This got my attention. This doesn't look like any COP or gambeson I've seen before. There's no rivets or quilting and the shoulders seem too stiff and stick up too far to be a civilian garment (I could be wrong there). It closes on the sides and the slit on the shoulder enables a tight fit at the neck. The question is what could this be made of? It's nice to see something being worn other than the usual items. I never liked the idea of soldiers just wearing a tunic and a helmet.
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Um, that looks distinctly like a tabard to me, on account of the tied-off bunching at the neck to ensure a tight fit, the string ties at the sides, and the fold creases down the front and at the bottom.

A coat of very stiff fabric? It seem to be tied like a catholic deacon garment, the dalmatic, which in itself is normally very stiff. A protection of a sort very simple and easy to wear (and I think not heavy like an aketon).

Where do you found this image?

I don't believe this is a knights tabard or a surcoat because of the lack of maille or armour. I found it here on this thread on leather armour http://www.tforum.info/forum/index.php?showtopic=11700&st=20 There's nothing in the text on the origin of the picture. There's a couple of leather helmets on the next page.

When and where is the picture from? It might be easier to discuss different alternatives if we can look at the context of the whole period...

I think it's from one of the folios of the Morgan Bible. So it would show mid 13th century armor.

What about raw hide or cuir bullie? Full thickness rawhide will turn a sword blade...