Abstract

Our ability to localize objects in three-dimensional space relies primarily on the stereoscopic capability of our visual system. It is generally believed that parallax disparities in the retinal images in our two eyes are required for experiencing stereovision. Traditionally, parallax disparities refer to points that are well defined within the objects, such as edges or boundaries. Shadows can create abrupt luminance changes in the scene but are neither edges nor boundaries, and their position varies with the position of the light sources. It is demonstrated that retinal images with no parallax disparity but with different shadows are fused stereoscopically, imparting depth perception to the imaged scene. Shadows are shown to be an important, hitherto undescribed stereoscopic cue for depth perception.

© 1989 Optical Society of America

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References

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  1. Leonardo da Vinci, Trattato della Pittura (Langlois, Paris, 1651).
  2. C. Wheatstone, “On some remarkable and hitherto unobserved phenomena of binocular vision,” Philos. Trans. 128, 371–394 (1838).
    [Crossref]
  3. K. N. Ogle, “Spatial localization through binocular vision,” in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 4, p. 271–320.
  4. H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Hamburg, 1910), Chap. 3. (1866).
  5. L. Kaufman, “On the nature of binocular disparity,” Am. J. Psychol. 77, 393–402 (1964).
    [Crossref] [PubMed]
  6. L. Kaufman, “Some new stereoscopic phenomena and their implications for the theory of stereopsis,” Am. J. Psychol. 78, 1–20 (1965).
    [Crossref] [PubMed]
  7. L. Kaufman, C. Pitblado, “Further observations on the nature of effective binocular disparities,” Am. J. Psychol. 78, 379–391 (1965).
    [Crossref] [PubMed]
  8. D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
    [Crossref] [PubMed]
  9. The position of the light sources is arbitrary, not necessarily symmetrically located around the camera, as illustrated in Fig. 1. For example, a setup organized as light source–light source–camera will record the same shadows as one ordered light source–camera–camera. This correspondence is easy to derive graphically and analytically. The correspondence is exact if distances between the light sources are small compared with the distance to the scene.
  10. Some movements of the Moon (librations) can present a slightly different view from Earth. Libration in longitude is slow, and therefore the angular change in 25 h is insignificant (~1°). Diurnal libration, evidenced by photographing the Moon when it is at different locations in the sky, is of the same order of magnitude.
  11. B. K. P. Horn, R. J. Woodham, W. M. Silver, “Determining shape and reflectance using multiple images,” Artificial Intelligence Memo 490 (Massachusetts Institute of Technology, Cambridge, Mass., 1978).
  12. R. J. Woodham, “Photometric stereo: A reflectance map technique for determining surface orientation from image intensity,” in Image Understanding Systems and Industrial Application I, R. Nevatia, ed., Proc. Soc. Photo-Opt. Instrum. Eng.155, 136–143 (1978).
    [Crossref]
  13. A solid of revolution, illuminated with a finite light source, will cast a shadow on itself so that about half the object will be illuminated and the other half will be in darkness. The line dividing these two zones is called the terminator. The position of the terminator will therefore change with the position of the light source. The angular extension of the dark side, subtended at the viewer’s location, will change accordingly. These shadow disparities were intentionally suppressed by using a translucent bulb. They are, however, present in Fig. 3, and we believe that they are responsible for the curvature that can be perceived stereoscopically along the terminator of the Moon.

1976 (1)

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[Crossref] [PubMed]

1965 (2)

L. Kaufman, “Some new stereoscopic phenomena and their implications for the theory of stereopsis,” Am. J. Psychol. 78, 1–20 (1965).
[Crossref] [PubMed]

L. Kaufman, C. Pitblado, “Further observations on the nature of effective binocular disparities,” Am. J. Psychol. 78, 379–391 (1965).
[Crossref] [PubMed]

1964 (1)

L. Kaufman, “On the nature of binocular disparity,” Am. J. Psychol. 77, 393–402 (1964).
[Crossref] [PubMed]

1838 (1)

C. Wheatstone, “On some remarkable and hitherto unobserved phenomena of binocular vision,” Philos. Trans. 128, 371–394 (1838).
[Crossref]

da Vinci, Leonardo

Leonardo da Vinci, Trattato della Pittura (Langlois, Paris, 1651).

Horn, B. K. P.

B. K. P. Horn, R. J. Woodham, W. M. Silver, “Determining shape and reflectance using multiple images,” Artificial Intelligence Memo 490 (Massachusetts Institute of Technology, Cambridge, Mass., 1978).

Kaufman, L.

L. Kaufman, “Some new stereoscopic phenomena and their implications for the theory of stereopsis,” Am. J. Psychol. 78, 1–20 (1965).
[Crossref] [PubMed]

L. Kaufman, C. Pitblado, “Further observations on the nature of effective binocular disparities,” Am. J. Psychol. 78, 379–391 (1965).
[Crossref] [PubMed]

L. Kaufman, “On the nature of binocular disparity,” Am. J. Psychol. 77, 393–402 (1964).
[Crossref] [PubMed]

Marr, D.

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[Crossref] [PubMed]

Ogle, K. N.

K. N. Ogle, “Spatial localization through binocular vision,” in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 4, p. 271–320.

Pitblado, C.

