1. 1 Invariant Image Improvement by sRGB Colour Space Sharpening 1 Graham D. Finlayson, 2 Mark S. Drew, and 2 Cheng Lu 1 School of Information Systems, University of East Anglia Norwich (U.K.) graham@cmp.uea.ac.uk 2 School of Computing Science, Simon Fraser University Vancouver (CANADA) {mark,clu}@cs.sfu.ca

2. 2 What is an invariant image? We would like to obtain a greyscale image which removes illuminant effects.

3. 3 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 Region Lit by Sunlight and Sky-light

4. 4 Model of illuminants Illumination is restricted to the Planckian locus represent illuminants by their equivalent Planckian black-body illuminants Wien’s approximation: Most typical illuminants lie on, or close to, the Planckian locus

5. 5 Image Formation Camera responses depend on 3 factors: light (E), surface (S), and sensor (Q)  is Lambertian shading

6. 6 Q 2 ( ) Sensitivity Q 1 ( )Q 3 ( ) = Delta functions “select” single wavelengths: Using Delta-Function Sensitivities

7. 7 For delta-function sensors and Planckian illumination we have: Back to the image formation equation Surface Light

8. 8 Band-ratio chromaticity R G B Plane G=1 Perspective projection onto G=1 Let us define a set of 2D band-ratio chromaticities: p is one of the channels, (Green, say) [or Geometric Mean]

9. 9 Let’s take log’s: Band-ratios remove shading and intensity with Gives a straight line: Shading and intensity are gone.

10. 10 Calibration: find invariant direction Log-ratio chromaticities for 6 surfaces under 14 different Planckian illuminants, HP912 camera Macbeth ColorChecker: 24 patches

11. 11 Deriving the Illumination Invariant This axis is invariant to shading + illuminant intensity/colour

12. 12 Algorithm, cont’d: Form greyscale I’ in log-space: exponentiate: Finlayson et al.,ECCV2002

13. 13 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

14. 14 Problem 2: Nonlinearity We generally have nonlinear image data.  Linearise images prior to invariant image formation Forming invariant image from nonlinear images

15. 15 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 XYZsRGB

16. 16 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.

17. 17 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.

18. 18 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: RGB → sRGB → XYZ → XYZ # SMT

19. 19 One more trick Logarithms of colour ratios in finding the invariant involves a singularity Modify by making use of a generalised logarithm function:

20. 20 Some examples