The WP article provides an abundance of referenced research from both sides. Quite interesting. http://en.wikipedia.org/wiki/Shroud_of_Turin
Kind of like a veiled women, i see God basically veiling Himself while giving enough revelation for those who honestly want what Christ represents to seek to know Him, and to take a step of faiths that results in a real revelation of Him and of His promises, in heart and life and according to obedience, while allowing the results of the Fall to be used by those who do “will not have this Man to reign over them.” (Lk. 19:14)
Liberals demand all the same benefits as those who earned the right to them, and some skeptics demand God do this or that as a condition of believing on Him while being opposed to His authority, and doing which miracles will not result in real faith. Israel under Moses proves that.
However, honest seeking prepares the heart for proper receiving, and “The secret of the Lord is with them that fear [reverence] him; and he will shew them his covenant.” (Psalms 25:14)