample Jacobian provides a rate of change from one domain to another Here we need to find the rate of change from the nearly stratified domain of the unit square (approximated by 1/N) to the BRDF-proportional domain

Ideal Sample Filter Design h – Filter function More expensive than illumination integral TODO: Change color of BRDF

Approximate Sample Filter Estimate for sample BRDF  PDF PDF is normalized BRDF Near constant over single sample Low frequency cosine approximation Use multiple samples to estimate effect Filter independent of BRDF and cosine