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Metamerism? What metamerism? Lewis D Griffin Computer Science, University College London
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Page 1: Metamerism? what metamerism?

Metamerism? What metamerism?

Lewis D Griffin

Computer Science,

University College London

Page 2: Metamerism? what metamerism?

http://www.onlandscape.co.uk/2012/02/the-myth-of-universal-colour/#/

Metamerism in Colour Vision

artificial illuminant

natural illuminant

cone sensitivity functions

The cone response triple is the same for both illuminants.

9.1

8.8

7.2

Page 3: Metamerism? what metamerism?

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 jetDerivatives-of-Gaussians area good model of V1 simple cells

Page 4: Metamerism? what metamerism?

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

J2,3 J7 J12,2,7……symmetry groups

Page 5: Metamerism? what metamerism?

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

2.4

0.7

2.1

1.3

Inner Product

6.3

Page 6: Metamerism? what metamerism?

0 0

T

1 1 0 0 1 1 2 2

2 2

1 0 0

, : 0 1 0

0 0 1

j k

j k j k j k j k j k j k

j k

There is an infinity of possible Inner Products on jets…

The dot product

Gram Matrix based

3

T 3

3 5

9 0 6

, 0 30 0

6 0 12

j k j k

The scale-space Inner Product

T 2

4

2 0 0

, 0 2 0

0 0

j k j k …but this one is best

Page 7: Metamerism? what metamerism?

A Jet Space IP induces an Image IP

T

1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1

j k

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

Page 8: Metamerism? what metamerism?

Image IPs can also be expressed in the Frequency Domain

T

T

Dot product

spatialdomain

frequencydomain

Gram Matrix Scale-Space

Page 9: Metamerism? what metamerism?

measure imageswith filters to make jets

4 62

0 0 1 1 2 2 3 32 6,j k j k j k j k j k

compare jets using the ‘scale space’ inner product

compare images using this fourier inner product

then =

filter imagesthen

window images compare images using this fourier inner product

=thencompare them

using a standard inner product

Page 10: Metamerism? what metamerism?

How good is the approximation?

• 1.0% error for images with flat spectra

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

Page 11: Metamerism? what metamerism?

fuzzy window

frosted glass

Approximately equal ‘views from the inside’

Simple cell assembly

Page 12: Metamerism? what metamerism?

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……J2,3 J7 J12,2,7……symmetry groups

Filtering has no effect on symmetries!

Page 13: Metamerism? what metamerism?

+2+2 +1

+1

+1

+1

Page 14: Metamerism? what metamerism?

Metamerism? What metamerism?

Thank you for your attention

fuzzy window

frosted glass

Approximately equal ‘views from the inside’

Simple cell assembly