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  1. Multidimensional Lightcuts Bruce WalterAdam ArbreeKavita BalaDonald P. Greenberg Program of Computer Graphics, Cornell University

  2. Problem • Simulate complex, expensive phenomena • Complex illumination • Anti-aliasing • Motion blur • Participating media • Depth of field

  3. Problem • Simulate complex, expensive phenomena • Complex illumination • Anti-aliasing • Motion blur • Participating media • Depth of field

  4. Problem • Simulate complex, expensive phenomena • Complex illumination • Anti-aliasing • Motion blur • Participating media • Depth of field

  5. Problem • Complex integrals over multiple dimensions • Requires many samples camera

  6. Multidimensional Lightcuts • New unified rendering solution • Solves all integrals simultaneously • Accurate • Scalable

  7. Related Work • Motion blur • Separable [eg, Korein & Badler 83, Catmull 84, Cook 87, Sung 02] • Qualitative [eg, Max & Lerner 85, Wloka & Zeleznik 96, Myszkowski et al. 00, Tawara et al. 04] • Surveys [Sung et al. 02, Damez et al. 03] • Volumetric • Approximate [eg, Premoze et al. 04, Sun et al. 05] • Survey [Cerezo et al. 05] • Monte Carlo • Photon mapping [Jensen & Christensen 98, Cammarano & Jensen 02] • Bidirectional [Lafortune & Willems 93, Bekaert et al. 02, Havran et al. 03] • Metropolis [Veach & Guibas 97, Pauly et al. 00, Cline et al. 05]

  8. Related Work • Lightcuts (SIGGRAPH 2005) • Scalable solution forcomplex illumination • Area lights • Sun/sky • HDR env maps • Indirect illumination • Millions of lights ®†hundreds of shadow rays • But only illumination at a single point

  9. Insight • Holistic approach • Solve the complete pixel integral • Rather than solving each integral individually

  10. Direct only (relative cost 1x) Direct+Indirect (1.3x) Direct+Indirect+Volume (1.8x) Direct+Indirect+Volume+Motion (2.2x)

  11. Point Sets • Discretize full integral into 2 point sets • Light points (L) • Gather points (G) Light points Camera

  12. Point Sets • Discretize full integral into 2 point sets • Light points (L) • Gather points (G) Light points Camera

  13. Point Sets • Discretize full integral into 2 point sets • Light points (L) • Gather points (G) Light points Pixel Camera Gather points

  14. Point Sets • Discretize full integral into 2 point sets • Light points (L) • Gather points (G) Light points Gather points

  15. Discrete Equation • Sum over all pairs of gather and light points • Can be billions of pairs per pixel  Pixel=  SjMji GjiVjiIi (j,i)ÎGxL Visibility term Material term Light intensity Gather strength Geometric term

  16. Key Concepts • Unified representation • Pairs of gather and light points • Hierarchy of clusters • The product graph • Adaptive partitioning (cut) • Cluster approximation • Cluster error bounds • Perceptual metric (Weber’s law)

  17. Product Graph • Explicit hierarchy would be too expensive • Up to billions of pairs per pixel • Use implicit hierarchy • Cartesian product of two trees (gather & light)

  18. L6 L4 L5 L2 L0 L1 L3 G2 G0 G1 Product Graph L1 L2 L3 L0 Light tree G1 G0 Gather tree

  19. L6 L4 L5 L2 L0 L1 L3 G2 G0 G1 Product Graph Product Graph G0 = Light tree G2 X G1 L0 L4 L1 L6 L2 L5 L3 Gather tree

  20. Product Graph L6 Product Graph L4 L5 G0 L2 L0 L1 L3 = Light tree G2 X G1 G2 L0 L4 L1 L6 L2 L5 L3 G0 G1 Gather tree

  21. Product Graph Product Graph G0 G2 G1 L0 L4 L1 L6 L2 L5 L3

  22. Product Graph Product Graph G0 G2 G1 L0 L4 L1 L6 L2 L5 L3

  23. Product Graph L6 Product Graph L4 L5 G0 L2 L0 L1 L3 = Light tree G2 X G1 G2 L0 L4 L1 L6 L2 L5 L3 G0 G1 Gather tree

  24. Cluster Representatives

  25. Cluster Representatives

  26. Error Bounds • Collapse cluster-cluster interactions to point-cluster • Minkowski sums • Reuse boundsfrom Lightcuts • Compute maximum over multiple BRDFs • Rasterize into cube-maps • More details in the paper

  27. Algorithm Summary • Once per image • Create lights and light tree • For each pixel • Create gather points and gather tree for pixel • Adaptively refine clusters in product graph until all cluster errors < perceptual metric

  28. Algorithm Summary • Start with a coarse cut • Eg, source node of product graph L0 L4 L1 L6 L2 L5 L3 G0 G2 G1

  29. Algorithm Summary • Choose node with largest error bound & refine • In gather or light tree L0 L4 L1 L6 L2 L5 L3 G0 G2 G1

  30. Algorithm Summary • Choose node with largest error bound & refine • In gather or light tree L0 L4 L1 L6 L2 L5 L3 G0 G2 G1

  31. Algorithm Summary • Repeat process L0 L4 L1 L6 L2 L5 L3 G0 G2 G1

  32. Algorithm Summary • Until all clusters errors < perceptual metric • 2% of pixel value (Weber’s law) L0 L4 L1 L6 L2 L5 L3 G0 G2 G1

  33. Results • Limitations • Some types of paths not included • Eg, caustics • Prototype only supports diffuse, Phong, and Ward materials and isotropic media

  34. Roulette 7,047,430 Pairs per pixel Time 590 secs Avg cut size 174 (0.002%)

  35. Roulette

  36. Scalability

  37. Scalability

  38. Metropolis Comparison Zoomed insets Metropolis Time 148min (15x) Visible noise 5% brighter (caustics etc.) Our result Time 9.8min

  39. Kitchen 5,518,900 Pairs per pixel Time 705 secs Avg cut size 936 (0.017%)

  40. Kitchen

  41. Tableau

  42. Temple

  43. Conclusions • New rendering algorithm • Unified handling of complex effects • Motion blur, participating media, depth of field etc. • Product graph • Implicit hierarchy over billions of pairs • Scalable & accurate

  44. Future Work • Other types of paths • Caustics, etc. • Bounds for more functions • More materials and media types • Better perceptual metrics • Adaptive point generation

  45. Acknowledgements • National Science Foundation grants ACI-0205438 and CCF-0539996 • Intel corporation for support and equipment • The modelers • Kitchen: Jeremiah Fairbanks • Temple: Veronica Sundstedt, Patrick Ledda, and the graphics group at University of Bristol • Stanford and Georgia Tech for Buddha and Horse geometry

  46. The End • Questions?

  47. Multidimensional Lightcuts Bruce WalterAdam ArbreeKavita BalaDonald P. Greenberg Program of Computer Graphics, Cornell University

  48. L3 Representatives Light Tree Gather Tree L6 L1 L2 G2 G1 G0 L4 L5 G0 G1 L1 L3 L0 L2 G1 G0 L2 L1 L3 L0 L1 L0 L2 Exists at first or second time instant.

  49. Lightcuts key concepts • Unified representation • Convert all lights to points • Hierarchy of clusters • The light tree • Adaptive cut • Partitions lights into clusters Lights Light Tree Cut

  50. 180 Gather points X 13,000 Lights = 234,000 Pairs per pixel Avg cut size 447 (0.19%)