Overall, participants were able to discriminate faces from non-faces using only the shading cues that were available in the two-tone images. As can be seen in
Figure 6, participants had close to ceiling performance for images that were spatially upright. This ability to detect faces in the two-tone images was largely robust to changes in the horizontal lighting direction. We consider this to be a surprising result given the drastic image changes associated with variations in light-source azimuth (see
Figures 2 and
4, for example).
The mean discrimination sensitivity for each experimental condition is shown in
Figure 6. For the upright images, participants’ discrimination sensitivity only reduced for the extreme light-source azimuths where only a small portion of the face was visible. A repeated-measures ANOVA indicated that there was a significant main effect of light-source azimuth on discrimination sensitivity,
F(8, 304) = 138.55,
p < 0.001, η
p2 = 0.79, and this main effect seems to be driven by the reduced discrimination sensitivity at the extreme azimuths. However, varying the light-source azimuth had a greater effect on discrimination sensitivity for inverted images compared with upright images. This was reflected in a significant interaction between light-source azimuth and spatial inversion,
F(8, 304) = 14.49,
p < 0.001, η
p2 = 0.28, and suggests that tolerance to changes in the horizontal illumination of the face relies partly on viewing the face in its most typical upright configuration. Unsurprisingly, spatially inverting the images also led to worse discrimination sensitivity overall, reflected in a main effect of spatial inversion,
F(1, 38) = 132.18,
p < 0.001, η
p2 = 0.77.
In addition to examining how face detection is affected by changes in the horizontal lighting direction, we were interested in whether discrimination sensitivity is best for front-on illumination that is relative to the face in the image or relative to the participant's perspective. As can be seen in
Figure 6, the distributions of
d′ for each head rotation condition overlap within one another for the relative light-source azimuths (
Figure 6A) and are separated for the absolute azimuths (
Figure 6B), suggesting that sensitivity is best for front-on illumination that is relative to the face. To examine this statistically, we compared the centroids for each head rotation condition. If front-on illumination relative to the face leads to better sensitivity, we would expect the centroids to be close to zero for the relative light-source azimuths. We would also expect the centroids to shift away from zero for the absolute azimuths: a leftward shift for the –30° head rotation condition and a rightward shift for the +30° condition. Conversely, if sensitivity was best for front-on illumination relative to the participant's perspective, we would expect the centroids to be close to zero for the absolute light-source azimuths and shifted for the relative azimuths (rightward for the –30° head rotation condition and leftward for the +30° condition).
The centroids for both the relative (
Figure 6A) and absolute (
Figure 6B) light-source azimuths suggest that participants were best at discriminating faces from non-faces for front-on illumination
relative to the face in an image. When the light-source azimuth was coded relative to the face, the half-difference between the centroids for the –30° and +30° head rotation condition was not significantly different from zero for the upright condition,
t(39) = 1.10,
p = 0.28, Cohen's
d = 0.17, and the inverted condition,
t(39) = –0.09,
p = 0.93, Cohen's
d = –0.01. For the absolute light-source azimuths, the centroid half-difference was significantly different from zero for both the upright condition,
t(39) = –5.92,
p < 0.001, Cohen's
d = –0.94, and the inverted condition,
t(39) = –12.48,
p < 0.001, Cohen's
d = –1.97. The centroid half-differences for the relative and absolute light-source azimuths are significantly different from each other for both spatially upright images,
t(39) = –10.40,
p < 0.001, Cohen's
d = –1.64, and inverted images,
t(39) = –14.30,
p < 0.001, Cohen's
d = –2.26. Thus, the horizontal direction of lighting relative to the face appeared more important for face detection than the direction of lighting relative to the viewer. The centroids for all participants can be seen in
Figure 7.
To ensure the robustness of our conclusions, we repeated the centroid analysis on the pooled data from all participants, with the centroids calculated without taking absolute d′ values in the denominator. Bootstrapped 95% confidence intervals (CIs) for the centroid half-differences were calculated from the pooled data by resampling the subject pool with replacement 10,000 times and repeating the centroid calculation for each iteration. The bootstrapped 95% CIs indicate that the centroid half-differences were significantly different from zero for the absolute light-source azimuths (upright images: 95% CI, –9.43 to –4.96; inverted images: 95% CI, –21.56 to –1.57) and not significantly different from zero for the relative light-source azimuths (upright images: 95% CI, –0.97 to 4.43]; inverted images: 95% CI, –6.73 to 1.70). This is consistent with the results of the main centroid analysis.
There was also a significant main effect of head rotation, F(2, 76) = 6.14, p = 0.003, ηp2 = 0.14, where sensitivity was slightly better for the 0° head rotation condition, and this effect interacted with light-source azimuth, F(16, 608) = 4.41, p < 0.001, ηp2 = 0.10. There was a small interaction between head rotation and spatial inversion, F(2, 76) = 5.69, p = 0.005, ηp2 = 0.13, where sensitivity for the 0° head rotation condition was slightly less affected by spatial inversion compared with the other two rotations. There was also a significant three-way interaction among light-source azimuth, head rotation, and spatial inversion, F(16, 608) = 2.27, p = 0.003, ηp2 = 0.06.
The mean criterion or response bias across participants for each condition is shown in
Figure 8. A repeated-measures ANOVA indicated that there was a significant effect of head rotation on response bias,
F(2, 78) = 20.96,
p < 0.001, η
p2 = 0.35, where participants were slightly less biased toward a non-face response for the 0° rotation condition. Response bias was also affected by the horizontal lighting direction,
F(8, 312) = 136.11,
p < 0.001, η
p2 = 0.78, with participants having a greater bias toward responding “non-face” at the extreme light-source azimuths. There was a significant interaction between head rotation and light-source azimuth,
F(16, 624) = 7.38,
p < 0.001, η
p2 = 0.16; the increase in criterion for the extreme light-source azimuth conditions depended on the rotation condition, where the bias toward “non-face” responses was greater for extreme light-source azimuths. Participants were also more biased toward responding “non-face” for spatially inverted faces compared with spatially upright faces,
F(1, 39) = 120.51,
p < 0.001, η
p2 = 0.77. The interaction between light-source azimuth and image orientation was significant,
F(8, 312) = 12.95,
p < 0.001, η
p2 = 0.25, as well as the interaction among all three factors,
F(16, 624) = 1.67,
p = 0.047, η
p2 = 0.04.