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No. 691: Burrows-Wheeler transformed Garfield II: Pixels

Burrows-Wheeler transformed Garfield II: Pixels

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Strip by: Henning Makholm

{A collection of coloured pixels, with definite patterns, but still a lot of noise}

The author writes:

Here, the bijective Burrows-Wheeler transform that I previously applied to letters in dialogue, instead scrambles the pixels of the comic image.

I started with the 2004-06-16 Garfield strip, and transformed each horizontal row of pixels independently. Then, for good measure, I transformed each vertical column of the result, to give the image shown here. This two-step 2D approach is inspired by how you generalise the Fourier transform from one to two dimensions, but is actually completely pointless for the BWT (because, among other things, BWT is not linear). It does, however, make moderately pretty pictures. Lookit the pretty pictures!

Because the BWT depends on a linear order on the pixel colours in the image, enterprising readers who want to undo the transformation and check my work need to know the comparison function I used. I compare pixels according to their luminance, which for this purpose I take to be 0.21279R' + 0.71507G' + 0.07214B'. These factors are close to the luma coefficients in BT.709, but adjusted slightly such that two different 24-bit colours never have the exact same luminosity, so the comparison is well-defined.