At around 6.20pm on May 3, a man in his 20s was walking his six-month-old Mastiff puppy in Franklins Row and was approached by two men.
One man grabbed the victim by his shoulder while the second suspect held a knife to his stomach.
They then demanded the man hand over his Audemars Piguet wristwatch, which has rose gold links and is valued at around £50,000.
Both suspects then made off towards Turks Row, leaving the victim "badly shaken" but uninjured.
They are described as white, aged between 25 to 30 and the second suspect, who held a knife to the victim's stomach, spoke with a London accent, police said.
Releasing CCTV images of the two suspects, detective constable John Fellows appealed for anyone who recognises the men or anyone with information to come forward.
He said: “These men used a knife to threaten and rob a man in broad daylight. They are clearly dangerous and we urgently want to identify and locate them.
"We are appealing for anyone who recognises these men to contact police immediately or contact Crimestoppers anonymously if you don't want to give your name.
"We are also asking for anyone who saw the incident or saw these men hanging around the area to contact us. Your information could be vital in helping us find these men."
Any witnesses or anyone with any information is asked to call police on 101 quoting CAD 6263/3May. To give information anonymously contact Crimestoppers on 0800 555 111.