Transcript
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 Vision
artificial illuminant
natural illuminant
cone sensitivity functions
The cone response triple is the same for both illuminants.
9.1
8.8
7.2
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
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
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
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
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
Image IPs can also be expressed in the Frequency Domain
T
T
Dot product
spatialdomain
frequencydomain
Gram Matrix Scale-Space
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
How good is the approximation?
≈
• 1.0% error for images with flat spectra
• 0.1% error for ‘natural’ images with 1/f spectra.
fuzzy window
frosted glass
Approximately equal ‘views from the inside’
Simple cell assembly
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!
+2+2 +1
+1
+1
+1
Metamerism? What metamerism?
Thank you for your attention
fuzzy window
frosted glass
Approximately equal ‘views from the inside’
Simple cell assembly
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