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The very earliest Roman depictions of Jesus show him as clean shaven and young, the classic bearded image we are familiar with never really became established until the 5th or 6th century. However, there are simply no paintings or inscriptions that depict him from the early 1st century so really any visual depiction is spurious. However, the fact that he came from Palestine makes it pretty obvious that he would have had a middle-eastern appearance.
Still, the Shroud image is irrelevant to belief - whether or not it depicts the image of Christ is immaterial as faith doesn't need artifacts to rely on. By it's very nature faith is scientifically irrational.
Personally, I think that the Shroud is a medieval construction and is scientifically fascinating no matter who it depicts. Even if it could ultimately be proven to be first century it doesn't prove a thing about the reality or not of Christian belief. It's an awful tragedy that the Vatican butchered the thing a couple of years ago by cutting great swathes out of the burned areas thus destroying vast amounts of data and committing a great act of vandalism on an iconic artifact.
Let's not also forget that the Shroud, like Hitler, Jack the Ripper or the Knights Templar, is a licence to print money. Each theory and counter theory generates a new and very lucrative book. There is too much money to be made there, thats why all such best-selling pseudo-histories (I'm thinking of you, Graham Hancock) should be treated with extreme scepticism. Codes here, hidden mysteries there, it's easy to be sucked in to the hype. It's better to sit back and question how an author with a six figure book contract can overturn years of painstaking historical research with a new and glamourous theory as the book propels it's way to the top of the best seller list with a Channel 4 series to follow.