Shroud of Turin new research disputing it's a fake

First the news that it is being shown 
Shroud of Turin shown amid new research disputing it's a fake | News.com.au


Then some of the new research
Latest Developments on the Shroud of Turin: Part I - there are link on bottom of page to Part II and then III

What I understand is that those talking fake allude to a C14 dating to middle ages and the idea that Da Vinci used some kind of photographic process to produce the image.

The C14 seems to be very much in doubt

The Da Vinci idea is just an invention and is all based on the shroud first appearing around his time.

Now the new latest is that there was a shroud in Constantinople around 1000 AD  and it had an image. This image appears in paintings from that time and looks like the image on the Turin Shroud. The Constantinople one looks like it came from Edessa see also Image of Edessa - Wikipedia, the free encyclopedia

Early paintings even show Jesus body on  a shroud like the Turin one......

So looks like the Turin Shroud has been around for a very long time