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Maybe you'll enjoy Piko and blinry's guide on reading QR codes without a computer: https://qr.blinry.org/

Yeah interesting, but not really any different than the original content. Maybe a little easier to grok.

I was looking for algorithms to extract out a QR code from an image.

Same. I always marvel at how my phone can decode a badly lit, blurry, 1/4 out of frame QR code as quickly as it does.

My first instinct would be to go look at the discrete cosine transform that JPEG uses. But I don't know how to do the other parts like aligning and using the timing patterns.

Yeah, I've been looking for a guide to implementing qr readers from 0. Explicitly not 'oh just plug in this CV library in, feed it the image and it spits out the result' like all the stuff I find in Google on the topic.

I am looking for a guide that walks you through implementing all the algorithms necessary after you have the decoded raw image data.

find a copy of the standard. A version of it is floating online. The latest version just added some clarifications, but is not needed. I built an implementation out of that, though the error correction part, of course, I had to learn somewhere else. But the spec is very readable