L. Kaufman, C. Pitblado, “Further observations on the nature of effective binocular disparities,” Am. J. Psychol. 78, 379–391 (1965).
[Crossref] [PubMed]

Poggio, T.

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[Crossref] [PubMed]

Silver, W. M.

B. K. P. Horn, R. J. Woodham, W. M. Silver, “Determining shape and reflectance using multiple images,” Artificial Intelligence Memo 490 (Massachusetts Institute of Technology, Cambridge, Mass., 1978).

von Helmholtz, H.

H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Hamburg, 1910), Chap. 3. (1866).

Wheatstone, C.

C. Wheatstone, “On some remarkable and hitherto unobserved phenomena of binocular vision,” Philos. Trans. 128, 371–394 (1838).
[Crossref]

Woodham, R. J.

R. J. Woodham, “Photometric stereo: A reflectance map technique for determining surface orientation from image intensity,” in Image Understanding Systems and Industrial Application I, R. Nevatia, ed., Proc. Soc. Photo-Opt. Instrum. Eng.155, 136–143 (1978).
[Crossref]

B. K. P. Horn, R. J. Woodham, W. M. Silver, “Determining shape and reflectance using multiple images,” Artificial Intelligence Memo 490 (Massachusetts Institute of Technology, Cambridge, Mass., 1978).

Am. J. Psychol. (3)

L. Kaufman, “On the nature of binocular disparity,” Am. J. Psychol. 77, 393–402 (1964).
[Crossref] [PubMed]

L. Kaufman, “Some new stereoscopic phenomena and their implications for the theory of stereopsis,” Am. J. Psychol. 78, 1–20 (1965).
[Crossref] [PubMed]

L. Kaufman, C. Pitblado, “Further observations on the nature of effective binocular disparities,” Am. J. Psychol. 78, 379–391 (1965).
[Crossref] [PubMed]

Philos. Trans. (1)

C. Wheatstone, “On some remarkable and hitherto unobserved phenomena of binocular vision,” Philos. Trans. 128, 371–394 (1838).
[Crossref]

Science (1)

D. Marr, T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
[Crossref] [PubMed]

Other (8)

The position of the light sources is arbitrary, not necessarily symmetrically located around the camera, as illustrated in Fig. 1. For example, a setup organized as light source–light source–camera will record the same shadows as one ordered light source–camera–camera. This correspondence is easy to derive graphically and analytically. The correspondence is exact if distances between the light sources are small compared with the distance to the scene.

Some movements of the Moon (librations) can present a slightly different view from Earth. Libration in longitude is slow, and therefore the angular change in 25 h is insignificant (~1°). Diurnal libration, evidenced by photographing the Moon when it is at different locations in the sky, is of the same order of magnitude.

B. K. P. Horn, R. J. Woodham, W. M. Silver, “Determining shape and reflectance using multiple images,” Artificial Intelligence Memo 490 (Massachusetts Institute of Technology, Cambridge, Mass., 1978).

R. J. Woodham, “Photometric stereo: A reflectance map technique for determining surface orientation from image intensity,” in Image Understanding Systems and Industrial Application I, R. Nevatia, ed., Proc. Soc. Photo-Opt. Instrum. Eng.155, 136–143 (1978).
[Crossref]

A solid of revolution, illuminated with a finite light source, will cast a shadow on itself so that about half the object will be illuminated and the other half will be in darkness. The line dividing these two zones is called the terminator. The position of the terminator will therefore change with the position of the light source. The angular extension of the dark side, subtended at the viewer’s location, will change accordingly. These shadow disparities were intentionally suppressed by using a translucent bulb. They are, however, present in Fig. 3, and we believe that they are responsible for the curvature that can be perceived stereoscopically along the terminator of the Moon.

K. N. Ogle, “Spatial localization through binocular vision,” in The Eye, H. Davson, ed. (Academic, New York, 1962), Vol. 4, p. 271–320.

H. von Helmholtz, Handbuch der Physiologischen Optik (Voss, Hamburg, 1910), Chap. 3. (1866).

Leonardo da Vinci, Trattato della Pittura (Langlois, Paris, 1651).

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Figures (3)

Fig. 1
Fig. 1

The same pair of photographs is obtained when an object with revolution symmetry is photographed against a background using (a) two cameras and one light source or (b) one camera in place of the light source and two light sources in place of the two cameras. The pairs are identical regardless of the location of the cameras (light sources) with respect to the light sources (cameras). All photographs in this paper were taken with both light sources to the left-hand side of the viewer.

Fig. 2
Fig. 2

Experiencing stereoscopic depth of an object without parallax disparity. Shadow stereopsis is isolated when viewing an object photographed as depicted in Fig. 1b (light sources at the left-hand side). The electric bulb is viewed binocularly in vivid depth, arising solely from the different shadows.

Fig. 3
Fig. 3

Depth information encoded in the shadows alone of Moon craters photographed approximately 25 h apart (right-hand image: September/11/1986, 9:50 p.m.; left-hand image: September/12/1986, 10:30 p.m.; telescope pointed to southwest; Boston, Massachusetts). The Sun in two different locations served as the light source. To experience the stereoscopic depth effect, gaze at the two images until they fuse. Observe the right-hand panel with the right eye and the left-hand panel with the left eye. The two crosses may be used to facilitate fusion.

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