In this study, with hybrid image paradigm and face images constructed from
different illumination conditions, we demonstrated the role of asymmetric low spatial
frequency information in face discrimination. The asymmetric low spatial frequency
information has a strong influence on face perception as illustrated by its ability to
change the perceived gender of the hybrid faces. In addition, such effect increased as the
lighting direction shifts sideward. In contrast, the symmetric low spatial frequency
information had little, if any, effect on face discrimination. In addition, the asymmetric
low spatial frequency information also affected the perceived depth of a face. Again,
this effect was more pronounced as the lighting direction shifts sideward. Hence, these
results are consistent with the notion that the sideward shift of lighting directions
provides more shading information that increases the perceived depth of
shape-from-shading and in turn improves the facial discriminability in the observers.
23
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List of Figures
C.
A. B.
D.
E.
Figure 1. The symmetric algorithm helps to dissociate the contribution of the surface albedo from illumination component in image.
A, LA, is asymmetric component of illumination of face image. Through the process of shape-from-shaping, the LA provided 3D information about a face on a 2D image.
B, CS, is surface albedo. The face containing only CS looks very flat. In addition, it is next to impossible to identify the identity of the owner of the face with only the CS information. C, Original image. D, Residual information. E, Put the LA and the CS together, it is easy to see that the hybrid image and the original are pictures of the same person even though a lot of information (D) was thrown away.
29
Figure 2. Examples of stimuli.
A, We generated a series of intermediate facial information by morphing the symmetric components of high special frequency (symHSF) between the two faces. There were seven morphed images with proportion of femininity from 0 (male) to 1 (female). B, Examples of female asymLSF and symLSF images. There were four lighting directions: 0°, 15°, 30°, and 60°. The original female face was low-pass filtered to preserve coarse-scale shading information. C, The hybrid face stimuli was a combination of the female (or male, not shown) asymLSF of one lighting direction and on one of the morphed face. Here are examples with the 0.5 femininity symHSF face. The symHSF face looks very flat and it is hard to judge the gender. When combined with a female asymLSF face, say, the one with 60° lighting direction, the resulting hybrid face was frequently categorized as female by most observers.
30
Fraction of Female Responses observer CIT
symHSF
Fraction of FemaleResponses Observer CIT symHSF
Fraction of Female Responses Observer CAE
symHSF
Fraction of Female Responses Observer CAE symHSF
Fraction of Female Responses Observer CAI
symHSF
Fraction of Female Responses Observer CAI symHSF
31
PSE shift from symHSF condition (proportion of femininity)
Male asymLSF + symHSF symHSF only
Figure 3. The effect of asymLSF on face discrimination.
A, B, C, D, E, and F, Psychometric functions from three naïve observers. The fraction of femininity responses is plotted as a function of the proportion of femininity of symHSF.
The black psychometric curve is from symHSF only condition as a comparison. The red, green, blue, magenta psychometric curves are results of asymmetric facial information.
Under the female asymLSF condition, when lighting direction was shifted to more lateral, the observers saw female faces more frequently, and the psychometric curves shifted gradually to left. On the contrary, under the male asymLSF condition, the psychometric curve shifted dramatically to right, and psychometric curve was saturated under 30° and 60° illumination conditions, especially in B and F. These two observers tend to saw male faces in every level of femininity. G, Averaged PSE shift from symHSF only condition by asymmetric low spatial frequency facial information. The error bars represent one standard error. The p-value shown in each lighting direction was calculated from a two-tailed paired t test. The averaged PSE shift in male 30o and 60o illumination condition was beyond measurable range, so we used an arrow to plot.
32 Fraction of female response Observer CIT
symHSF
PSE shift from symHSF condition (proportion of femininity)
LSF information
Figure 4. Comparisons of the effect of asymLSF and symLSF on face discrimination.
A, B, C, Psychometric function from three naïve observers. The fraction of female responses is plotted as a function of the proportion of femininity. The black psychometric curve is from symHSF only condition in corresponding observers. The cyan psychometric curves are results of symLSF + symHSF in the female and male conditions. The magenta curves are results of asymLSF + symHSF faces. Results show that the symLSF had very little influence on face discrimination, because the psychometric curves were not significantly shifted. D, The average PSE shift relative to the symHSF only condition. The p-values denote the result of the paired t test. The averaged PSE shift in male 60o illumination condition was beyond measurable range, so we used an arrow to plot.
33
Figure 5. Results of depth judgment.
A, female condition. B, male condition. The depth rating value of the hybrid faces:
asymLSF (under four lighting directions) combined with symHSF, symLSF combined with symHSF (under 60o), and female and male 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 genders show a positive increase in proportion to the lighting directions.
The slope parameters were significantly larger than zero (t(2) = 10.67, p= .0086 for the
34
Figure 6. Face discrimination performance is highly correlated with perceived depth.
A, female condition, Pearson correlation coefficient of depth rating value and averaged PSE shift, , and B, male condition . The averaged PSE shift in male 30o and 60o illumination condition was beyond measurable range, so we used arrows to plot. PSE shift from symHSFcondition (proportion of femininity)
Y= 0.37-0.167X
PSE Beyond measurable range
1 2 3 4 5
PSE shift from symHSF condition (proportion of femininity)
Depth rating
35
Fraction of Female Responses observer CIT
symHSF
Fraction of FemaleResponses Observer CIT symHSF
Fraction of Female Responses Observer CAE
symHSF
Fraction of Female Responses Observer CAE symHSF
Fraction of Female Responses Observer CAI
symHSF
Fraction of Female Responses Observer CAI symHSF
36 Fraction of Female Responses Observer CPY
symHSF Fraction of Female Responses Observer CPY
symHSF Fraction of Female Responses Observer CBN
symHSF Fraction of Female Responses Observer CBN
symHSF Fraction of Female Responses Observer LNL
symHSF Fraction of Female Responses Observer LNL
symHSF 0 ° 15 ° 30 ° 60 °
Figure 7. All seven observers’ asymLSF condition data.
The fraction of femininity responses is plotted as a function of the proportion of femininity.
37 Fraction of female response Observer CIT
symHSF Fraction of female response Observer CPY
symHSF Fraction of female response Observer CBN
F Fraction of female response Observer LNL
symHSF F_asymLSF + Morphs M_asymLSF + Morphs F_symLSF + Morphs M_symLSF + Morphs
38
G
0 0.2 0.4 0.6 0.8 1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
LSF information
Proportion of femininity Fraction of female response Observer RYT
symHSF F_asymLSF + Morphs M_asymLSF + Morphs F_symLSF + Morphs M_symLSF + Morphs
Figure 8. All seven observers’ symLSF condition data (compared with asymLSF data).
The fraction of femininity responses is plotted as a function of the proportion of femininity.