If the same watermark is added to each image, then you can estimate the watermark by averaging many images and subtract it to get original image back.

If each image has a slightly different watermark, then simple averaging won't work. Instead you need to come up with a model that describes how the watermark is changing, then estimate parameters of that model. The more complex the change, the more images you need for parameter estimation.

Image stabilization won't work here because it relies on large features and therefore won't be sensitive to relatively weak watermark signal. Besides, it's only stabilizing in three dimensions (pitch, roll, yaw) and won't help with warping within the image.

Averaging will still provide the average watermark given a large enough sample set. Which is then a single geometric transformation from the used watermark. Estimating that transformation for a specific image should be fairly straightforward as they could easily reverse a watermark that was offset. At which point it's reversible.

Not really, because in each image parts of the watermark will be in different places. You don't even need to warp the watermark to achieve that, it's enough to randomly reposition it.

It has crisp edges. If the same watermark is repositioned it's trivial to figure out the adjustment and remove it. Warping is harder but still largely doable by finding each part of the watermark's exact location.

Supose you have 4 points on a box. If you randomly increase or decrease the location of each point by some random value say +-3% then averaged 100,000 of those boxes, you get a smaller box(1) surrounded by a larger increasingly blurry box. This is true even if no single picture shows that single smaller box, but it will show up on the average.

(1) Rather than a true box the midpoints are going to be slightly buldging, but with a large sample set it's very close to a box.

Sure, you can get into cat and mouse games ever stranger geometry. But, the water mark is limited by how much it distracts from the image.

The article shows the result of this approach, and it clearly does not work well.

As I said you need a new step: "Estimating that transformation for a specific image should be fairly straightforward".

It does show a good average and simply moving the watermark was easily reversible suggesting detection of a watermark in an image was easy.

But wouldn't it require you to find how the target image's particular watermark was warped? None of the other watermarks will have precisely the same warping parameters as that image's watermark. You could attempt to de-warp the watermark in place on the image, but that would seem to be likely to warp the image as well, no?

you could de-warp the watermark in place, and this would warp the image but you could reverse the warp after you're done removing the watermarks.

straightening a plane e.g. a whole video frame, is a bit different from removing a random warp on a watermark (where the warp is more complex than tilting/angling the watermark), while its overlaid with partial visibility on a non-warped image