Transcript Efficient Isotropic BRDF Measurement Hanspeter Pfister Wojciech Matusik

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
Efficient Isotropic
BRDF Measurement
Wojciech Matusik
Hanspeter Pfister
[email protected]
[email protected]
Matthew Brand
Leonard McMillan
[email protected]
[email protected]
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Our Goal: Data-Driven
Reflectance Modeling
• Given a set of precise reflectance
measurements from real surfaces is it possible
to interpolate other plausible surface models?
• Bidirectional Reflectance Distribution Function
– Assumes all interaction occurs at a point
– Generally, a 4D function
r
i
i
r
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Our Goal: Data-Driven
Reflectance Modeling
• Given a set of precise reflectance
measurements from real surfaces is it possible
to interpolate other plausible surface models?
• Bidirectional Reflectance Distribution Function
– Assumes all interaction occurs at a point
– Generally, a 4D function
– Isotropic simplification
r
(3D, independent of i)
i
d
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Classical Analytical BRDF
Reflectance models
• Blinn-Torrance-Sparrow (1977)
• Cook-Torrance (1982)
• He-Torrance-Sillion-Greenberg (1991)
• Ward (1992)
• Koenderink-van Doorn-Stavridi (1996)
• Lafortune-Foo-Torrance-Greenberg (1997)
Physically Motivated Era:
Model parameters which “could” be measured
Compact yet Plausible Era:
Models which could be fit to measured data
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BRDF Data Acquisition
• BRDF capture device inspired by Steve
Marschner’s design
• A homogeneous sphere of material
illuminated by a point light source
• Each image contains thousands of BRDF
measurements
• Megapixel+ digital camera
(QImaging Retiga 1300 – 1300 x 1030)
• HDR Images
(18 10-bit exposures from 40 s to 20 s)
• Stable wide spectrum light source
(Hamamatsu SQ Xenon lamp)
• Precision turntable (Kaidan) and
contact digitizer (Faro)
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Data Binning and
Parameterization
• 20-80 million reflectance
measurements per material
• Each BRDF entails
90 x 90 x 360 x 3 “degreesized” measurement bins
• Enforcing reciprocity
Standard
Rusinkiewicz’s
Parameterization Parameterization
• Bilateral symmetry
• Outlier removal to reduce
effects of noise and nonhomogeneity
• Validation
“Real”
“Tabulated”
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BRDF Raw Numbers
• Each Image: 62500 - 250000 BRDF measurements
(projected sphere radii between 200 – 400 pixels w/approx
half in shadow)
• 330 HDR images for light positions covering a 177º arc
(20.625 – 82.5 M measurements)
• Measurements distributed into 3x90x90x180 = 4.374 M bins
• Average bin has ~10 measurements
(~20 with Bilateral symmetry)
• Estimates derived from ~5 to ~10 samples/bin
(with lower and upper quartiles removed)
Resulting Model: 17 MB/BRDF
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Rendering from Tabulated
BRDFs
• Even without further analysis, our BRDFs are
immediately useful.
• Renderings made with Wann Jensen’s Dali
renderer with a custom isotropic BRDF shader.
Nickel
Hematite
Gold Paint
Pink Felt
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IT WAS PAINFUL!!!
