Improved Radiance Gradient Computation

1. Computer Graphics Group Improved Radiance Gradient Computation Jaroslav Křivánek Pascal Gautron Kadi Bouatouch Sumanta Pattanaik

2. Indirect lighting on glossy surfaces With indirect Without indirect Improved Radiance Gradient Computation

3. Indirect lighting on glossy surfaces With indirect Without indirect Improved Radiance Gradient Computation

4. Problem to solve • Illumination integral evaluation at each visible point Improved Radiance Gradient Computation

5. Brute Force Approach • Monte Carlo gathering • For each visible point • Slow convergence rate Cast hundreds of rays Improved Radiance Gradient Computation

6. Slow Monte Carlo Convergence - Example • 40 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/ Improved Radiance Gradient Computation

7. Slow Monte Carlo Convergence - Example • 100 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/ Improved Radiance Gradient Computation

8. Slow Monte Carlo Convergence - Example • 300 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/ Improved Radiance Gradient Computation

9. Slow Monte Carlo Convergence - Example • 600 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/ Improved Radiance Gradient Computation

10. Slow Monte Carlo Convergence – Example • 1200 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/ Improved Radiance Gradient Computation

11. Observation • Indirect lighting on rough glossy surfaces is rather smooth: abrupt changes are rare Improved Radiance Gradient Computation

12. Radiance Caching Approach • Sparse sampling of indirect illumination • Interpolation • Based on gradients Improved Radiance Gradient Computation

13. Radiance cache lookup Radiance cache lookup Cache Miss! P1 P2 Radiance Caching Radiance Cache Scene Store in cache P1 Sample hemisphere Project to hemispherical harmonics Lo=∫x BRDF(P1) x cos θdω Lo(P2)=∫ x BRDF(P2) x cos θdω Lo(P1) Lo(P2) Improved Radiance Gradient Computation

14. P1 P2 P1 P2 Problem Reality With radiance caching Wrong extrapolation Li(P1) !=Li(P2) Li(P1) =Li(P2) Improved Radiance Gradient Computation

15. Wrong Extrapolation • How does Li(P)change with P? ( Li(P) = incoming radiance at P ) • First approximation = RADIANCE GRADIENT • Our contribution • New radiance gradient computation Improved Radiance Gradient Computation

16. Wrong Extrapolation Improved Radiance Gradient Computation

17. Corrected with the New Gradients Improved Radiance Gradient Computation

18. Radiance Gradients: Problem Definition – Prerequisites • Incoming radiance Li(P) representation • Li(P) is defined over a hemisphere • Represented using hemispherical harmonics • Li(P) represented by a set of coefficients Basis functions Coefficients Improved Radiance Gradient Computation

19. Radiance Gradients: Problem Definition – Prerequisites • Coefficients computed with Monte Carlo quadrature • Uniform hemisphere sampling • Stratification Sum over all strata Multiplied by thebasis function Incoming radiance from the sampled direction Improved Radiance Gradient Computation

20. Radiance Gradients: Problem Definition • Coefficients – hemisphere sampling • Gradients from the same hemisphere sampling • Something like Improved Radiance Gradient Computation

21. Previous Work - Polygonal emitters • Arvo 1994 • Irradiance Jacobian due to partially occluded polygonal emitters of constant radiosity • Holzschuch and Sillion 1995 • Polygonal emitters of arbitrary radiosity Improved Radiance Gradient Computation

22. Previous Work - Hemisphere sampling • Ward and Heckbert 1992 “Irradiance gradients” • Specifically for irradiance • Cosine-proportional, uniformly weighted samples over the hemisphere • We extend this to uniformly distributed, arbitrarily weighted samples • Křivánek et al. 2005, Annen 2004 • Radiance gradient • Works mostly fine, except when there is occlusion in the sampled environment • We improve quality of this Improved Radiance Gradient Computation

23. Gradient Computation • Compute contribution from each hemisphere cell • Sum it all together Improved Radiance Gradient Computation

24. Gradient Computation for One Cell Improved Radiance Gradient Computation

25. Gradient Computation for One Cell Improved Radiance Gradient Computation

26. Gradient Computation for One Cell • Wall movement => cell area changes • Cell area change => solid angle changes • Solid angle change => incoming radiance changes Improved Radiance Gradient Computation

27. Cell area change Weighting by the basis function Incoming radiance change Putting it all together • Sum incoming radiance changes from all cells • Use the basis functions H as a weighting factor • Basis functions do not change with displacement Improved Radiance Gradient Computation

28. Results Old gradients Improved Radiance Gradient Computation New gradients - smooth

29. Results Old gradients Improved Radiance Gradient Computation New gradients

30. Results Old gradients Improved Radiance Gradient Computation

31. Results New gradients Improved Radiance Gradient Computation

32. P Gradients for GPU-based irradiance and radiance caching • Hemisphere sampling = GPU rasterization • Camera position = hemisphere center • Very non-uniform density of samples over the hemisphere • The same gradient derivation still holds (and WORKS!). Improved Radiance Gradient Computation

33. Gradients for GPU-based irradiance and radiance caching • Irradiance caching video • Offline irradiance caching video • Radiance caching video – castle, walt disney hall Improved Radiance Gradient Computation

34. Conclusion • New translational gradient computation • Use information from hemisphere sampling • Based on the Irradiance Gradients by Ward and Heckbert • Generalized to support • Arbitrary distribution of radiance samples over the hemisphere • Arbitrary weighting of radiance samples Improved Radiance Gradient Computation

35. Thank you ? ? Improved Radiance Gradient Computation