Multidimensional Lightcuts

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)
DirectIndirect (1.3x)
DirectIndirectVolume (1.8x)
DirectIndirectVolumeMotion (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 ? Sj Mji Gji Vji Ii
( j,i) Î GxL
Visibility term
Material term
Light intensity
Geometric term
Gather strength
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 (Webers 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
Product Graph
L1
L2
L3
L0
Light tree
G1
G0
Gather tree
19
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
G1
G0
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
G1
G0
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 lt perceptual metric

28
Algorithm Summary

• Start with a coarse cut
• Eg, source node of product graph

L6
L1
L2
L3
L4
L5
L0
G0
G2
G1
29
Algorithm Summary

• Choose node with largest error bound refine
• In gather or light tree

L6
L1
L2
L3
L4
L5
L0
G0
G2
G1
30
Algorithm Summary

• Choose node with largest error bound refine
• In gather or light tree

L6
L1
L2
L3
L4
L5
L0
G0
G2
G1
31
Algorithm Summary

• Repeat process

L6
L1
L2
L3
L4
L5
L0
G0
G2
G1
32
Algorithm Summary

• Until all clusters errors lt perceptual metric
• 2 of pixel value (Webers law)

L6
L1
L2
L3
L4
L5
L0
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
Representatives
Light Tree
Gather Tree
L6
L1
L2
G2
G1
G0
L4
L5
G1
G0
L3
L2
L1
L0
G1
G0
L1
L2
L3
L0
L0
L1
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)
51
114,149,280 Pairs per pixel Avg cut size
821 Time 1740 secs
52
Types of Point Lights

• Omni
• Spherical lights
• Oriented
• Area lights, indirect lights
• Directional
• HDR env maps, sunsky