Sparsely Precomputing the Light Transport
Matrix for Real Time Rendering
Fu-Chung Huang
Ravi Ramamoorthi
University of California, Berkeley
Precomputed Radiance Transfer (PRT)
[Sloan et al. 02] [Ng et al. 03, 04] [Liu et al. 04] [Wang et al. 04]
Precomputation Time: 13 hours 22 mins
The Problem
 Reflectance equation
 Separable
 Dynamic lighting
 Static geometry
Lighting
Visibility
BRDF
Ng et al. 04
Limited to
static scene
B ( x, ) 


L ( x ,  i )  VT ( x ,  i )  f r ( x ,  ,  r )  cos  i d  i
Storage and Time
 Matrix T ( x ,  i )
 50K vert. (rows)
 24K directions
(cols)
 1.2B Rays
Wavelet +
Quantization
 Compression
 10x to 50x
 Precomputation time
is not reduced!
Clustered
PCA
Precomputation Time
 Buddha Scene
 5x speed up in precomputation
Sparse Sampling
Full Sampling
2 hours 36 mins
13 hours 22 mins
Precomputation Time
 Bunny Scene
 4x speed up precomputation
Sparse Sampling
Full Sampling
3 hours 25mins
13 hours 8 mins
Outline
 Motivation / Introduction
 Related Work
 Algorithm
 Results
 Conclusion / Future Work
Related Work
 Precomputation based rendering
 [Nimeroff et al. 94] [Dorsey et al. 95]
 Focus only on added functionality
[Sloan et al. 02,03]
Low frequency shadows
CPCA compression
[Ng et al. 03,04]
High frequency shadows
Triple product integral
[Wang et al. 04,06]
Glossy materials
Related Work
 Compressive sensing
 [Candes et al. 06] [Candes and Tao 06]
 Sampling Rate = k logN for k-sparse signal
 Not applicable to PRT
 No random pattern sampling in virtual scene
 Must sample one ray at a time
[Peers et al. 09]
[Sen and Darabi. 09]
Related Work
 Row-column sampling
 Column selection is fixed across all rows
A
C
[Hasan et al. 07]
R
B = CA+R
[Wang et al. 09]
Related Work
 Hierarchical and Sparse Sampling




[Kontkanen et al. 06]
[Hasan et al. 07]
[Lehtinen et al. 08]
[Krivanek and Gautron 09]
 Adaptive Methods
 [Guo 98]
 [Krivanek et al. 04]
[Krivanek
[Krivanek
andetGautron
al. 04] 09]
Outline
 Motivation / Introduction
 Related Work
 Algorithm
 Results
 Conclusion / Future Work
Algorithm Outline
 Overview
 Dense Vertex Sampling
 Sparse Vertex Sampling
 Integrating Clustered PCA
Overview - 2 Phase Sampling
 Dense vertex
 Spatial: 20%~25%
Angular: ~30%
 Sparse vertex
 Spatial: 75%~80%
Angular: 5%~7%
Overview - 2 Phase Sampling
 Row-column sense
Angular: ~30%
Dense Vertex
Spatial:
20%~25%
=6%~7%
Sparse Vertex
Spatial:
75%~80%
=4%~5%
Angular: 5%~7%
Algorithm Outline
 Overview
 Dense Vertex Sampling
 Where?
 How?
 What?
 Sparse Vertex Sampling
 Integrating Clustered PCA
Dense Vertex Distribution
 Observation from CPCA
 Non-uniform cluster sizes
 Large cluster: low rank
 Small cluster: high rank
 Non-uniform sampling
 But how?
Dense Vertex Spatial Sampling
 Sampling by exploration
 1st iteration
High rank area
 Uniform
 Local rank -> probability
 2nd iteration
 Local rank -> probability
 And so on….
 Zoom-Up
rd
th
st iteration]
[2
[3
[4
[1nd
Dense Adaptive Angular Sampling
 1st pass: regularly
 2nd pass: adaptively

