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

Shape from Shading

Depth-reversal ambiguity in shape-from- shading

hillvalley

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”

Procedure

Fixation Mark (1 sec.)

Task: hill or valley ?

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)

Examples:

87%(best)

15% (worst)

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.

Open questions

• What are the spatial scales over which shading information is analyzed?

• How does the prior on global shape depend on visual angle?

• What are the spatial scales over which shading information is analyzed?

• How does the prior on global shape depend on visual angle?