Lightness constancy in reality, in virtual reality, and on flat-panel displays

Abstract

Virtual reality (VR) displays are being used in an increasingly wide range of applications. However, previous work shows that viewers often perceive scene properties very differently in real and virtual environments and so realistic perception of virtual stimuli should always be a carefully tested conclusion, not an assumption. One important property for realistic scene perception is surface color. To evaluate how well virtual platforms support realistic perception of achromatic surface color, we assessed lightness constancy in a physical apparatus with real lights and surfaces, in a commercial VR headset, and on a traditional flat-panel display. We found that lightness constancy was good in all three environments, though significantly better in the real environment than on the flat-panel display. We also found that variability across observers was significantly greater in VR and on the flat-panel display than in the physical environment. We conclude that these discrepancies should be taken into account in applications where realistic perception is critical but also that in many cases VR can be used as a flexible alternative to flat-panel displays and a reasonable proxy for real environments.

Appendices

Appendix A

We assume that all surfaces are Lambertian. Let the reference stimulus have reflectance $r_1$ and illuminance $i_1$, so following Eq. 1 for a Lambertian surface, the luminance is $\ell _1 = r_1 i_1 / \pi$. Let the observer’s match setting at the test stimulus be reflectance $r_m$, under illuminance $i_m$, and so have luminance $\ell _m = r_m i_m / \pi$. If the observer has no lightness constancy and simply matches the luminance of the reference and test stimuli, then their match setting $r_0$ satisfies $r_0 i_m = r_1 i_1$, or $r_0 = r_1 i_1 / i_m$. If we substitute this expression for $r_0$ into Eq. 3 and solve for the match setting $\log r_m$, we find

$$\begin{aligned} \log r_m = (\tau -1)(\log i_m - \log i_1) + \log r_1 \end{aligned}$$

(8)

which is an affine function of $\log i_m$ with slope $m=\tau -1$.

Appendix B

Fig. 10

Results for additional observers in the lightness matching task. See caption of Fig. 5 for details

Fig. 11

Results for additional observers in the lightness matching task. See caption of Fig. 5 for details

Fig. 12

Results for additional observers in the lightness matching task. See caption of Fig. 5 for details

Fig. 13

Results for an additional observer in the lightness matching task. See caption of Fig. 5 for details

Appendix C

Here we provide details of the bootstrapped significance tests of mean Thouless ratios.

Figure 6 shows Thouless ratios for each display method, reference reflectance, and observer. This data can be represented as a $3 \times 3 \times 12$ matrix $T_{ijk}$, where each entry is the Thouless ratio for display method i (an integer from 1 to 3), reference reflectance j (also an integer from 1 to 3), and observer k (an integer from 1 to 12). The red dots in Fig. 6 show mean Thouless ratios across observers, which can be represented as a $3 \times 3$ matrix $M_{ij}$, where each element is the average of $T_{ijk}$ for k from 1 to 12.

On each bootstrap iteration, we simulate a repetition of the experiment by creating a new $3 \times 3 \times 12$ matrix $T^{(b)}_{ijk}$ of Thouless ratios. We generate this matrix by choosing 12 observers with replacement from the 12 observers in the experiment. That is, each $3 \times 3$ slice of $T^{(b)}_{ijk}$ for a given value of k is a randomly chosen $3 \times 3$ slice of the original data $T_{ijk}$, representing the Thouless ratios of a single observer. (“With replacement” means that the observer’s data may appear more than once in the resampled matrix $T^{(b)}_{ijk}$.) We then calculate the bootstrapped $3 \times 3$ matrix of means $M^{(b)}_{ij}$ by taking the average of $T^{(b)}_{ijk}$ over k from 1 to 12.

We repeat this sampling procedure $B=10^6$ times, producing B simulated repetitions of the experiment, represented as $T^{(b)}_{ijk}$ and $M^{(b)}_{ij}$, where b ranges from 1 to B.

This resampled data forms the basis of the bootstrapped significance tests. For example, to test whether the mean Thouless ratio in condition $i=1$, $j=1$ (say, the physical condition and reference reflectance 0.18) is significantly greater than the Thouless ratio in condition $i=1$, $j=2$ (say, the physical condition and reference reflectance 0.39), we find the proportion of bootstrapped samples for which $M^{(b)}_{11}$ is greater than $M^{(b)}_{12}$. If this is true for at least 95% of the samples, then we conclude that the first mean is significantly greater than the second mean at a significance level of $p$ 0.05.

For additional details of bootstrapping methods, see Efron and Tibshirani (1994). We provide MATLAB code that implements these significance tests as Supporting Information.