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Invariant Image Improvement by sRGB Colour Space Sharpening
1Graham D. Finlayson, 2Mark S. Drew, and 2Cheng Lu1School of Information Systems, University of East Anglia
Norwich (U.K.) [email protected] of Computing Science, Simon Fraser University
Vancouver (CANADA) {mark,clu}@cs.sfu.ca
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What is an invariant image?
We would like to obtain a greyscale image which removes illuminant effects.
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Shadows stem from what illumination effects?
Changes of illuminant in both intensity and colour• Intensity – can be removed in chromaticity space
• Colour – ? shadows still exist in the chromaticity image!
Region Lit by Sky-light only
)/(},,{ BGRBGR
Region Lit by Sunlight and
Sky-light
)/(},,{ BGRBGR
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Model of illuminantsIllumination is restricted to the Planckian locus
• represent illuminants by their equivalent Planckian black-body illuminants
Wien’s approximation:
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
r/(r+g+b)
g/(
r+g
+b
)
Illuminant Chromaticities
Most typical illuminants lie on,
or close to, the Planckian locus
T
c
ecIE 2
51)(
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)(S
)(E )()( SE
Image Formation
Camera responses depend on 3 factors: light (E), surface (S),
and sensor (Q) is Lambertian shading
,)()()( dQSE kk
BGRk ,,
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Q2()
Sen s
i tiv
i ty
Q1() Q3()
=
Delta functions “select” single wavelengths:
R R1 qQ
Using Delta-Function Sensitivities
RRRRR SEqdESq
GGqQ 2
BBqQ 3
RRR SEqR
GGG SEqG
BBB SEqB
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For delta-function sensors and Planckian illumination we have:
Back to the image formation equation
T
c
kkkkkecIqS 2
51)(
Surface Light
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Band-ratio chromaticity
R
G
B
Plane G=1
Perspective projection onto G=1
,2..1,/ kpkk
Let us define a set of 2D band-ratio chromaticities:
p is one of the channels,(Green, say) [or Geometric Mean]
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Let’s take log’s:
Band-ratios remove shading and intensity
Teess pkpkkk /)()/log()log('
with ,)(51 kkkk qScs kk ce /2
Gives a straight line:
)(
)())/log(()/log(
1
21
'12
'2
p
ppp ee
eessss
Shading and intensity are gone.
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Calibration: find invariant direction
Log-ratio chromaticities for 6 surfaces under 14 different Planckian
illuminants, HP912 camera
Macbeth ColorChecker:
24 patches
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Deriving the Illumination Invariant
This axis is invariant to shading + illuminant
intensity/colour
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Algorithm, cont’d:
eI k''
Form greyscale I’ in log-space:
)'exp(II exponentiate:
Finlayson et al.,ECCV2002
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Problems in Practice
What if camera sensors are not narrowband?
Find a sensor transform M that sharpens camera sensors
• Equivalent to transforming RGB to a new colour space
Kodak DCS420 camera
sensors
3 x 3
colors
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Problem 2: Nonlinearity We generally have nonlinear image data.
Linearise images prior to invariant image formation
Forming invariant image from nonlinear images
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Approach : solve for sharpened sRGB space
sRGB – standard RGB• Color Management strategy proposed by Microsoft and HP• A device independent color space – small cost for storage
and transfer• Transform CIE tristimulus values so as to suit to current
monitors
XYZ sRGB
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sRGB-to-XYZ conversionTwo steps:
• Nonlinear sRGB to linear RGB – Gamma correction
• Transformation to CIE XYZ tristimulus with a D65 white point
– Using a 3 by 3 matrix M
The problem of nonlinearity• solved ! (well enough)
The problem of non-narrowband sensors • XYZ D65 color matching functions are quite
sharp, but can be sharper.
)(S
)(SM
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Spectral sharpening for XYZ D65
∴ Apply database spectral sharpening • mapping two sets of patch images formed with the camera
under two different lights, with a 3 x 3 matrix P
• For diagonal color constancy, compute eigenvectors T of P
• The sharpened XYZ color matching functions under D65 have narrower curves.
.)( 1 TDdiagTP
5065 DD XYZPXYZ
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Linear sRGB color space sharpening
Concatenating the conversion to the XYZ tristimulus values by the spectral sharpening transform T: a sharpened sRGB space.
Performing the invariant image finding routine in this new sharpened linear color space:
)( TMS
RGB → sRGB → XYZ →XYZ#
S M T
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One more trickLogarithms of colour ratios in finding the invariant involves a singularity
Modify by making use of a generalised logarithm function:
)1()( /1 xxg
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Some examples