Realtime Shading with Filtered Importance Sampling Mark Colbert

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 Real-time Shading with Filtered Importance Sampling

Demo

Our Approach • BRDF proportional sampling • Environment map filtering Real-time Shading with Filtered Importance Sampling

Related Work • A Unified Approach to Prefiltered Environment Maps [ Kautz et al. 2000 ] • Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions [ Mc. Allister 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 ] Real-time Shading with Filtered Importance Sampling

Illumination Integral • Ignores visibility [ Kozlowski and Kautz 2007 ] • Computationally expensive Li f Incoming Radiance (Environment Map) Material Function (BRDF) Angle between normal and incoming direction Real-time Shading with Filtered Importance Sampling

Importance Sampling • Choose a few random samples • Select according to the BRDF Real-time Shading with Filtered Importance Sampling

Importance Sampling Result Real-time Shading with Filtered Importance Sampling 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 Real-time Shading with Filtered Importance Sampling

Same Sequence Result Real-time Shading with Filtered Importance Sampling 40 samples per pixel

Filtered Importance Sampling • Filter environment map between samples over hemisphere – Samples distributed by the BRDF • Support approximately equivalent to: N p Real-time Shading with Filtered Importance Sampling Number of samples Probability density function

Filtering • Use MIP-maps • Level proportional to log of filter size Real-time Shading with Filtered Importance Sampling

Implementation • Auto-generated MIP-map • Dual paraboloids • Single GPU Shader – Sum together filtered samples Real-time Shading with Filtered Importance Sampling

Reference Real-time Shading with Filtered Importance Sampling No Filtering Sphere – Grace Probe Our Result Stochastic Results

Reference Real-time Shading with Filtered Importance Sampling No Filtering Bunny – Ennis Probe Our Result Stochastic Results

Approximations • Constant BRDF across filter • Isotropic filter shape • Tri-linear filtering Real-time Shading with Filtered Importance Sampling

RMS Error Phong Reflection - Ennis Light Probe n=1000 Real-time Shading with Filtered Importance Sampling

Performance 512 x 512 Sphere Real-time Shading with Filtered Importance Sampling

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

Questions

Additional Slides

Performance Real-time Shading with Filtered Importance Sampling

Which distribution? • Product of lighting and BRDF – Requires bookkeeping – Too expensive • Lighting • BRDF Real-time Shading with Filtered Importance Sampling

Which distribution? • Product of lighting and BRDF • Lighting – Too many samples for glossy surfaces • BRDF Real-time Shading with Filtered Importance Sampling

Which distribution? • Product of lighting and BRDF • Lighting • BRDF – Computationally efficient Real-time Shading with Filtered Importance Sampling

Environment Mapping • Dual Paraboloid Error Support Region Real-time Shading with Filtered Importance Sampling

Environment Mapping • Cube Maps – Low distortion – Accelerated by GPU – Decimation/reconstruction filters non-spherical – Introduces Seams Real-time Shading with Filtered Importance Sampling

Environment Mapping • Latitude/Longitude – Too much distortion at poles Real-time Shading with Filtered Importance Sampling

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 [ Mc. Cool and Harwood 1997 ] Real-time Shading with Filtered Importance Sampling

Importance Sampling Random Samples on Unit Square PDF-Proportional Samples on Hemisphere 1 PDF Mapping 0 0 1 Real-time Shading with Filtered Importance Sampling

Pseudocode float 4 Filtered. IS(float 3 viewing : TEXCOORD 1 uniform sampler 2 D env) : COLOR { float 4 c = 0; // sample loop for (int k=0; k < N; k++) { float 2 xi = quasi_random_seq(k); float 3 u = sample_material(xi); float pdf = p(u, viewing); float lod = compute_lod(u, pdf); float 3 L = tex 2 Dlod(env, float 4(u, lod)); c += L*f(u, viewing)/pdf; } return c/N; } Real-time Shading with Filtered Importance Sampling

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 Real-time Shading with Filtered Importance Sampling

Ideal Sample Filter Design • h – Filter function • More expensive than illumination integral Real-time Shading with Filtered Importance Sampling

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 Real-time Shading with Filtered Importance Sampling