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No. 2731: Autocorrelated Wallpaper

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Autocorrelated Wallpaper

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Permanent URL: https://mezzacotta.net/garfield/?comic=2731

Strip by: Alien@System

{A mostly dark image with a bright central spot, clearly defined central horizontal and vertical lines, some more less clearly defined horizontal lines, and a clear overall periodic structure}

The author writes:

Computer-assisted image interpretation is a difficult field, since getting the computer to "see" isn't easy. One of the simplest and easiest to understand tools is the cross-correlation operation, which allows you to compare two images and see if there's something in one of them that's also in the other.

The way it works is so simple, it could even be done without a computer. To get how good the images "fit", we just multiply every pixel value of one picture with the corresponding pixel value of the other, and then sum them all up. Obviously, the more pixels have similar values, the higher the resulting number will be. We put that number into the pixel (0,0) of our result, and then fill the rest with the result of the above operation after we shift one picture with that vector in regards to the other. So we shift it down one pixel for the pixel (1,0), one to the right for (0,1), and so on. This way, we get a picture the size of our input pictures, which is brighter at spots that correspond to a shift which makes the two pictures overlap nicely.

You can see this in the above picture, which is the cross-correlation of the last frame of the 1981-05-11 comic with itself. If you go and look at the original picture, you'll see that it has a regular pattern to it, from the wallpaper. Scientists call such a pattern periodic, as you can shift it by some fixed lengths and directions, and get the same pattern again. Notice how this ties into the way the cross-correlation works: if we do the cross-correlation of a periodic pattern with itself (also called auto-correlation), we should see bright spots at places which correspond to our pattern periodicity.

And lo and behold, we do. The other spots aren't as bright as the center one (which corresponds to no shift, therefore perfect matching), because our picture isn't perfectly periodic. Not only did Jim Davis draw all those stripes by hand, so that they're not quite copies of each other, we also have the ledge, Garfield's face and his thought bubble, which don't fit in, and therefore reduce the correlation when we shift the picture. Still, a computer could interpret the auto-correlation and arrive at the result that there are periodic components to the picture we've given it.

[[Original strip: 1981-05-11.]]

Original strip: 1981-05-11.