James Cornforth was last seen leaving the cinema in Ocean Terminal shopping centre, Leith, shortly after 3pm on Tuesday February 5.
But CCTV revealed the 36-year-old visited the Tesco Express store on Queensferry Road at 5:42pm later that day, and officers believed he walked west towards Barnton junction.
Mr Cornforth has links to the Granton area of the city but is also known to travel across Scotland.
Extensive enquiries have been carried out since he was reported missing but there have been no confirmed sightings.
The force has also released new images of Mr Cornforth which reflect how his appearance may have changed since he vanished.
Officers are working with train and travel companies to establish if he has left the Capital.
James is described as white, around 5ft 10ins tall, of medium build with short light-brown hair and speaks with a local accent.
He has a tribal sleeve tattoo on his right arm from his shoulder to elbow, and a coloured thistle tattoo on his right ankle. When last seen he was wearing a grey hoodie, blue jeans, and was carrying a dark-coloured medium sized rucksack that was packed full.
Inspector Jonny Elliott, of Drylaw Police Station, said: “James’ family and friends are understandably becoming increasingly concerned for his safety as time passes, and this is extremely out of character for him not to have made contact with them for this amount of time.
“Our inquiries have focussed on the west of the city and where James may have travelled since he left the Tesco store on Queensferry Road. I would appeal to anyone who has seen, or spoken to James, since Tuesday 5 February to come forward and report this to officers.
“The public should be mindful that he may have since changed his clothing and appearance.
“Anyone who has any information that can help us trace James’s current whereabouts is asked to get in touch with police immediately.”
Those with information can contact Police Scotland on 101, quoting incident number 1134 of 7 February.”
Police are also still looking for missing Muirhouse man, Thomas Saunders, who was last seen before Christmas.
The 58-year-old’s blue Volkswagen Golf GTI, with registration number S274 0GB, was found apparently abandoned near a forestry track in Ardgartan, Argyll. It is believed he travelled to the area sometime between December 16th and December 28th.
The last confirmed sighting of Mr Saunders was at the Premier Inn, Leith, on Sunday December 16, when he was seen driving from the hotel car park in the Volkswagen Golf.
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