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Author Topic: The Klein Bottle in your eyes  (Read 361 times)
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kram1032
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Posts: 1863


« on: August 30, 2016, 01:44:49 AM »

That title is to be read tongue-in-cheek  smiley

Studying small high-contrast patches of natural images with a technique called "bar codes", it was discovered that these patches neatly fit on a surface that corresponds to a Klein bottle. This can be used in various ways. For instance, it was used to write a (lossy) image compression algorithm that improves a good deal on JPEG and it was applied to texture recognition.

Here a couple papers with lots of illustrations:
BARCODES: THE PERSISTENT TOPOLOGY OF DATA

A Klein-Bottle-Based Dictionary for Texture Representation

On the local behavior of spaces of natural images

The Kleinbottle stuff is interesting because KLEIN BOTTLES but it's also a nice example of how such barcodes, which are applied topology, can be super useful to figure out interesting things about data which you wouldn't ever have noticed otherwise.
Perhaps some of you want to experiment with this, if you have random data sets lying around. - The point of these bar codes is that, if you don't happen to know that your data should fit, say, a line, and if it could be something a lot more complex, then they can give you valuable hints at the true structure.
Nobody would have guessed at this Klein bottle structure if they didn't look at the bar code of the data set.
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