## MatheMUSEments

Articles for kids about math in everyday life, written by Ivars Peterson for Muse magazine.

## April 7, 2007

### Eye Reflections

Ever caught someone staring off into space and wondered what the heck they are looking at? To find out, you might follow their gaze, study their expression, or hey, just ask them, right? But now there's an even better, more precise way: Observe what is being reflected on the surface of their eyes.

Here's how to try this out: Get close and look right into a friend's eyes. You'll see a curved reflection of your face, a nearby window, a bench, a tree, or whatever else might be in view. Among the many important things they do, eyes can act like little mirrors that reflect exactly what a person is looking at. So, you can learn a lot about what a person is looking at and what his or her surroundings are like just by studying these reflections.

Interestingly, the curved panorama that you see reflected in an eye is broader than the image that falls on the retina at the back of the eye, which converts light into electrical impulses that go to the brain and tell you what you are seeing. This means that the wide-angle reflection shows more of the surroundings than the viewer (the person whose eyes are doing the looking) would actually detect at any given moment.

You can observe these reflections in a detailed, high-resolution photograph of a person's eye. If you look closely at the enlarged image, you might even catch a glimpse of the photographer who took the picture. A digital image of the reflection in the eye at that moment would also show what the viewer might have seen if he or she had gazed in another direction.

Two computer scientists, Ko Nishino of Drexel University and Shree K. Nayar of Columbia University, have developed a system for gleaning information from these reflected images. They use a digital camera to snap closeups of people's faces. A computer then processes the resulting images, letting the researchers reconstruct the views. By studying the reflections, they can even work out exactly what a person in any photo is actually looking at. There goes the "I just didn't notice" excuse!

In one recent application, photo buffs enlarged images of eyes in black-and-white portraits taken more than 150 years ago. Though fuzzy, the resulting light-and-dark patterns provided tantalizing glimpses of the places where the pictures were taken.

And, if you're like James Boind in the movie Goldfinger, a reflection in a villain's eye might save your life when you glimpse the villain's accomplice trying to sneak up behind you.

Muse, April 2007, p. 29.

Photo credits:
Nishino and Nayar