Calimero000 said:
How well does this algorithm cope with JPEG compression? I would assume that re-compressing an image would mess up the outcome of the fourier transform. Or the artefacts introduced by the watermark would have to be much more noticable than the artefacts introduced by the JPEG compression.

Proportional to resolution. More resolution means, in effect, that the same data is spread (semi-redundantly) over more pixels. If you were to, say, save a JPG with quality 30, that might well nuke most of it (with the obvious downside that you've also nuked a lot of what was actually attractive about the image.). Most image editing programs aren't silly enough to select that kind of quality by default, though - my guess at the average setting would be 75 quality, which it should stand up to unless the image is very small (<400x300).

There is no 'simple' answer because the strength of JPGification itself depends on the image resolution. Saving a high res JPG with quality 30 is less damaging to the integrity of the picture[1] than saving a medium res JPG with quality 30.

[1] not just the watermarking, the picture in general.

To be specific, any damage would mean that the watermark would become more faint; this is not the kind of thing where specific individual pixels are crucial to the integrity of the watermark. You have to damage a good number of pixels before there is any risk.

EDIT: The strongest attack against fourier watermarking is probably heavily denoising the image. Supposing someone wanted to rip a section of an image out and use it as an avatar; they could take a high resolution image, crop it, denoise it, sharpen it a bit, and then shrink it by 2x or more. The denoising step introduces blurriness/smudginess, sharpening and shrinking reduce the apparent strength of this blurring.