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Multidimensional Lightcuts Bruce Walter Adam Arbree Kavita Bala Donald P. Greenberg Program of Computer Graphics, Cornell University Problem Simulate complex, expensive phenomena Complex illumination Anti-aliasing Motion blur Participating media Depth of field Problem

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Multidimensional Lightcuts

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Multidimensional lightcuts l.jpg

Multidimensional Lightcuts

Bruce WalterAdam ArbreeKavita BalaDonald P. Greenberg

Program of Computer Graphics, Cornell University


Problem l.jpg

Problem

  • Simulate complex, expensive phenomena

    • Complex illumination

    • Anti-aliasing

    • Motion blur

    • Participating media

    • Depth of field


Problem3 l.jpg

Problem

  • Simulate complex, expensive phenomena

    • Complex illumination

    • Anti-aliasing

    • Motion blur

    • Participating media

    • Depth of field


Problem4 l.jpg

Problem

  • Simulate complex, expensive phenomena

    • Complex illumination

    • Anti-aliasing

    • Motion blur

    • Participating media

    • Depth of field


Problem5 l.jpg

Problem

  • Complex integrals over multiple dimensions

    • Requires many samples

camera


Multidimensional lightcuts6 l.jpg

Multidimensional Lightcuts

  • New unified rendering solution

    • Solves all integrals simultaneously

    • Accurate

    • Scalable


Related work l.jpg

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]


Related work8 l.jpg

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


Insight l.jpg

Insight

  • Holistic approach

    • Solve the complete pixel integral

    • Rather than solving each integral individually


Slide10 l.jpg

Direct only (relative cost 1x)

Direct+Indirect (1.3x)

Direct+Indirect+Volume (1.8x)

Direct+Indirect+Volume+Motion (2.2x)


Point sets l.jpg

Point Sets

  • Discretize full integral into 2 point sets

    • Light points (L)

    • Gather points (G)

Light points

Camera


Point sets12 l.jpg

Point Sets

  • Discretize full integral into 2 point sets

    • Light points (L)

    • Gather points (G)

Light points

Camera


Point sets13 l.jpg

Point Sets

  • Discretize full integral into 2 point sets

    • Light points (L)

    • Gather points (G)

Light points

Pixel

Camera

Gather points


Point sets14 l.jpg

Point Sets

  • Discretize full integral into 2 point sets

    • Light points (L)

    • Gather points (G)

Light points

Gather points


Discrete equation l.jpg

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


Key concepts l.jpg

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)


Product graph l.jpg

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)


Product graph18 l.jpg

L6

L4

L5

L2

L0

L1

L3

G2

G0

G1

Product Graph

L1

L2

L3

L0

Light tree

G1

G0

Gather tree


Product graph19 l.jpg

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


Product graph20 l.jpg

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


Product graph21 l.jpg

Product Graph

Product Graph

G0

G2

G1

L0

L4

L1

L6

L2

L5

L3


Product graph22 l.jpg

Product Graph

Product Graph

G0

G2

G1

L0

L4

L1

L6

L2

L5

L3


Product graph23 l.jpg

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


Slide24 l.jpg

Cluster Representatives


Slide25 l.jpg

Cluster Representatives


Error bounds l.jpg

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


Algorithm summary l.jpg

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


Slide28 l.jpg

Algorithm Summary

  • Start with a coarse cut

    • Eg, source node of product graph

L0

L4

L1

L6

L2

L5

L3

G0

G2

G1


Slide29 l.jpg

Algorithm Summary

  • Choose node with largest error bound & refine

    • In gather or light tree

L0

L4

L1

L6

L2

L5

L3

G0

G2

G1


Slide30 l.jpg

Algorithm Summary

  • Choose node with largest error bound & refine

    • In gather or light tree

L0

L4

L1

L6

L2

L5

L3

G0

G2

G1


Slide31 l.jpg

Algorithm Summary

  • Repeat process

L0

L4

L1

L6

L2

L5

L3

G0

G2

G1


Slide32 l.jpg

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


Results l.jpg

Results

  • Limitations

    • Some types of paths not included

      • Eg, caustics

    • Prototype only supports diffuse, Phong, and Ward materials and isotropic media


Roulette l.jpg

Roulette

7,047,430 Pairs per pixel Time 590 secs

Avg cut size 174 (0.002%)


Roulette35 l.jpg

Roulette


Scalability l.jpg

Scalability


Scalability37 l.jpg

Scalability


Metropolis comparison l.jpg

Metropolis Comparison

Zoomed insets

Metropolis

Time 148min (15x)

Visible noise

5% brighter (caustics etc.)

Our result

Time 9.8min


Kitchen l.jpg

Kitchen

5,518,900 Pairs per pixel Time 705 secs

Avg cut size 936 (0.017%)


Kitchen40 l.jpg

Kitchen


Tableau l.jpg

Tableau


Temple l.jpg

Temple


Conclusions l.jpg

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


Future work l.jpg

Future Work

  • Other types of paths

    • Caustics, etc.

  • Bounds for more functions

    • More materials and media types

  • Better perceptual metrics

  • Adaptive point generation


Acknowledgements l.jpg

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


The end l.jpg

The End

  • Questions?


Slide47 l.jpg

Multidimensional Lightcuts

Bruce WalterAdam ArbreeKavita BalaDonald P. Greenberg

Program of Computer Graphics, Cornell University


Slide48 l.jpg

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.


Lightcuts key concepts l.jpg

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


Slide50 l.jpg

180 Gather points X 13,000 Lights = 234,000 Pairs per pixel

Avg cut size 447 (0.19%)


Slide51 l.jpg

114,149,280 Pairs per pixel Avg cut size 821

Time 1740 secs


Types of point lights l.jpg

Types of Point Lights

  • Omni

    • Spherical lights

  • Oriented

    • Area lights, indirect lights

  • Directional

    • HDR env maps, sun&sky


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