Faith alone is all that is required. In addition, it's nice that science has never been able to replicate the shroud image using the most modern of techniques.
I was in northen Italy last Novemeber on business and visited Turin. The church is in the downtown area and was sadly closed. The feelings I had walking by the church was simply awe inspiring.
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.