8/6/2019 Talk Gatech Lighting 2001
1/22
Linear Color Representation for Full
Spectral Rendering
Mark Peercy
Presented by Weidong Shi, 2001
8/6/2019 Talk Gatech Lighting 2001
2/22
Overview
Use full color distribution, not tri-stimulus RBG.
Decompose color distribution into a linear space of basisfunctions.
Represent color distribution as a coefficient vector.
Model surface reflectance as matrices.
Convert results into tri-stimulus RGB.
Find optimal set of basis functions.
8/6/2019 Talk Gatech Lighting 2001
3/22
Why Full Spectral Information?
Non-uniform spectral distribution. Photo-realisticrendering needs more samples of wavelengths than tri-
stimulus.
8/6/2019 Talk Gatech Lighting 2001
4/22
Existing Methods of Handling Full Spectrum
Point sampling.
- Sample surfaces and lights at certain number of
wavelengths.
- Numerically integration into RGB required for display.
Polynomial representation of light.
Linear models of surfaces and light.
8/6/2019 Talk Gatech Lighting 2001
5/22
Point Sampling
wavelength
Spectral powerS3 SnS1 S2
i
N
i
iSRRd
1
i
N
i
iSGGrn
1
i
N
i
iSBBl
1
)(I
8/6/2019 Talk Gatech Lighting 2001
6/22
Basis Function and Linear Representation
Orthonomal basis functions, a set of functionsf1(x),f2(x),
Given a function g(x), compute coefficient by,
g(x) is approximated by a vector of m-length.
dxxfxfx
ji )()(0
dxxfxfx
ii )()(1
dxxfxgx ii )()(
m
i
ii xfxg1
)()(
For any fi(x)
For any two different functions fi(x)andfj(x)
orthogonal
normal
8/6/2019 Talk Gatech Lighting 2001
7/22
Linear Representation of Power Distribution
Describe spectral power distribution of light as a
linear combination of m orthonormal basis
functions
dEIii )()(
m
i
iiEI1
)()(
E1
E2
E3
m
i
iiE
1
)(
8/6/2019 Talk Gatech Lighting 2001
8/22
Surface Reflectance
Lighting Model
)()()()()()()()(),(
ssssddaao IRGIRGIRI
)(s
I
)()()( sddIRG
)()()( sss IRG
reflected light as
a function of wavelength
and surface geometry
ambient light
input lightBRDF diffuse terms
BRDF specular terms
8/6/2019 Talk Gatech Lighting 2001
9/22
Surface Reflectance- cont
Represent ambient light, directional light, and reflected
light as coefficient vectors.
a
m
a
1
s
m
s
1
om
o
1
),( oI)(sI)(aI
ambient light light source reflected light
= = =
8/6/2019 Talk Gatech Lighting 2001
10/22
Surface Reflectance - cont
Through math deduction, surface reflectance can
be represented by m*m matrices
)(aR )()( dd RG )()( ss RG
aR11
dR11
sR11
)(d
G )(sG
dEERR jidd
ij )()()( dEERR jis
s
ij )()()( dEERRjia
a
ij )()()(
surface ambient property surface diffuse property surface specular property
)()()()()()()()(),( ssssddaao IRGIRGIRI
8/6/2019 Talk Gatech Lighting 2001
11/22
Surface Reflectance - cont
New lighting equation
a
m
a
1
aR11
dR11
s
m
s
1
)(d
G
sR11
s
m
s
1
)(sG
o
m
o
1
= +
+
ambient termdiffuse term
specular term
)()()()()()()()(),( ssssddaao IRGIRGIRI
output light ambient light
light source
light source
8/6/2019 Talk Gatech Lighting 2001
12/22
Light Distribution at Each Pixel
The next step is to convert it into RGB.
m
i
i
p
ip EI1
)()(
p
m
p
1
Lights arrive at each pixel is also represented as a m-lengthvector
8/6/2019 Talk Gatech Lighting 2001
13/22
8/6/2019 Talk Gatech Lighting 2001
14/22
Convert Light at Each Pixel to RGB
dExdIxXi
m
i
p
ip
)()()()(1
dEydIyY i
m
i
p
ip )()()()(1
dEzdIzZ i
m
i
p
ip )()()()(1
Integrate lights at each pixel (m-length vector) over three
color matching functions X,Y, and Z.
8/6/2019 Talk Gatech Lighting 2001
15/22
Selection of Basis Function
Consider computation complexity
Nature of the spectral power distribution in the
scene. Point sampling is sufficient if powerdistribution is smooth.
8/6/2019 Talk Gatech Lighting 2001
16/22
8/6/2019 Talk Gatech Lighting 2001
17/22
Method2 - Character Vector Analysis (CVA)
Given a representative set of spectral distributionsin a scene (I1(), I2(), ), find m basis function
automatically
The set of basis functions minimizes
The representative set of lights may contain light sources,
once-reflected light, and multi-reflected light
dEIErrl
m
i
ilil
2
1
,)()(
8/6/2019 Talk Gatech Lighting 2001
18/22
Examples
Scene under fluoresecnt light, CVA on light source, first
order, and second order surface reflectance from four
sample of the surface
8/6/2019 Talk Gatech Lighting 2001
19/22
Examples - Result basis functions
8/6/2019 Talk Gatech Lighting 2001
20/22
Rendering Result
2 3 4 5
4 9 16 25
8/6/2019 Talk Gatech Lighting 2001
21/22
Summary of Rendering Procedure
Determine Basis Functions
Represent Lights as Coefficient Vector
Represent Surface Reflectance as Matrices
Render
Convert Results at Each Pixel into XYZ
Convert XYZ into RGB
8/6/2019 Talk Gatech Lighting 2001
22/22
Conclusion
Provide a general efficient way of full spectral color
rendering
Represent color distribution by linear combination of basis
functions
Capture surface reflectance by matrices
Linear lighting equation
Better photo-realistic rendering result
Easy to implement
Top Related