The attack happened in Cartmell Drive shortly after 1am on Sunday, October 17.
The main victim, a 36-year-old man, suffered a broken jaw in the incident.
His friend, a 33-year-old man, received cuts and bruises during the attack.
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His partner, a 34-year-old woman, was also assaulted during the incident.
She told the Yorkshire Evening Post how she woke up after hearing a disturbance and went outside in her pyjamas.
She was then was punched and had some of her hair pulled out.
The terrified woman said: "They were very aggressive without any reason. They were drunk. They didn't want to listen or anything, they just attacked.
"One kid was with them and he was watching everything. He was maybe nine or 10.
"It was very scary and horrendous. The police came and the street was closed all night."
Damage was also caused to a car parked outside the house.
A folding chair was used to smash the back windscreen and the group dented the bodywork by kicking the car repeatedly.
Police said the two male victims had been in the nearby Halton Moor Social Club shortly before the attack.
Detectives have now released the CCTV footage as they continue to appeal for information to identify those responsible.
While the footage is not clear enough to identify the suspects’ faces it is hoped someone will recognise them from their general appearance and clothing.
It is believed they will be local to the area.
Anyone with any information that could assist the investigation is asked to contact Leeds District CID via 101 quoting crime reference 13210530628 or online.
Information can be given anonymously to the independent charity Crimestoppers on 0800 555 111