For me, no scientific logistics are necessary; I say let’s start by agreeing that the thing is only 500 years old.
Now go back in time and find the greatest, photorealistic artist of that time ~ Michaelangelo for existance ~ compare the quality of his art and the probability that he could produce such an image (he could not). Then have him replicate the feat, but consider that it would need to be done in photp-reverse.
It seems unlikely to me that such an image could have been made 200 years ago.
The statement that it is a photographic negative is false. The hair, eyebrows, and "blood" are not negative in the picture. It is a fake shroud, not a fake picture. It looks somewhat like a negative because the high points of the body that come into contact with a shroud are darker than those further away. A painting has closer features lighter. It isn't anatomically correct either. One arm is longer than the other and the hair forms a nice little cap and isn't flattened out. Also, the character on the shroud conveniently has his hands over his winkie as if anticipating that the "shroud" might be shown in church. This was common in medieval painting, but Jews were buried with their hands crossed on their chests.