My true feelings are that the Shroud is most unlikely to be authentic. "Most unlikely" could change to "somewhat possible" if reliable carbon-14 testing showed appropriate dating. But there is no possible scientific way to "prove" the Shroud image is Jesus. For one, a reliable chain of custody is not there, and neither do we have a scientific explanation of how the image may have formed.
Any scholar will tell you there is only so much -- and that is not very much -- which we can possibly know historically about 1st century Judea in general and Jesus in specific. And many have spent their careers trying to tease out whatever data various records may offer.
I think these scholars are sincere and very serious minded, but their image of Jesus far far more closely resembles the one on the right than the left:
