Invariant Image Improvement by sRGB Colour Space Sharpening

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Invariant Image Improvement by sRGB Colour Space
Sharpening

• 1Graham D. Finlayson, 2Mark S. Drew, and 2Cheng
  Lu
• 1School of Information Systems, University of
  East Anglia
• Norwich (U.K.) graham_at_cmp.uea.ac.uk
• 2School of Computing Science, Simon Fraser
  University
• Vancouver (CANADA) mark,clu_at_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 Sunlight and Sky-light
Region Lit by Sky-light only
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Model of illuminants

• Illumination is restricted to the Planckian locus
• represent illuminants by their equivalent
  Planckian black-body illuminants
• Wiens approximation

Most typical illuminants lie on, or close to, the
Planckian locus
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Image Formation
Camera responses depend on 3 factors light (E),
surface (S), and sensor (Q)
? is Lambertian shading
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Using Delta-Function Sensitivities
Q2(l)
Q1(l)
Q3(l)

Sensitivity
l
Delta functions select single wavelengths
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Back to the image formation equation
For delta-function sensors and Planckian
illumination we have
Surface
Light
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Band-ratio chromaticity
Let us define a set of 2D band-ratio
chromaticities
p is one of the channels, (Green, say) or
Geometric Mean
Perspective projection onto G1
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Band-ratios remove shading and intensity
Lets take logs
Shading and intensity are gone.
Gives a straight line
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Calibration find invariant direction
Macbeth ColorChecker 24 patches
Log-ratio chromaticities for 6 surfaces under 14
different Planckian illuminants, HP912 camera
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Deriving the Illumination Invariant
This axis is invariant to shading illuminant
intensity/colour
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Algorithm, contd
Form greyscale I in log-space
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 conversion

• Two 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.

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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.

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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

XYZ
?
?
?
RGB
sRGB
XYZ
S
M
T
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One more trick

• Logarithms of colour ratios in finding the
  invariant involves a singularity
• Modify by making use of a generalised logarithm
  function

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Some examples