If values are
inconsistent
 50%-70% savings
Algorithm Outline
 Overview
 Dense Vertex Sampling
 Sparse Vertex Sampling
 Angular Sampling
 Local Reconstruction
 Integrating Clustered PCA
Sparse Vertex Angular Sampling
 Remember in overview…
 The sparse set of important
angular features
The
Union
Variances
lightoftransport
these
of neighboring
features,
from
its
Weighted
Neighboring
selection,
angular
5%~7%
features
neighboring
but
angular
too many
features
dense vertices
Sparse Vertex Reconstruction
Reconstructed
light transport
?


i

i
Sampled directions as constraints
s .t .


i
i


Sparse Vertex Reconstruction
 How many neighbors?
 In reality
 L1 sparse solver
 [Kim et al. 07]
 No exact radius needed
Algorithm Outline
 Overview
 Dense Vertex Sampling
 Sparse Vertex Sampling
 Integrating Clustered PCA
Clustered PCA
 Incrementally adding
bases
1. for each PCA basis
for each LBG iteration
 [Sloan et al. 03]
 Avoid local minimum
run clustering on
*dense*
vertices
*all*
vertices
end for
 Linear combination
assumption!
end for
2. Assign sparse vertex
to nearest cluster
3. Run inner loop for all vertices
Outline
 Motivation / Introduction
 Related Work
 Algorithm
 Results
 Error analysis
 Performance
 Conclusion / Future Work
Analysis: Angular Sampling
Adaptive sampling
[Ours]
Sampling important
directions
Non-adaptive angular sampling
[Wang et al. 09]
[Hasan et al. 07]
A lot of directional samples are wasted
Analysis: L2 Error for Bunny
 35K + 29K vertices
 Scanned
 High error at seams
Analysis: L2 Error for Horse
 8.5K + 29K vertices
 Low resolution
 Man made
Performance
 Precomputation time only
 Rendering is real-time with the same quality
Model
CPCA
Full New Sparse
CPCA Sampling
Sampling
CPCASampling
Speed Up Rate
Speed Up
Horse
52m
12.6x
4h 2m 4m 54m
~11%
4.47x
Dancer
45m
12.6x
5h 40m3m 1h 15m
~11%
4.77x
Bunny
81m
12.8x
13h 8m6m 3h 26m
~11%
3.83x
Performance for Glossy Objects
 In-Out Factorization for glossy BRDFs
 [Liu et al. 04] [Wang et al. 04]
Model
Size
Full
Sampling
Sparse
Sampling
Sampling
Rate
Speed Up
Armadillo
55K
10h 7m
2h 17m
11.43%
4.75x
Buddha
55K
13h 22m
2h 36m
11.11%
5.12x
Dragon
55K
10h 31m
2h 1m
11.16%
5.22x
Bench
50K
7h 7m
1h 56m
18.54%
3.67x
Precomputation Time
 Bench Scene
 3.6x speed up in precomputation
Sparse Sampling
Full Sampling
1 hours 56mins
7 hours 7 mins
Detailed Timing
Conclusion
 PRT research on real-time functionality
 Precomputation is often the bottleneck
 Adaptive and sparse sampling
 Exploit both spatial and angular coherence
 Accelerated Clustered PCA compression
 Sparse precomputation possible
 5x speed-up
 12x speed-up computing CPCA
Future Work
 GPU acceleration
 Interactive precomputation
 New capabilities
 Rapid prototyping
 Lighting design
 Dynamic scenes
 General theory of sparse sampling
 Avoid heuristic parameter tuning
 Broader context
 Appearance acquisition
 Offline rendering
The End
 Acknowledgements








Ryan S. Overbeck
Anonymous reviewers
NSF CAREER Grant IIS-0924968
ONR PECASE N0001409-1-0741
Intel
NVIDIA
Adobe
Pixar