Abstract

Objects with bilateral symmetry, such as faces, animal shapes, and many man-made objects, play an important role in everyday vision. Because they occur frequently, it is reasonable to conjecture that the brain may be specialized for symmetric objects. We investigated whether the human visual system processes three-dimensional (3D) symmetric objects more efficiently than asymmetric ones. Human subjects, having learned a symmetric wire object, discriminated which of two distorted copies of the learned object was more similar to the learned one. The distortion was achieved by adding 3D Gaussian positional perturbations at the vertices of the wire object. In the asymmetric condition, the perturbation was independent from one vertex to the next. In the symmetric condition, independent perturbations were added to only half of the object; perturbations on the other half retained the symmetry of the object. We found that subjects’ thresholds were higher in the symmetric condition. However, since the perturbation in the symmetric condition was correlated, a stimulus image provided less information in the symmetric condition. Taking this into consideration, an ideal-observer analysis revealed that subjects were actually more efficient at discriminating symmetric objects. This reversal in interpretation underscores the importance of ideal-observer analysis. A completely opposite, and wrong, conclusion would have been drawn from analyzing only human discrimination thresholds. Given the same amount of information, the visual system is actually better able to discriminate symmetric objects than asymmetric ones.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
    [CrossRef] [PubMed]
  2. J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
    [CrossRef] [PubMed]
  3. M. Leyton, Symmetry, Causality, Mind (MIT, Cambridge, Mass., 1992).
  4. H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
    [PubMed]
  5. P. A. Parsons, “Fluctuating asymmetry: an epigenetic measure of stress,” Biol. Rev. 65, 131–145 (1990).
    [CrossRef] [PubMed]
  6. A. P. Møller, “Female swallow preference for symmetrical male sexual ornaments,” Nature 357, 238–240 (1992).
    [CrossRef] [PubMed]
  7. R. Thornhill, “Fluctuating asymmetry and the mating system of the Japanese scorpionfly Panorpa japonica,” Anim. Behav. 44, 867–879 (1992).
    [CrossRef]
  8. A. L. R. Thomas, “On avian asymmetry: the evidence of natural selection for symmetrical tails and wings in birds,” Proc. R. Soc. London Ser. B 252, 245–251 (1993).
    [CrossRef]
  9. A. L. R. Thomas, “The aerodynamic costs of asymmetry in the wings and tails of birds: asymmetric birds can’t fly round tight corners,” Proc. R. Soc. London Ser. B 254, 181–189 (1993).
    [CrossRef]
  10. K. Grammer, R. Thornhill, “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness,” J. Comp. Psychol. 108, 233–242 (1994).
    [CrossRef] [PubMed]
  11. P. J. Watson, R. Thornhill, “Fluctuating asymmetry and sexual selection,” Trends Ecol. Evol. 9, 21–25 (1994).
    [CrossRef] [PubMed]
  12. M. Enquist, A. Arak, “Symmetry, beauty and evolution,” Nature 372, 169–172 (1994).
    [CrossRef] [PubMed]
  13. R. Thornhill, S. W. Gangestad, “Human fluctuating asymmetry and sexual behavior,” Psych. Sci. 5, 297–302 (1994).
  14. G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).
  15. A. P. Møller, R. Thornhill, “Bilateral symmetry and sexual selection: a metaanalysis,” Am. Nat. 151, 174–192 (1998).
    [CrossRef]
  16. C. W. Tyler, ed., Human Symmetry Perception and Its Computational Analysis [VSP (VNU Science Press) BV, Utrecht, The Netherlands, 1996].
  17. D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
    [CrossRef]
  18. B. Jenkins, “Component processes in the perception of bilaterally symmetric dot textures,” J. Exp. Psychol. 9, 258–269 (1983).
  19. B. S. Tjan, Z. Liu, “Symmetry discrimination of faces,” in ARVO Abstracts. Investigative Ophthalmology and Visual Science, Vol. 39, Suppl. 4 (Association for Research in Vision and Ophthalmology, Fort Lauderdale, Fla., 1998), p. s170.
  20. Z. Liu, B. S. Tjan, “Near-bilateral symmetry impedes symmetry discrimination,” in Proceedings of the European Conference on Visual Perception, Vol. 27 (Suppl.) (Pion Ltd., London, 1998), p. 6.
  21. D. C. Knill, D. Kersten, “Ideal perceptual observers for computation, psychophysics and neural networks,” in Pattern Recognition by Man and Machine, R. Watt, ed., Vol. 14 of Vision and Visual Dysfunction, J. Cronly-Dillon, gen. ed. (MacMillan, London, 1991), Chap. 7.
  22. R. A. Eagle, A. Blake, “Two-dimensional constraints on three-dimensional structure from motion tasks,” Vision Res. 35, 2927–2941 (1995).
    [CrossRef] [PubMed]
  23. Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
    [CrossRef] [PubMed]
  24. B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
    [CrossRef] [PubMed]
  25. Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
    [CrossRef] [PubMed]
  26. W. Knecht, Z. Liu, D. Kersten, “Symmetry detection for 2D projections of 3D wire objects,” in ARVO Abstracts: Investigative Ophthalmology, Vol. 34, Suppl. 4 (Association for Research in Vision and Ophthalmology, Rockville, Md., 1993), p. s1867.
  27. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, Huntington, N.Y., 1974).
  28. A. Burgess, H. B. Barlow, “The precision of numerosity discrimination in arrays of random dots,” Vision Res. 23, 811–820 (1983).
    [CrossRef] [PubMed]
  29. H. B. Barlow, “The efficiency of detecting changes of density in random dot patterns,” Vision Res. 18, 637–650 (1978).
    [CrossRef]
  30. A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
    [CrossRef] [PubMed]
  31. H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979).
    [CrossRef] [PubMed]
  32. T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
    [CrossRef] [PubMed]
  33. P. Wenderoth, “The effects on bilateral-symmetry detection of multiple symmetry, near symmetry, and axis orientation,” Perception 26, 891–904 (1997).
    [CrossRef] [PubMed]
  34. R. A. Johnstone, “Female preference for symmetrical males as a by-product of selection for mate recognition,” Nature 372, 172–175 (1994).
    [CrossRef] [PubMed]
  35. T. Poggio, T. Vetter, “Recognition and structure from one 2D model view: observations on prototypes, objects classes and symmetries,” (MIT, Cambridge, Mass., 1992).
  36. P. Verghese, S. L. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
    [CrossRef] [PubMed]
  37. I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
    [CrossRef]
  38. Z. Liu, D. Kersten, “2D observers for human 3D object recognition?” Special issue on Models of Recognition, Vision Res. 38, 2507–2519 (1998).
    [CrossRef] [PubMed]