• Each ball took over 12
hours
• In 2 years we measured
slightly more than 100
balls
• We repeated the whole
process two times, using
different light sources, and
photometric calibrations
• Can we apply what
we’ve learned thus far to
speed up the process in
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Our Pipedream, In a Nutshell
2. Reduce Model’s Size
(Compression)
1. Measure BRDFs
3. Find Compact Basis
3. Optimize Sampling
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Principle Component Analysis of
BRDFs
• PCA applied across the entire
corpus of acquired BRDFs
• Compact Representation
• PCA Basis Vectors are
non-intuitive
– Global support
– Negative values
– Input sensitive
• More details in upcoming
SIGGRAPH paper “Data-Driven BRDF Modeling”
mean
5
10
20
30
45
60
all
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Wavelet Analysis of BRDFs
• Signal Localization – Typical BRDFs exhibit high frequencies
in only very specific regions of their parameter space
• Wavelets – Spatially compact basis functions of varying scale
• Used before (Schröder & Sweldens, 95) (Lalonde & Fournier,
97)
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Wavelet Analysis of BRDFs
• For a given BRDF, Gi, 97% of the information is in only a few
wavelet coefficients (~50000)
• This gives a set of coefficients Ci
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Wavelet Analysis of BRDFs
• For a given BRDF, Gi, 97% of the information is in only a few
wavelet coefficients (~50000)
• This gives a set of coefficients Ci
• Repeat for all
BRDFs, and compute their union
N
CWB =i=1U Ci (~69000) Common Wavelet Basis
(CWB)
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BRDF Compression
• 69,000 CWB approximately 4.7% the size of the raw data
Gi    jHj
(to better than 3%)
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CWB Representations of BRDFs
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Orange
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Aluminum
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CWB reconstructions on left, dense samples on right
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BRDF Estimation
• In order to optimize sampling we’d like bases
with local support (not necessarily the case with
PCA)
• The problem of approximating a new BRDF
gnew  Hc
4M x 1
BRDF
69K x 1
unknowns
4M x 69K
Large, but relatively sparse,
wavelet basis
thanks to wavelets
(~ 40 non-zero elements on average) functions
We have 4M equations, which do we
use?
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BRDF Equation Selection
• Find a set of 69K equations
(making sure selected rows are linearly
independent)
H g'new  c
1
Large (69K x 69K), but
relatively sparse, thanks to wavelets
(~ 40 non-zero elements/row on average)
• Does not robustly compute wavelet coefficients
from low levels in the tree (remedy described in
paper)
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Sampling Implications of CWB
• We know 69K specific places to measure each BRDF
–
–
–
–
Each “row” is a (h,d,d) specification
Measure and then solve for c
Still needs HDR and averaging to reduce noise
Down from 82M
• To reconstruct BRDF set coefficients not in CWB to zero
and invert wavelet
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BRDFs Reconstructed from CWB
samples
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BRDFs based on 69K samples on left, dense samples on right
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Pull-Push Reconstruction of
BRDFs
• Alternatively, use Pull-Push to reconstruct
(Gortler, et al 96)
• Treat as scattered data interpolation problem
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Push-Pull Reconstructions
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Linear Combinations of BRDFs
(LCB)
• Can we find a linear combination of our existing
BRDFs that match any new one?
• Our PCA analysis tells us we can do this
• It is even more compact (100 coeff/BRDF vs.
65K)
 1
 2
 3
 5
 6

 4
  N
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Finding a Linear Combination of
BRDFs
• Set up the following linear system
bnew  Pa
4M x 1
BRDF
100 x 1
unknowns
4M x 100
BRDFs
• Each column of P is a BRDF
• Each row of P is a (h,d,d) BRDF
measurement
• Once again more equations than unknowns
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LCB Solution Method
• Randomly select a set of N equations, X
• Find the ratio of the largest and smallest
eigenvalues of XTX (N x N SVD)
• Randomly replace one row in X with an unused
row from P
• Find ratio of the largest and smallest
eigenvalues of new XTX, if smaller accept new
row, else reject
• Repeat process until the set becomes stable
• Try for various values of N
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Linear Combinations of BRDFs
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Gold
paint
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Orange
plastic
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Aluminum
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2.5%
BRDFs based on 800 samples
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Advantages and Disadvantages
of Methods
• CWB and Push-Pull require 69K
measurements, but they don’t require our BRDF
database for reconstruction
• Linear Combination of BRDFs requires fewer
overall measurements (800), but it relies on the
availability of our BRDF database
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Conclusions & Future Work
• Presented 2 novel methods for representing
and sampling BRDFs
• We’ve built a system for the rapid and accurate
acquisition of BRDFs, in theory
• Better wavelets, Anisotropic BRDFs
• Not all linear combinations of BRDFs are valid
• Not all convex combinations of BRDFs are valid
• What combinations are valid?
• Intuitive linear parameters for BRDF design
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Acknowledgements
• Henrik Wann Jensen for assistance with Dali
• Paul Lalonde for his wavelet shader
• Paul Debevec for his environment maps
• Markus Gross, Steven Gortler for their helpful
insights
Thank you!
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