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

Mark Colbert University of Central Florida Jaroslav Křivánek Czech Technical University in Prague

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**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

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Demo

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Our Approach BRDF proportional sampling Environment map filtering

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Related Work A Unified Approach to Prefiltered Environment Maps [ Kautz et al ] Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions [ McAllister et al ] Efficient Reflectance and Visibility Approximations for Environment Map Rendering [ Green et al ] Interactive Illumination with Coherent Shadow Maps [ Ritschel et al ] 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)

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**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

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**Importance Sampling Choose a few random samples**

Select according to the BRDF PDF – guides

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**Importance Sampling Result**

40 samples per pixel

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**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

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Same Sequence Result 40 samples per pixel

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**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

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**Filtering Use MIP-maps Level proportional to log of filter size**

Spherical Harmonics diffuse component [Ramamoorthi and Hanrahan 2001]

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**Implementation Auto-generated MIP-map Dual paraboloids**

Single GPU Shader Sum together filtered samples

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**Results Sphere – Grace Probe**

Stochastic No Filtering Our Result Reference

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**Results Bunny – Ennis Probe**

Stochastic No Filtering Our Result Reference

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**Approximations Constant BRDF across filter Isotropic filter shape**

Tri-linear filtering

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**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

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

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**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/

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Questions

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Additional Slides

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

From 7800 to : 5.75x faster

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**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….

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**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….

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**Which distribution? Product of lighting and BRDF Lighting BRDF**

Computationally efficient Sample-Importance Resample (SIR) Lighting – already know BRDF is higher frequency, so….

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**Environment Mapping Dual Paraboloid Error Support Region**

Use because cube maps cause seams artifacts when using MIP-maps Support Region

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**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

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**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

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

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**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

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**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;

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**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

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**Ideal Sample Filter Design**

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

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**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

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