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A preference for global convexity in local shape perception
Michael S. Langer Heinrich H. Bülthoff
Max-Planck-Institute for Biological CyberneticsTübingen, Germany
Michael S. Langer Heinrich H. Bülthoff
Max-Planck-Institute for Biological CyberneticsTübingen, Germany
Hollow Mask Illusion (Luckiesh, 1916)Hollow Mask Illusion (Luckiesh, 1916)Hollow Mask Illusion (Luckiesh, 1916)Hollow Mask Illusion (Luckiesh, 1916)
Hollow mask illusion is the sum of two factors (Johnston et a. ’92, Hill & Bruce ’94)
face
familiarity + global convexity
face
familiarity + global convexity
Global shape discrimination is easy
convex concaveconvex concave
“ “face” “mask”face” “mask”
convex concaveconvex concave
“ “face” “mask”face” “mask”
Three prior assumptions were tested
1. light source direction (Rittenhouse 1786,…..)
2. viewpoint direction (Reichel & Todd 1990, Mamassian &
Landy 1998)
3. global shape (Johnston et. al 1992, Hill & Bruce 1994 )
1. light source direction (Rittenhouse 1786,…..)
2. viewpoint direction (Reichel & Todd 1990, Mamassian &
Landy 1998)
3. global shape (Johnston et. al 1992, Hill & Bruce 1994 )
Example in which all three priors assumptions are met
1. light from above 2. viewpoint from above 1. light from above 2. viewpoint from above
3. shape is convex3. shape is convex
1. light from above 2. viewpoint from above 1. light from above 2. viewpoint from above
3. shape is convex3. shape is convex
Example in which all three prior assumptions fail
shape is concave viewpoint from below shape is concave viewpoint from below
light from belowlight from below
shape is concave viewpoint from below shape is concave viewpoint from below
light from belowlight from below
light source direction (collimated source)
lightlight
fromfrom
aboveabove
lightlight
fromfrom
belowbelow
lightlight
fromfrom
aboveabove
lightlight
fromfrom
belowbelow
viewing direction (Reichel and Todd 1990)
view from aboveview from above
view from belowview from below
view from aboveview from above
view from belowview from below
viewing direction (globally concave surface)
view from belowview from below
viewview from abovefrom above
view from belowview from below
viewview from abovefrom above
Design
• three factors :
- light direction
- viewpoint
- global shape
• 2 x 2 x 2 within observer
• 512 trials (64 per condition)
• three factors :
- light direction
- viewpoint
- global shape
• 2 x 2 x 2 within observer
• 512 trials (64 per condition)
ANOVA Results (12 naïve observers)
Main effects:
• light direction F(1,11) = 6.8, p = .025
• viewpoint F(1,11) = 9.6, p = .01
• global shape F(1,11) = 46.1, p < .001
Main effects:
• light direction F(1,11) = 6.8, p = .025
• viewpoint F(1,11) = 9.6, p = .01
• global shape F(1,11) = 46.1, p < .001
Linear Regression
percent correct
= 51 + 10 * light source direction
+ 11 * viewing direction
+ 13 * global shape
(Each factor had value of –1 or 1)
percent correct
= 51 + 10 * light source direction
+ 11 * viewing direction
+ 13 * global shape
(Each factor had value of –1 or 1)
Conclusion
• The prior for global convexity is used in local shape from shading.
• The global convexity prior had roughly the same strength as the light-from-above and viewpoint-from-above priors.
• The prior for global convexity is used in local shape from shading.
• The global convexity prior had roughly the same strength as the light-from-above and viewpoint-from-above priors.