I don't know of a rule, and I've never felt the need to look for one. If someone has something, you use the participle.
He has blue eyes -> he is blue-eyed
She has brown eyes -> she is brown-eyed
The pig has a pot-belly -> it is a pot-bellied pig
The stool has three legs -> it is a three-legged stool
He has short hair -> he is short-haired
The man is wearing a blue suit - the blue-suited man ...[this is always attributive - it'd be most strange to say 'The man is blue-suited']
Some languages handle attributes differently, but I think the English usage is quite consistent (in this case, that is)