Image copyright HANNAH GAL / SPL Image caption Approachable? Intelligent? People's responses to 1,000 photographs were used to build the model

Whether it's a curled lip or a keen cheekbone, we all make quick social judgements based on strangers' faces.

Now scientists have modelled the specific physical attributes that underpin our first impressions.

Small changes in the dimensions of a face can make it appear more trustworthy, dominant or attractive.

The results, published in the journal PNAS, could help film animators or anyone looking to create an instant impression on a social network.

Dr Tom Hartley, a neuroscientist at the University of York and the study's senior author, said the work added mathematical detail to a well-known phenomenon.

"If people are forming these first impressions, just based on looking at somebody's face, what is it about the image of the face that's giving that impression - can we measure it exactly?"

Three key dimensions of a first impression Approachability: how likely is this person to help (or hinder) me?

Dominance: how capable is this person of carrying out those intentions?

Attractiveness: is this person young and good looking - a potential romantic partner?

Positive first impressions are especially important in a world dominated by social media, from LinkedIn to Tinder.

Dr Hartley sees the commercial potential in applying his numerical model to the photos people use to present themselves online. "It's obviously potentially very useful," he told the BBC.

To make the calculations, each of 1,000 face photos from the internet was shown to at least six different people, who gave it a score for 16 different social traits, like trustworthiness or intelligence.

Overall, these scores boil down to three main characteristics: whether a face is (a) approachable, (b) dominant, and (c) attractive.

Media playback is unsupported on your device Media caption Cartoon faces based on the new mathematical model, sliding along 3 scales: approachability, dominance and attractiveness

By measuring the physical attributes of all 1,000 faces and putting them together with those scores, Dr Hartley and his team built a mathematical model of how the dimensions of a face produce those three impressions.

The next step was to get the computer to extrapolate. Using their new model, the team produced cartoon versions of the most (and least) approachable, dominant and attractive faces - as well as all the possibilities in between.

Image copyright T Hartley / PNAS Image caption Six faces and their computerised approximations, including study author Dr Tom Hartley (second from left)

Image caption The same treatment given to the Today programme's John Humphrys

You could use these kind of numbers to decide when is a good time to take a photograph, or to choose the photograph that's really optimal in putting forward the best possible impression Dr Tom Hartley, University of York

Finally, and most importantly, these cartoon results could be tested. When the researchers quizzed more participants about their impressions of the artificial, cartoon faces, the ratings matched. People said that the computer's cartoon prediction of an approachable face was, indeed, approachable - and so on.

So has all this work revealed humanity's ultimate trustworthy jawline, or the most assertive shape for eyebrows? Dr Hartley is cautious.

"Lots of the features of the face tend to vary together," he explained. "So it's very difficult for us to pin down with certainty that a given feature of the face is contributing to a certain social impression."

There are some obvious trends however - including the tendency for masculine faces to be perceived as dominant, or for a broadly smiling face to seem more approachable and trustworthy.

This points to a potentially worrying implication: brief facial expressions can make a big difference to how we are received by strangers.

"It might be problematic if we're forming these kind of judgements based on these rather fleeting impressions," Dr Hartley said, "particularly in today's world where we only might see one picture of a face, on social media, and have to form our impression based on that."

Image copyright T Hartley / PNAS Image caption A mathematical model produced cartoon faces based on how people rated various facial dimensions

On the other hand, the findings could help people put their best face forward.

"It might be very useful for organisations who are interested in people's faces," said Dr Hartley.

[Being] approachable is tied to smiling expressions and unapproachable to frowning or angry expressions, while dominance is tied to masculine features Dr Anthony Little, University of Stirling

That might include interests as diverse as photographers, Facebook and Pixar.

"You would be able to use these kind of numbers to decide when is a good time to take a photograph, or maybe to choose the photograph that's really optimal in putting forward the best possible impression - and you might want to put forward different kinds of social impressions in different situations."

Animators, on the other hand, "have to give life, and give some social meaning, to the faces of their characters just by changing small things," Dr Hartley said.

"What we're doing is trying to put that on a scientific footing. It's been fascinating to find out more about it."

Dr Anthony Little, a reader in psychology at the University of Stirling, said the findings point to something "simple and important" about the way physical attributes guide our social responses.

Image copyright Thinkstock Image caption Impressions included attractiveness and trustworthiness - potential mate or used car salesman?

"The results highlight that the way we see other people may be in relatively simple terms, as approachable/unapproachable and dominant/submissive," said Dr Little, whose own research on faces and psychology includes using a website to crowd-source ratings.

"Each of these two factors looks to be tied to specific face features. So, approachable is tied to smiling expressions and unapproachable to frowning or angry expressions, while dominance is tied to masculine features.

"The third factor, youthful-attractiveness, appears less distinct."

This is because of interplay between attractiveness and the other two factors, Dr Little explained.