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Metamerism? what metamerism?

Jul 12, 2015

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Metamerism? What metamerism?Lewis D Griffin

Computer Science,University College London

http://www.onlandscape.co.uk/2012/02/the-myth-of-universal-colour/#/Metamerism in Colour Visionartificial illuminantnatural illuminantcone sensitivity functionsThe cone response triple is the same for both illuminants.

2.1-1.20.72.1-0.61.4-3.2-2.80.12.2-3.40.1-0.20.84.5=

.

Metamerism in local Spatial Visiona jetDerivatives-of-Gaussians area good model of V1 simple cells3Why is Metamerism a problem?2.1-1.20.72.1-0.61.4-3.2-2.80.12.2-3.40.1-0.20.84.5=Non-linear feature classifier circuitryedgebarT-junction

.

Q: How should this work, given this?

Metamery ClassJ2,3J7J12,2,7symmetry groupsNeed 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 Product6.3

There is an infinity of possible Inner Products on jetsThe dot productGram Matrix based

The scale-space Inner Product

but this one is bestA Jet Space IP induces an Image IP

TA way to measure how similar jets are, is equivalent to a rule to measure how similar images areDot product

Gram MatrixScale-Space

Image IPs can also be expressed in the Frequency Domain

T

TDot productspatialdomainfrequencydomain

Gram Matrix

Scale-Space

measure imageswith filters to make jets

compare jets using the scale space inner productcompare images using this fourier inner productthen=

filter imagesthen

window imagescompare images using this fourier inner product=thencompare them using a standard inner productHow good is the approximation?

1.0% error for images with flat spectra

0.1% error for natural images with 1/f spectra.

fuzzy windowfrosted glassApproximately equal views from the insideSimple cell assembly2.1-1.20.72.1-0.61.4-3.2-2.80.12.2-3.40.1-0.20.84.5=

.Non-linear feature classifier circuitryedgebarT-junctionJ2,3J7J12,2,7symmetry groups

Filtering has no effect on symmetries!

+2+2+1+1+1+1

Metamerism? What metamerism?

Thank you for your attention

fuzzy windowfrosted glassApproximately equal views from the insideSimple cell assembly

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