Pupil Size Estimation Based on Spatially Weighted Corneal Flux Density

Abstract

The pupil size is an important parameter in different studies on vision and ophthalmology. A pupil size estimation model is constantly needed when actual measurements are unavailable. The reported pupil estimation models commonly adopt the product of light intensity and viewing field area, supposing the light contributes uniformly across the spatial domain. In this paper, the pupil diameters were measured for stimuli with different intensities and different sizes. Spatially varying effect were observed, especially for large field stimuli and annular bright stimuli. A spatially weighted flux density is proposed which shows a high correlation with pupil diameters. A hyperbolic equation is fitted to estimate the natural pupil diameter with independent light spatial distributions. The goodness of fit R 2 reaches 0.97. The accuracy of the model is further verified with a natural indoor scene for different viewing distances and different illumination levels. The model predicted pupil diameters show a high correlation with the measured data.

9.1: Invited Paper: Pupil Size Estimation Model Based on Revised Spatially Weighted Corneal Flux Density and Chromaticity Coordinates

“…Among them, stimuli with more concentrated luminance distribution (such as square stimuli) cause smaller pupil size. This proves Zhang's conclusion that pupil size is not only related with the size of adapting area, but also the luminance distribution [12].…”

“…However, it also can be seen in Figure 3 that for Group A(1) and Group A(2), the data points and the curve show obvious asymmetry. According to Zhang's theory [12], rotational symmetry stimuli should result in the same spatially weighted corneal flux density and thus the same pupil diameter. This shows that Zhang's theory is incomplete.…”

“…It can be found that the changing range of pupil diameter varies in different formulas. For example, in Stanley's model, the pupil diameter varies from 2mm to 7.75mm while in Zhang's model, the pupil diameter varies from 2.36mm to 5.12mm [9,12]. Studies have shown that many factors including age and refractive status can affect pupil size [14].…”

“…In 2011, Watson introduced the concept of effective corneal flux density to describe the quantity that effectively controls the pupil diameter, including luminance, adapting field size, age and whether one or both eyes are adapted [3]. In 2019, Zhang modified corneal flux density into spatially weighted corneal flux density by introducing a weighting function, which is actually a Gaussian function, to weight the light stimulation in a large field size [12]. All of their studies improved the accuracy of the pupil size calculation model.…”

Influence of the Location of a Decision Cue on the Dynamics of Pupillary Light Response

“…In the phototopic range, pupil size decreases with increasing corneal flux density (CFD) that depends on the product of luminance and the adapting field size of the stimulus ( Stanley and Davies, 1995 ; Park and McAnany, 2015 ). During passive viewing of the stimulus of steady luminance, the estimated pupil size based on CFD weighted by a two-dimensional (2D) Gaussian function with the peak of the function at the location of gaze fixation (i.e., center of the display screen) closely followed the measured pupil size ( Zhang et al, 2019 ). Here, we further tested whether CFD filtered by the scope of attention drives pupillary response.…”