1. 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

2. Table of Contents Introduction RGB Illumination Invariant
Multispectral Image Formation
Synthetic Multispectral Images
Measured Multispectral Images
Conclusion

3. New  Introduction Invariant Images – RGB:
Information from one pixel, with calibration
Information from all pixels – use entropy
New 
Multispectral data:
Information from one pixel without calibration, but knowledge of narrowband sensors peak wavelengths

4. RGB Illumination Invariant
Removing Shadows from Images, ECCV 2002
Graham Finlayson, Steven Hordley, and Mark Drew 4

5. An example, with delta function sensitivities
RGB…
An example, with delta function sensitivities B W R Y G P
Narrow-band (delta-function sensitivities)
Log-opponent chromaticities for 6 surfaces under 9 lights

6. Deriving the Illuminant Invariant
RGB…
Deriving the Illuminant Invariant
Log-opponent chromaticities for 6 surfaces under 9 lights
Rotate chromaticities
This axis is invariant to illuminant colour

7. An example with real camera data
RGB…
An example with real camera data
Normalized sensitivities of a SONY DXC-930 video camera
Log-opponent chromaticities for 6 surfaces under 9 different lights

8. Deriving the invariant
RGB…
Deriving the invariant
Log-opponent chromaticities
Rotate chromaticities
The invariant axis is now only approximately illuminant invariant (but hopefully good enough)

9. Image Formation Multispectral
Illumination : motivate using theoretical assumptions, then test in practice
Planck’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):

10. Multispectral Image Formation …
To equalize confidence in 31 channels, use a geometric-mean chromaticity:
Geometric Mean Chromaticity: 
with

11. Multispectral Image Formation …
surface-dependent
sensor-dependent
illumination-dependent
So take a log to linearize in (1/T) ! 11

12. Multispectral Image Formation …
Logarithm:
known because, in special case of multispectral,
*know* k !
 Only sensor-unknown is ! ( spectral-channel gains)

13. Multispectral Image Formation …
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: D  30-D
Now 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

14. Algorithm: Form 31-D chromaticity k Take log
Project  to (ek – eM) using projector Pe

15. What’s different from RGB? 
Algorithm:
What’s different from RGB? 
For RGB have to get “lighting-change direction”
(ek – eM) either from
calibration, or
internal evidence (entropy) in the image.
For multispectral, we know (ek – eM) !

16. First, consider synthetic images, for understanding:
Surfaces: 3 spheres, reflectances from Macbeth ColorChecker
Camera: Kodak DSC 420
31 sensor gains qk()
Carry out all in 31-D, but show as camera would see it.

17. Synthetic Images shading, for light 1, for light 2
Under blue light, P10500
Under red light, P2800

18. Synthetic Images
Original: not invariant
Spectral invariant

19. Measured Multispectral Images
Under D75
Under D48
Invt. #1
Invt. #2

20. Measured Multispectral Images
After invt. processing
In-shadow, In-light

21. Measured Multispectral Images

22. Measured Multispectral Images

23. Measured Multispectral Images

24. Next: removing shadows from
Conclusion
A novel method for producing illumination invariant, multispectral image
Successful in removing effects of
Illuminant strength, colour, and shading
Next: removing shadows from
remote-sensing data.

25. Funding: Natural Sciences and Engineering Research Council of Canada
Thanks!
Funding: Natural Sciences and
Engineering Research Council of Canada
Multispectral Images Invariant to Illumination Colour, Strength and Shading