Beyond the Face

We see caricatures everywhere: in political cartoons, magazine covers, billboard ads, and wharfs all over the world. Why are caricatures so compelling?

Caricature artists are experts at identifying the characteristics that make each of our faces unique, and highlighting or exaggerating those characteristics in their drawings. A master caricaturist can convey the essence of a person, even their expression and personality , with a few strokes of a paintbrush.

How caricaturists are able to capture these identifying facial cues remains a mystery. Luckily for the rest of us without a caricaturist’s eye and training, researchers have developed mathematical ways to generate caricatures. The approach relies on the face space theory (Brennan, 1985; Valentine, 1991). According to this theory, we can think of faces points in a high-dimensional space. The dimensions refer to the different ways in which faces vary from each other: the distance between the eyes, the height of the eyebrows, the length of the nose, the protrusion of the chin, etc. Thinking of each of these variations as a dimension, each face can be defined as a set of values along each of these dimensions, defining a unique code or high-dimensional vector to represent each face.

Jennifer Day and Nicolas Davidenko

A representation of face space on the parametric face drawings model.

Source: Jennifer Day and Nicolas Davidenko

Figure 1. A representation of face space based on the parametric face drawings model by Day & Davidenko (2018). The central face represents a composite average of 400 faces of women and men of diverse ethnic backgrounds.

By thinking of faces as vectors in a high-dimensional face space, the process of generating caricatures becomes straight forward. Caricatures, according to face space theory, are simply faces that lie along the same vector as the original face, but further away from the average face. The image below shows an example of a randomly generated original face on the left, and three levels of caricature produced by distorting the original face further and further from the average face.

Debra Messing (mom of son Roman): “The priority shift is a relief. There are so many things that used to monopolize my time and my energy that I realize now, in the face of being a mother, are just completely irrelevant.”

Jennifer Day and Nicolas Davidenko

An original face and three levels of caricatures.

Source: Jennifer Day and Nicolas Davidenko

Figure 2. Left: a randomly generated original face generated using the parametric face drawings model (Day & Davidenko, 2018). Right: three levels of caricatures generated by distorting the original face further and further away from the average face.

If you begin by looking at the original face on the left, you can see that each face that follows is a more exaggerated version of the original, going from distinctive, to unusual, to down-right bizarre.

But if caricatures are defined as distortions away from the average face, what exactly is the average face? Researchers disagree about the nature of the average face – whether the brain represents it explicitly or not; whether each person holds a single average, or multiple average corresponding to different genders, ethnicities, or other demographic variables. However, most researchers agree that each person’s face space is uniquely and fundamentally shaped by the particular set of faces they are exposed to and interact with. A person growing up in Japan will develop a very different face space than a person growing up in Norway. They will develop different average faces, which means they will likely perceive caricatures differently.

The figure below shows how a caricature can change depending on which average face it is based on:

 Jennifer Day and Nicolas Davidenko

Four different caricatures of the original face from Figure 2.

Source: Jennifer Day and Nicolas Davidenko

Figure 3. Four different caricatures of the original face from Figure 2. Each caricature has been defined with respect to a different demographic distribution of faces.

Research suggests that caricatures may be central to the way the brain represents faces. A study by Robert Mauro and Michael Kubovy (1992) showed that people were faster at recognizing caricatured faces than the original faces. An advantage for recognizing caricatures may stem from the fact that caricatures tend to be unusual and unique; different from other faces you’ve seen. For example, there are probably very few faces that you have ever encountered that look like the right-most caricature in Figure 2. By storing a caricature rather than an original face, the brain may be creating a more unique face code; one that that will make you less likely to confuse that face with any other face you encounter, past or future.

Heidi Klum (mom of four: Leni, Henry, Johan and Lou (above)): “I’m not someone who [lives] like, ‘OK, this is a museum and you can’t sit here and you can’t touch this and everything has to be put in its place - [the kids] live here as much as we do. You come into our house and a giant elephant and lion are welcoming you. We have toys and things everywhere.”

Caricatures, whether defined algorithmically as in the examples above, or crafted by the masterful skill of a trained artist, may ultimately help us understand how the brain is able to create unique codes to store and recognize the thousands of faces we know.