Lines and Shapes-from-shadows

Juan Bai

Purpose: Where do lines fail in vision? What is its implication for the function of lines in

touch?

2

We see objects by means of their surfaces, and source of illumination.

Lines and Surfaces

We touch objects by means of their surfaces, i.e., no brightness information is involved.

For example, touch can often accurately discern this line drawing as depicting a cup.

3Lines, Surfaces, and ShadowsLines copying surface edges give us surface edge impressions (e.g., roof, hill, etc. in the image below).

However, lines copying shadow borders do not give us the impression of the darkness of shadow (e.g., the shadow on the ground; from Kennedy, 1993).

shadow border

surface borders

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Contour = reflectance/emission change on a surface. A line has two contours, one on each side.

Contour, Line, and Outline

Lines copying surface edges can be called ‘outlines.’

shadow border

surface borders

The image below shows that outlines cannot show shadows (Kennedy, 1993).

5Hering’s ‘Outlined’ Shadow

Hering (1874) might contend that for the cup’s cast shadow in (a), shadow perception fails in (b) because the penumbra is lost to the dark line (after Goldstein, 2002).

a b

umbra

penumbrapenumbra

umbra

6Outlined Sharp-contoured

Shadow

But shadows without penumbras (a, adapted from Mooney, 1957) convey information about a girl’s face, and dark lines in (b) impair percept of the same face.

a b

Note that shadowed areas in (b) are darker than illuminated areas (Cavanagh & Leclerc, 1989), yet shape-from-shadow perception is diminished.

7Shape-from-Shadow: Figure-

Ground?Here is another shape-from-shadowed face (adapted from Mooney, 1957), shown with a color image.

8Lines, Contours, and Kinds of

BordersHere are different kinds of figure-ground segregations along borders (Kennedy, Juricevic, & Bai, 2003):

figure-figure along a line

figure-figure along a contour figure-ground along a contour

ground-figure-ground along a line

figure-ground-figure along a line

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c

Theory of Dark Lines and Shadows

Line version (a), negative (c), and Hering-dark-line version (d) all have negative contours (light-to-dark from shadow to non-shadow), and all three fail to show the face in (b).

So it may be the dark line’s negative contour bordering the shadow in (d) that diminishes shape-from-shadow perception – a ‘border-polarity’ hypothesis.

dba

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Alternatively, dark lines in (a) and (b) may impair shape-from-shadow perception because a line has two contours rather than one (c) – a ‘number-of-contours’ account.

Alternative Theory

a b c

The number-of-contours account is based on an ‘axis’ theory of a line (Kennedy, 1993).

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a b c

Kennedy & Bai (2000): Polarity vs. Number-of-contours

Border-polarity predicts the face in (a) should be easy to see, but number-of-contours predicts otherwise.Results = (a) and (c) were equally easy, only (b) difficult, supporting border-polarity.

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An arm-and-hand is relatively easy to see in gray-line version (a) but not in black-line version (b). It is evident in no-line version (c). So only dark line fails.

Demonstrations for K & B (2000)

arm-and-hand (adapted from Kennedy, 1988)

a b c

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figure

ground

Kennedy & Bai (2004): Testing Belongingness

wire or

crack

ground

figure

ba c

A ‘belongingness’ hypothesis may propose that a dark-to-light shadow border has to belong to both the shadowed and the illuminated areas to allow perception of a continuous face bearing the shadow.

The purpose of K & B (2004) is to test this hypothesis.

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Result = the dot-grating figure showed the face, possibly because on average the border polarity is positive, despite negative polarity along the final dots.

K & B (2004)’s Dotted Shadow for Belongingness Test

final dots

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When two areas share a common border, it is said that the common border belongs to the closer area – the figure; it does not belong to the area that is farther away – the ground (e.g., Nakayama et al., 1989).

If so, when stereo depth indicates that the bordering elements belong only to a closer, shadow area or a closer, non-shadow area, the inappropriate belongingness should impair shape-from-shadow perception.

Rationale for K & B (2004) Stereo Test

16Stereo Stimuli

Only right eye sees

smaller dots

unpaired dotsmost shadow

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Only left eye sees smaller dots

unpaired dotsmost shadow

Stereo Stimuli (Continued)

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Both eyes see smaller dots

at the shadow border

binocular percept

same stereo depth

Stereo Stimuli (Control)

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Results = in binocular percept, positive images showed the face in shadow, even when stereo depth signaled different belongingness of the border.

The results rejected predictions from belongingness, but supported border-polarity.

Negatives did not show the face.

Stereo Stimuli (Negative Control)

20ConclusionsA Hering line added along a shadow border may have impaired shape-from-shadow perception because of negative polarity of its contour bordering the shadow.

There are 8 kinds of borders in a visual display that can cause perception of surfaces. These include luminance/spectral, monocular/binocular, and static/moving borders (Kennedy et al., 2003). Among these 8 combinations, only luminance matters for shape-from-shadow: From shadow to non-shadow the border has to be from darker to lighter to allow perception of shapes from shadows.