Clustered Principal Components for Precomputed Radiance Transfer

1
Clustered Principal Components for Precomputed
Radiance Transfer

• Peter-Pike Sloan
• Microsoft Corporation
• Jesse Hall, John Hart
• UIUC
• John Snyder
• Microsoft Research

2
Demo
3
PRT Terminology
4
PRT Terminology
5
PRT Terminology
6
PRT Terminology
7
PRT as a Linear Operator

• l light vector (in source basis)
• Mp source-to-exit transfer matrix
• ep exit radiance vector (in exit basis)
• y(vp) exit basis evaluated in direction vp
• ep(vp) exit radiance in direction vp

8
PRT Special Case Diffuse Objects
transfer vector rather than matrix
PRT02 SH Xi03 Directional Ng03 Haar Ash
ikhmin02 Steerable

• independent of view (constant exit basis)
• matrix is row vector
• previous work uses different light bases
• image relighting

9
PRT Special Case Surface Light Fields
transfer vector rather than matrix
Miller98 Nishino99 Wood00 Chen02 Matusik0
2

• frozen lighting environment
• matrix is column vector

10
Factoring PRT (BRDFs)

• Tp source ? transferred incident radiance
• Rp rotate to local frame
• B integrate against BRDF Westin92
• y(vp) ep evaluate exit radiance at vp

11
Hemispherical Projection

• exit radiance is defined over hemisphere, not
  sphere
• spherical harmonics not orthogonal over
  hemisphere
• how to project hemispherical functions using SH?
• naïve projection assumes underside is zero
• least squares projection minimizes approximation
  error
• see appendix

12
Factoring PRT (BRDFs)
13
Extending PRT to BSSRDFs

• already handled by original equation
• use Jensen02, only multiple scattering (matrix
  with only 1 row)
• mix with conventional BRDF

14
Problems With PRT

• Big matrices at each surface point
• 25-vectors for diffuse, x3 for spectral
• 25x25-matrices for glossy
• at 50,000 vertices
• Slows glossy rendering (4hz)
• Frozen View/Light can increase performance
• Not as GPU friendly
• Limits diffuse lighting order
• Only very soft shadows

15
Compression Goals

• Decode efficiently
• As much on the GPU as possible
• Render compressed representation directly
• Increase rendering performance
• Make non-diffuse case practical
• Reduce memory consumption
• Not just on disk

16
Compression Example
Surface is curve, signal is normal
17
Compression Example
Signal Space
18
VQ
Cluster normals
19
VQ
Replace samples with cluster mean
20
PCA
Replace samples with mean linear combination
21
CPCA
Compute a linear subspace in each cluster
22
CPCA

• Clusters with low dimensional affine models
• How should clustering be done?
• Static PCA
• VQ, followed by one-time per-cluster PCA
• optimizes for piecewise-constant reconstruction
• Iterative PCA
• PCA in the inner loop, slower to compute
• optimizes for piecewise-affine reconstruction

23
Static vs. Iterative
24
Related Work

• VQPCA Kambhatla94 (static)
• VQPCA Khambhatla97 (iterative)
• Mixture PC Dony95 (iterative)
• More sophisticated models exist
• Brand03, Roweis02
• Mapping to current GPUs is challenging
• Variable storage per vertex
• Partitioning is more difficult (or requires more
  passes)

25
Equal Rendering Cost
VQ
PCA
CPCA
26
Rendering with CPCA
27
Rendering with CPCA
Constant per cluster precompute on the
CPU Rendering is a dot product Compute linear
combination of vectors Only depends on rows of
M
28
Non-Local Viewer

• Assume
• vp constant across object (distant viewer)

Rendering independent of view light orders -
linear combination of colors
29
Rendering
30
Overdraw

• faces belong to 1-3 clusters
• OD 1 ? face drawn once
• OD 2 ? face drawn 2x
• OD 3 ? face drawn 3x
• coherence optimization
• reclassification
• superclustering

31
GPU Dataflow
Vertices
Vertex Shader
PixelShader
32
Demo
33
Results
All examples have 25x25 matrices, 256 clusters,
8 PCA vectors
34
Conclusions

• CPCA
• works in signal space, not surface space
• uses affine subspace per-cluster
• compresses PRT well
• is used directly without blowing out signal
• requires small, uniform state storage
• provides
• faster rendering
• higher-frequency lighting

35
Future Work

• time-dependent and parameterized geometry
• higher-frequency lighting
• combination with bi-scale rendering
• better signal continuity

36
Questions?

• DirectX SDK for PRT available soon.
• Jason Mitchell, Hugues Hoppe, Jason Sandlin,
  David Kirk
• Stanford, MPI for models