According to tradition, St. Veronicas veil exists and is located in a Catholic Church in Rome. You should be able to find it on the internet.
Also, what everyone in this discussion has forgotton is that the Jews, being Semites are classified as being racially Caucasion. However, one must bear in mind that the Ashkanizim, or Eastern European Jews are not pure Semites due to centuries of intermarriage and sometimes forced mating with other Eastern European peoples. The Sephardic Jews, the ones who were kicked out of Spain in 1492, are more pure blooded because they were given haven by the Moslem Calif in Turkey and North Africa and there was less intermarriage because mixed marriages were forbidden by the Moslems.
It should also be noted that the Palestinian Jews of Christ’s time were swarthy due to the climate in Palestine. All exposed parts of the body was deeply suntanned.
The Arabs, the other large part of the Semites, are not pure blooded Semites today. All Moslem men were allowed 4 wives, and during the Moslem conquest in the early years of their religion, intermarriage with African Negroes was common so that contemporary Arabs have darker skins than many mulatoes and have many other negroid physical traits.
So, the computor images derived from the Shroud of Turin is about as exact picture we will ever have of Christ.