We all know a pleasing smile when we see one, but how to build one step by step? Every day, surgeons try to do just that as they reconstruct the facial anatomy of people who have suffered accidents, strokes, and other conditions. Robbed of their ability to express emotion by smiling, these patients run an elevated risk of depression. But “facial reanimation” surgeons have had no rigorous criteria to guide them in giving patients a sociably pleasing smile.

Until now. In a study published June 28 in the journal PLoS One, a team of University of Minnesota researchers plumbed the preferences of Minnesota State Fairgoers and parsed out several elements of successful smiles. They discovered how factors like the shape of a smile and its degree of “toothiness” can work together to produce a pleasing result. They also found that timing counts. “The time it takes to develop a smile is important,” says team member Nathaniel Helwig, an assistant professor of psychology. “For example, if a person smiles too slowly, it could be misinterpreted.”

The researchers, including facial reconstructive surgeon Sofia Lyford-Pike and Assistant Professor of Computer Science and Engineering Stephen Guy, expect the findings will guide surgeons and rehabilitative medicine practitioners as they help patients relearn how to smile, not smirk.

Surgeons reconstructing a smile often focus on how far the corners of the mouth can move—that is, on making the patient’s smile as broad as possible. But Lyford-Pike suspected that optimizing that feature alone wouldn’t be enough to make a socially pleasing smile.

To find out what criteria matter most, she contacted Guy and Helwig. The three, along with graduate student Nick Sohre (M.S. ’17) and undergrad Mark Ruprecht, designed a 3-D computer-animated face that could turn a neutral expression into any of 27 different smiles in a quarter second. 

Each had a unique combination of three criteria: smile “extent,” a measure of width; “dental show,” or toothiness, defined as the distance between the lips; and smile angle, which describes how pronounced a V-shape the mouth makes. Angle increases as the corners of the mouth turn up and/or the lower lip moves down.

“This was a first attempt to define what we as human beings do intuitively every day when we interact with each other,” Lyford-Pike explains.

The researchers tested all 27 smiles on adult members of the public in the U’s Driven to Discover building at the 2015 Minnesota State Fair. A total of 802 volunteers rated how effective, genuine, and pleasant each appeared.

If you’re thinking that crinkling of the eyes is also important, you’re right. But in this early study the team focused on mouth movements because they are easier to restore surgically and because evidence suggests they may be the single strongest factor in conveying the meaning of a smile.

The data revealed that none of the three criteria should necessarily be high, medium, or low; it’s the combination that counts. The best smiles display an optimal—not extreme—smile angle and width, and, given that, an appropriate amount of dental show.

A clear example of this interplay turned up in the different responses to two smiles with either a larger or a smaller extent/angle combination. When the amount of dental show was expanded, the smile with more limited extent and angle rated worse while the broader, more V-shaped smile rated higher. 

“This suggests that people with limited mouth motion—who don’t have a broad smile—might do better with limited dental show,” says Helwig. “[Overall] there’s a Goldilocks position, or sweet spot, where all the criteria work best together. The very best smiles are where the extent and angle are medium to high. With that, there’s an optimal range of dental show.”

However, if a smile had too much extent/angle—that is, was extremely broad and upturned—showing more teeth lowered the smile quality.

“The main take-home for surgeons is that the extent isn’t the sole outcome measure to use,” says Helwig.

“Given the diversity in human faces and smiles, the finding that many smiles are interpreted as pleasant is encouraging for the applicability of our results,” Lyford-Pike says.

Also important was whether the smile developed at the same speed on both sides of the mouth. As long as neither side lagged the other by more than 125 milliseconds (an eighth of a second), the smile lost none of its quality. But in one test, a short lag—between 25 and 50 milliseconds—was preferred over absolute synchrony. That wasn’t surprising, says Helwig, because “some dental literature suggests that perfect symmetry might look robotic.”

“That is an important lesson for computer graphics in general,” says Guy. “Too often, we are tempted to make digital animations mathematically perfect. However, the real world is full of interesting and wonderful imperfections . . . it was nice to see that reflected in our data.”

Among the researchers’ forthcoming studies are ratings of smiles on patients with partial facial paralysis. They also have performed 3-D studies of real people smiling. The scientists also hope to study the role of other facial features, such as eye crinkling.

And that’s something to smile about.