1999 (1)

Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
[CrossRef] [PubMed]

1998 (4)

I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
[CrossRef]

Z. Liu, D. Kersten, “2D observers for human 3D object recognition?” Special issue on Models of Recognition, Vision Res. 38, 2507–2519 (1998).
[CrossRef] [PubMed]

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

A. P. Møller, R. Thornhill, “Bilateral symmetry and sexual selection: a metaanalysis,” Am. Nat. 151, 174–192 (1998).
[CrossRef]

1997 (1)

P. Wenderoth, “The effects on bilateral-symmetry detection of multiple symmetry, near symmetry, and axis orientation,” Perception 26, 891–904 (1997).
[CrossRef] [PubMed]

1996 (2)

P. Verghese, S. L. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
[CrossRef] [PubMed]

1995 (4)

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
[CrossRef] [PubMed]

R. A. Eagle, A. Blake, “Two-dimensional constraints on three-dimensional structure from motion tasks,” Vision Res. 35, 2927–2941 (1995).
[CrossRef] [PubMed]

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

1994 (6)

K. Grammer, R. Thornhill, “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness,” J. Comp. Psychol. 108, 233–242 (1994).
[CrossRef] [PubMed]

P. J. Watson, R. Thornhill, “Fluctuating asymmetry and sexual selection,” Trends Ecol. Evol. 9, 21–25 (1994).
[CrossRef] [PubMed]

M. Enquist, A. Arak, “Symmetry, beauty and evolution,” Nature 372, 169–172 (1994).
[CrossRef] [PubMed]

R. Thornhill, S. W. Gangestad, “Human fluctuating asymmetry and sexual behavior,” Psych. Sci. 5, 297–302 (1994).

R. A. Johnstone, “Female preference for symmetrical males as a by-product of selection for mate recognition,” Nature 372, 172–175 (1994).
[CrossRef] [PubMed]

T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

1993 (2)

A. L. R. Thomas, “On avian asymmetry: the evidence of natural selection for symmetrical tails and wings in birds,” Proc. R. Soc. London Ser. B 252, 245–251 (1993).
[CrossRef]

