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Multispectral Image Invariant to Illumination Colour, Strength, and Shading. Mark S. Drew and Amin Yazdani Salekdeh School of Computing Science, Simon Fraser University, Vancouver, BC, Canada {mark/ayazdani}@cs.sfu.ca. Table of Contents. Introduction RGB Illumination Invariant - PowerPoint PPT Presentation
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Mark S. Drew and Amin Yazdani Salekdeh
School of Computing Science,Simon Fraser University,Vancouver, BC, Canada
{mark/ayazdani}@cs.sfu.ca
Multispectral Image Invariant to Illumination Colour, Strength, and
Shading
Table of ContentsIntroductionRGB Illumination InvariantMultispectral Image FormationSynthetic Multispectral ImagesMeasured Multispectral ImagesConclusion
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IntroductionInvariant Images – RGB:
Information from one pixel, with calibrationInformation from all pixels – use entropy
New Multispectral data: Information from one pixel without
calibration, but knowledge of narrowband sensors peak wavelengths
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RGB Illumination Invariant
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Removing Shadows from Images, ECCV 2002Graham Finlayson, Steven Hordley, and Mark Drew
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log(r/g)lo
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An example, with delta function sensitivities
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Wavelength
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B
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PNarrow-band
(delta-function sensitivities)
Log-opponent chromaticities for 6 surfaces under 9 lights
RGB…
Deriving the Illuminant Invariant
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log(r/g)
log
(b/g
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Log-opponent chromaticities for 6 surfaces under 9 lights
This axis is invariant to illuminant colour
Rotate chromaticities
RGB…
Normalized sensitivities of a SONY DXC-930 video
camera
An example with real camera data
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Wavelength
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Log-opponent chromaticities for 6
surfaces under 9 different lights
RGB…
Deriving the invariant
Log-opponent chromaticities
The invariant axis is now only approximately illuminant
invariant (but hopefully good enough)
Rotate chromaticities
RGB…
Image FormationIllumination : motivate using theoretical
assumptions, then test in practicePlanck’s Law in Wien’s approximation:
Lambertian surface S(), shading is , intensity is I
Narrowband sensors qk(), k=1..31, qk()=(-k)
Specular: colour is same as colour of light (dielectric):
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Multispectral
To equalize confidence in 31 channels, use a geometric-mean chromaticity:
Geometric Mean Chromaticity:
with
Multispectral Image Formation …
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{ }
Multispectral Image Formation …
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sensor-dependent
illumination-dependent
surface-dependent
So take a log to linearize in (1/T) !
Logarithm:
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Multispectral Image Formation …
known because, in special case of multispectral, *know* k !
Only sensor-unknown is ! ( spectral-channel gains)
klog
If we could identify at least one specularity, we could recover log k ??
Nope, no pixel is free enough of surface colour .So (without a calibration) we won’t get log k, but
instead it will be the origin in the invariant space.Note: Effect of light intensity and shading removed:
31D 30-DNow let’s remove lighting colour too: we know 31-
vector (ek – eM) (-c2/k - c2/M)
Projection to (ek – eM) removes effect of light, 1/T : 30D 29-D
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Multispectral Image Formation …
Algorithm:
-Form 31-D chromaticity k
- Take log
- Project to (ek – eM) using projector Pe
Algorithm:
What’s different from RGB? For RGB have to get “lighting-change
direction”(ek – eM) either from (i)calibration, or (ii) internal evidence (entropy) in the
image.
For multispectral, we know (ek – eM) !
First, consider synthetic images, for understanding:
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Camera: Kodak DSC 420
31 sensor gains qk()
Surfaces: 3 spheres, reflectances from Macbeth ColorChecker
Carry out all in 31-D, but show as camera would see it.
Synthetic Images
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Under red light, P2800
Under blue light, P10500
shading, for light 1, for light 2
Synthetic Images
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Spectral invariant
Original: not invariant
Measured Multispectral Images
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Under D75 Under D48
Invt. #1 Invt. #2
Measured Multispectral Images
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In-shadow, In-light
After invt. processing
Measured Multispectral Images
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Measured Multispectral Images
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Measured Multispectral Images
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ConclusionA novel method for producing illumination
invariant, multispectral image Successful in removing effects of
Illuminant strength, colour, and shading
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Next: removing shadows from remote-sensing data.
25Multispectral Images Invariant to Illumination Colour, Strength and Shading
Thanks!
Funding: Natural Sciences and Engineering Research Council of Canada
