Today the Orthodox Church observes the feast of the "Acheiropoietos" Icon -- the Icon not made by hands. In Constantinople, prior to the sack of that city by the Crusaders, there was a folded cloth bearing a mysterious, dim image of the Lord's face. This folded cloth, which had for centuries been venerated in Edessa, was brought to the Imperial capital at the end of the first millenium. Since the image was obviously not painted, it was believed it must have been made by direct contact with Christ. Hence all paintings of Christ were based on it.
The Crusaders apparently took the cloth, which when unfolded dimly showed the whole body, front and back, to France. Now it is in Turin, and is venerated as the Lord's burial shroud.
That is why, from early on, icons of Our Lord (such as the 6th century encaustic icon at Mount Sinai pictured here) resemble the face in the Shroud of Turin.