Better Pupillometry Using Corneal Refraction

Research Digest

Author(s): Doran Amos, Neil M. Thomas, Kai Dierkes

December 13, 2021

Image credit: Photo from Unsplash by Daniil Kuželev.

Shedding light on pupillometry

From sitting at a candle-lit dinner table to lying on a tropical beach in the blazing sun, our vision must adapt to a wide range of lighting conditions. To achieve this, the pupils in our eyes become bigger or smaller, like the aperture of a camera, to let in just the right amount of light.

However, pupil size not only depends on external light levels, but also reflects our physiological and psychological states. For example, during emotional arousal and effortful mental work, the pupils dilate. In contrast, when we are tired and fatigued, the pupils constrict.

Interest in the measurement of changes in pupil size, known as pupillometry, is growing among researchers in academia and industry, given its potential as a powerful diagnostic and research tool. But with pupil size fluctuations often being subtle, particularly in response to changes in arousal and mental workload, accurate measurements of pupil size are critical.

How is pupil size measured?

A common approach to measuring pupil size is to record images of the pupils with digital cameras positioned close to the eyes, for example using a head-mounted eye tracker. However, the exact size and shape of the pupil image depends on the angle of the eye relative to the camera (Figure 1).

Left: diagram that shows pupil foreshortening based on corneal refraction; Right: real world images that demonstrate pupil foreshortening based on changes on gaze angle.

Figure 1. The effect of viewing angle on recorded pupil shape. (A) When looking straight into a recording camera, the pupil image is circular in shape. From a different viewing angle, the same pupil appears as a squashed circle (i.e., an ellipse). Note, while it appears smaller in the image, due to an effect referred to as pupil foreshortening, the size of the actual pupil is unchanged. (B) Example pupil images recorded from two viewing angles (top and bottom) in a very bright and a very dark environment (left and right). Note the size difference between the two environments.

When the eye is looking directly toward the camera, the pupil appears circular, but when the eye looks past the camera, the pupil appears as a squashed circle (i.e., an ellipse). The change in the perspective of the pupil causes the size and shape of the pupil in the camera image to change, even though the actual pupil size remains the same. This apparent change in pupil size as the eye rotates away from the camera is known as pupil foreshortening.

However, the biggest complication in measuring pupil size is due to the cornea, the clear outer layer of the eye that covers the pupil. The cornea distorts the size and shape of the pupil image via refraction, much like a magnifying glass would.

Although methods exist to correct for pupil foreshortening caused by changes in the perspective of the pupil relative to the camera, correcting for distortions in pupil size and shape caused by the cornea has proven to be more of a challenge.

Pupil Labs’ novel method dramatically reduces corneal distortion errors

In a recent study, Bernhard Petersch and Kai Dierkes (both employees of Pupil Labs) compared two established methods for measuring pupil size with a novel method developed at Pupil Labs.

The most basic method uses only 2D information extracted directly from the pupil image to estimate pupil size. In contrast, the other two methods each employ a 3D geometric eye model that is adjusted per subject based on recorded pupil images. However, while the established method ignores the optical effect of the cornea, the novel Pupil Labs method explicitly takes corneal distortion into account.

Using the Pupil Core eye tracker, the researchers recorded a large, real-world dataset of pupil images over a wide range of viewing angles. Crucially, the experiment was designed to keep the actual pupil size of each recorded subject approximately constant across viewing angles (see Figure 1B).

Graphs of viewing angle vs relative pupil size; real world measurements and simulated

Figure 2. Comparison of three methods for measuring pupil size. For each recorded eye, pupil size (relative to a baseline) is shown as a function of viewing angle (1.0 corresponds to the eye looking straight at the camera). Colors denote the three different methods (red: basic method using only 2D image information; blue: method without corneal modeling; green: Pupil Labs method with corneal modeling). The method recently developed by Pupil Labs (green lines) is the only one that provides pupil-size measurements which are independent of viewing angle on average.

Alongside the eye tracker recordings, the researchers ran computer simulations of an eye model to generate realistic images of how the pupil would appear through the cornea at a range of viewing angles.

As shown in Figure 2, the novel Pupil Labs method (green lines) estimated the correct pupil size on average regardless of the viewing angle in both the real-world and simulated datasets, dramatically reducing the optical effect of corneal distortion. In contrast, the other two methods diverged towards erroneously smaller and larger pupil size estimates (red and blue lines, respectively) across pupil viewing angles.

These results demonstrate that the novel method can be relied upon to provide accurate pupil size measurements, even in tasks and applications that involve a high degree of eye movement.

Towards better algorithms for measuring ocular parameters

At Pupil Labs, we work hard to develop new eye tracking technologies, including novel methods for measuring ocular parameters such as pupil size. We are proud that our efforts to improve the measurement of pupil size have produced a method that outperforms current state-of-the-art alternatives. We look forward to seeing how this novel method will be applied to advance pupillometry-based diagnosis and research in academia and industry.

You can read the full paper here: Petersch, B., Dierkes, K. Gaze-angle dependency of pupil-size measurements in head-mounted eye tracking. Behav Res (2021).

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