The 34-year-old was wearing a dark, zip-up jacket, black jeans, a dark blue striped shirt and black Rockport Boots.
Police believe he was the victim of an assault, but are unclear how and when his skull was fractured.
He had been drinking in town and was seen walking in Roseville Street with the injury some time before being found near the Marett Road junction in Green Street.
He was found by two men, who called an ambulance, and he was taken to hospital shortly after 3.30 am.
His condition today was described as stable and slowly improving.
The police are appealing for anyone who may have seen the victim on either Saturday night or Sunday morning to call them on 612612 or Crimestoppers on 0800 555 111.