3 Less Present Natural Patterns, Correlations and Symmetry

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3 Less Present Natural Patterns, Correlations and Symmetry

Postby henriette on October 6th, 2018, 6:30 am 

Dear,

Among the necklaces with 6 beads, "012012", "010101" and "012102" are by far the less present in rings of 6 pixels extracted from whatever measured image of natural scenes (at least 2D data).
I am currently trying to explain this observation.
Image

Remarks :
Neither optics nor electronics (exposure time, sampling, quantization, blurring, etc.) are responsible for this observation.
"000011" appears more often than "001001" : this other observation makes sense because of spatial correlations in natural patterns : similar labels are closer to each other in 000011 than in 001001.
The 3 less present patterns (there are a total of 43 possible unlabeled necklaces of length 6) present symmetries.

Spatial correlations and symmetries seem to be at work behind this observation. Any comment would be welcome.
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Re: 3 Less Present Natural Patterns, Correlations and Symmet

Postby TheVat on October 6th, 2018, 11:17 am 

If you want an image to be visible in the img brackets, you need to make it a jpeg format.

And the whole post may need some clarification. I don't really understand your question here.
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Re: 3 Less Present Natural Patterns, Correlations and Symmet

Postby henriette on October 6th, 2018, 1:04 pm 

Dear Braininvat,

Thank you for the reply.
Let me be clearer. Image are I=I(M,lambda), M the location (pixels) and lambda the color or spectral channels (3 channels only in RGB images, up to thousands channels in spectral imagery)

All rings of 6 contiguous pixels are extracted from the image and reduced to their equivalent unlabeled necklaces (there are only 42 such necklaces).
Reduction of a ring into a necklace follows a rule for labeling measurements : pixels with the same color (spectra) into the ring get the same label.
The density of state of those necklaces (the histogram of the necklaces) systematically yields a minimum for the 3 following necklaces.

The density of states of the necklaces within images depends on a bunch of parameters (optics, electronics)
However, the following 3 necklaces always show the 3 minimum densities .
https://photos.app.goo.gl/FxXbeS2WpqK17eLt6
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