Thanks for the info. I've been thinking I should do this for awhile. Cane either of these watermarks be removed?
As with most questions, the answer is simple: it depends.
Let's imagine I have 10 pictures, all with the same "trivial" watermark, which has been applied as a translucent square in the lower right hand corner. To apply this watermark, the editor simply "muted" the pixels in the region of the watermark. (e.g. if the pixel had a value of "40", it was turned into a value of "30" instead.) By applying this formula across that part of the picture, the effect was to create that translucent square. (The formula might be to reduce the value by a certain percent (e.g. -25%) or a specific value (-10), with a minimum result of zero (non-negative).)
To remove this watermark, I can do either of two things: first, I can apply that same formula to the rest of the picture, or I can inflate the values in the marked area by the inverse (+10, or +33%). Because there was some loss in applying the watermark (rounding error, or applying the "zero floor"), the recovered image won't be perfect, but it will be pretty close.
Now, a square in the corner of an image is a pretty stupid watermark, and figuring out what pixels need to be "unmarked" to recover the original if the watermark is more complicated (like, say, text) is itself more complicated. But if you have a number of samples, you could find commonalities among the samples and determine a "mask" for the original watermark, and then apply the steps outlined above.
And "greying out" (or applying a translucent watermark) is pretty simple, too, compared to applying a translucent colour logo to that same image. But the principles are the same: instead of (say) applying the same formula to all parts of the pixel, different colours are added (or subtracted) individually for each pixel. Maybe add 10% red, subtract 5% blue, and subtract 8% green for one pixel, and +8, -3, -11 for another pixel. And so on. But again, if the underlying watermark can be discovered (and with enough samples, it should be possible), the inverse formula could be applied with some success.
All of this assumes a translucent watermark, and discusses the losses associated with making it translucent. The more opaque the watermark is, the more loss there is in applying it, and the less successful these methods are in removing it. If a completely opaque watermark is applied, there is nothing left in those pixels when removing it.
But even if there is nothing left in those pixels, all is not lost. Instead, software would be required to "interpolate" the pixels which had surrounded the watermark, creating some sort of "averaging" of the picture to fill in the blanks. It wouldn't be very good with most pictures, but then again it depends on what was under the watermark - on a picture of a sand dune, filling in the missing sand with the surrounding sand would probably be a pretty close approximation.
The question then becomes: how much effort is there in removing the watermark, and how much damage is done if someone does so?
