Metamerism? what metamerism?

Talk at Christmas 2013 meeting of the AVA in Leuven, Belgium.

1. Metamerism? What metamerism? Lewis D Griffin Computer Science, University College London

2. http://www.onlandscape.co.uk/2012/02/the-myth-of-universal-colour/#/ Metamerism in Colour Vision a rtificial illuminant n atural illuminant c one sensitivity functions The cone response triple is the same for both illuminants.

3. 2.1 -1.2 0.7 2.1 -0.6 1.4 -3.2 -2.8 0.1 2.2 -3.4 0.1 -0.2 0.8 4.5 = . Metamerism in local Spatial Vision a jet Derivatives-of-Gaussians are a good model of V1 simple cells

4. Why is Metamerism a problem? 2.1 -1.2 0.7 2.1 -0.6 1.4 -3.2 -2.8 0.1 2.2 -3.4 0.1 -0.2 0.8 4.5 = Non-linear feature classifier circuitry edge bar T-junction …… . Q: How should this work, given this? Metamery Class J 2,3 J 7 J 12,2,7 …… s ymmetry groups

5. Need to decide when jets are similar. Jet similarity should conform to the linearity of the measurement process. Therefore what is needed is an Inner Product structure. The Beezer 1962 Inner Product 6.3

6. There is an infinity of possible Inner Products on jets… The dot product Gram Matrix based The scale-space Inner Product …but this one is best

7. A Jet Space IP induces an Image IP T A way to measure how similar jets are, is equivalent to a rule to measure how similar images are Dot product Gram Matrix Scale-Space

8. Image IPs can also be expressed in the Frequency Domain T T Dot product spatial domain frequency domain Gram Matrix Scale-Space

9. m easure images with filters to make jets c ompare jets using the ‘scale space’ inner product c ompare images using this fourier inner product then = f ilter images then window images c ompare images using this fourier inner product = then c ompare them using a standard inner product

10. How good is the approximation? ≈ 1.0% error for images with flat spectra 0.1% error for ‘natural’ images with 1/f spectra.

11. f uzzy window f rosted glass Approximately equal ‘views from the inside’ Simple cell assembly

12. 2.1 -1.2 0.7 2.1 -0.6 1.4 -3.2 -2.8 0.1 2.2 -3.4 0.1 -0.2 0.8 4.5 = . Non-linear feature classifier circuitry edge bar T-junction …… J 2,3 J 7 J 12,2,7 …… s ymmetry groups Filtering has no effect on symmetries!

13. + 2 + 2 + 1 + 1 + 1 + 1

14. Metamerism? What metamerism? Thank you for your attention f uzzy window f rosted glass Approximately equal ‘views from the inside’ Simple cell assembly