Figure 1.
A demo of the dissociation the surface reflectance (CS) from the symmetric and asymmetric illumination components (LS, LA) in an image.
Through the process of shape-from-shaping, the LA provided 3D information about a face on a 2D image. The face containing only CS looks very flat. By putting the LA and the CS together, it is easy to see that the hybrid image (LA+CS) and is similar to the original (O) even though a lot of information (LS+CA) was thrown away. The original images (O) were created from Lin et al. (2002, 2005).
Figure 2.
Examples of the low and high spatial frequency hybridization.
A, A series of intermediate face examples were generated by morphing the symmetric components of high special frequency (symHSF) between the two faces, while holding the low spatial frequency information invariant. There were seven levels of this component with proportion of the female face from 0 (entirely male face) to 1 (entirely female face). B, Examples the low spatial frequency (asymLSF) components from the female face after low-pass filtering the original face to preserve coarse-scale shading information, computed for four illumination directions: 0°, 15°, 30°, and 60°. C, The hybrid face stimuli were a combination of the asymLSF female face (or male face, not shown) of one illumination direction on the morphed face. Here examples are shown with the 0.5 female symHSF component, combined with a female asymLSF component at the four lighting directions, which can be seen to enhance the perceived depth as the illumination angle increases. The resulting hybrid face at the 60° illumination angle was categorized as female by most observers. The images were rendered from 3D models by Lin et al. (2002, 2005). The models have given written consent to publication of their photos.
Table 1.
Stimuli used in the experiments.
Figure 3.
The effect of asymLSF on face discrimination.
Each row shows the psychometric functions from one of the three naïve observers. The fraction of “female face” responses is plotted as a function of the proportion of female face in the combined images. The black psychometric function is for the symHSF-only condition plotted here for comparison. The red, green, blue and magenta psychometric functions represent different illumination directions as indicted in the legend. In the female-face asymLSF condition (left column), the psychometric functions shifted gradually to the left as illumination angle increased. Conversely, in the male-face asymLSF condition (right column), the psychometric functions shifted dramatically to the right.
Figure 4.
(A) AsymLSF effect on PSE shift from the symHSF only condition averaged across observers. (B) Relative PSE shift from the 0° lighting direction. The error bars represent one standard error. The statistically significant difference at p<.05, and 0.01 in a two-tailed paired t-test after Bonferroni correction are indicated by one, and two asterisks respectively. The averaged PSE shifts at male face 30° and 60° illumination directions were so great that they were beyond the measurable range, as indicated by the arrows.
Figure 5.
Comparisons of the effect of the asymLSF and symLSF information on face discrimination.
A-C, Psychometric functions from three naïve observers. The fraction of “female face” responses is plotted as a function of the proportion of female face. Black curves: symHSF-only condition in the corresponding observers. Cyan curves: symLSF+symHSF in the female and male conditions. Magenta curves: asymLSF+symHSF faces. The symLSF component had very little influence on face discrimination, as indicated by the fact that the psychometric curves are not significantly shifted. D, The average PSE shifts relative to the symHSF-only condition. Other conventions as in Figure 3.
Figure 6.
A Comparison of the effect of asymHSF and symHSF on face discrimination.
The fraction of “female face” responses is plotted as a function of the proportion of the female face in the shading image. Black curve and closed squares: the symmetric HSF condition. The green curve and open squares: the asymmetric HSF condition. Other conventions as in Figure 3.
Figure 7.
Depth judgments Depth judgments.
The depth rating value of the hybrid faces: asymLSF (under four illumination directions) combined with symHSF, symLSF combined with symHSF (under 60°), and female (A) and male (B) symHSF. The depth value of the reference sphere was set to 3. Using least squares analysis, the linear regression lines of asymLSF condition of both faces show a positive increase in proportion to the illumination direction.
Figure 8.
The shading effect holds for faces of the same gender.
(a) The original images of two male faces were from a publicly available database prepared by Shyi et al. (2011). (b) The 50–50 morph of the symHSF components of the two faces. (c) The combination of (b) and asymLSF components of 0° lighting images. These two reconstructed images look very similar. (d) The combination of (b) and asymLSF components of 45° lighting images. These two images are clearly from two different individuals. The models have given written consent to publication of their photos.
Figure 9.
The effect of asymLSF on discriminating two male faces.
The fraction of “Person 2” responses is plotted against the source of asymLSF component. The black square and dash line is for the symHSF-only condition plotted here for comparison. The red and blue circles represent 0° and 45° illumination directions as indicted in the legend.
Figure 10.
Face discrimination performance is highly correlated with perceived depth.
Pearson correlation coefficient of depth rating value and averaged PSE shift was r = 0.90 for the female-face and r = 0.86 for the male-face conditions The averaged PSE shift in the male-face 30° and 60° illumination conditions was beyond measurable range, as indicated by the arrows.