A. L. R. Thomas, “The aerodynamic costs of asymmetry in the wings and tails of birds: asymmetric birds can’t fly round tight corners,” Proc. R. Soc. London Ser. B 254, 181–189 (1993).
[CrossRef]

1992 (2)

A. P. Møller, “Female swallow preference for symmetrical male sexual ornaments,” Nature 357, 238–240 (1992).
[CrossRef] [PubMed]

R. Thornhill, “Fluctuating asymmetry and the mating system of the Japanese scorpionfly Panorpa japonica,” Anim. Behav. 44, 867–879 (1992).
[CrossRef]

1990 (1)

P. A. Parsons, “Fluctuating asymmetry: an epigenetic measure of stress,” Biol. Rev. 65, 131–145 (1990).
[CrossRef] [PubMed]

1983 (3)

B. Jenkins, “Component processes in the perception of bilaterally symmetric dot textures,” J. Exp. Psychol. 9, 258–269 (1983).

A. Burgess, H. B. Barlow, “The precision of numerosity discrimination in arrays of random dots,” Vision Res. 23, 811–820 (1983).
[CrossRef] [PubMed]

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

1979 (1)

H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979).
[CrossRef] [PubMed]

1978 (1)

H. B. Barlow, “The efficiency of detecting changes of density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

1977 (1)

D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
[CrossRef]

1970 (1)

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

Arak, A.

M. Enquist, A. Arak, “Symmetry, beauty and evolution,” Nature 372, 169–172 (1994).
[CrossRef] [PubMed]

Bailit, H. I.

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

Barlow, H. B.

A. Burgess, H. B. Barlow, “The precision of numerosity discrimination in arrays of random dots,” Vision Res. 23, 811–820 (1983).
[CrossRef] [PubMed]

H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979).
[CrossRef] [PubMed]

H. B. Barlow, “The efficiency of detecting changes of density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

Blake, A.

R. A. Eagle, A. Blake, “Two-dimensional constraints on three-dimensional structure from motion tasks,” Vision Res. 35, 2927–2941 (1995).
[CrossRef] [PubMed]

Braje, W. L.

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

Bülthoff, H. H.

I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
[CrossRef]

T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

Bülthoff, I.

I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
[CrossRef]

Burgess, A.

A. Burgess, H. B. Barlow, “The precision of numerosity discrimination in arrays of random dots,” Vision Res. 23, 811–820 (1983).
[CrossRef] [PubMed]

Carmody, D. P.

D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
[CrossRef]

Eagle, R. A.

R. A. Eagle, A. Blake, “Two-dimensional constraints on three-dimensional structure from motion tasks,” Vision Res. 35, 2927–2941 (1995).
[CrossRef] [PubMed]

Enquist, M.

M. Enquist, A. Arak, “Symmetry, beauty and evolution,” Nature 372, 169–172 (1994).
[CrossRef] [PubMed]

Gangestad, S. W.

R. Thornhill, S. W. Gangestad, “Human fluctuating asymmetry and sexual behavior,” Psych. Sci. 5, 297–302 (1994).

Grady, J. M.

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

Grammer, K.

K. Grammer, R. Thornhill, “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness,” J. Comp. Psychol. 108, 233–242 (1994).
[CrossRef] [PubMed]

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, Huntington, N.Y., 1974).

Jenkins, B.

B. Jenkins, “Component processes in the perception of bilaterally symmetric dot textures,” J. Exp. Psychol. 9, 258–269 (1983).

Johnstone, R. A.

R. A. Johnstone, “Female preference for symmetrical males as a by-product of selection for mate recognition,” Nature 372, 172–175 (1994).
[CrossRef] [PubMed]

Kappers, A. M. L.

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
[CrossRef] [PubMed]

Kersten, D.

Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
[CrossRef] [PubMed]

Z. Liu, D. Kersten, “2D observers for human 3D object recognition?” Special issue on Models of Recognition, Vision Res. 38, 2507–2519 (1998).
[CrossRef] [PubMed]

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

W. Knecht, Z. Liu, D. Kersten, “Symmetry detection for 2D projections of 3D wire objects,” in ARVO Abstracts: Investigative Ophthalmology, Vol. 34, Suppl. 4 (Association for Research in Vision and Ophthalmology, Rockville, Md., 1993), p. s1867.

D. C. Knill, D. Kersten, “Ideal perceptual observers for computation, psychophysics and neural networks,” in Pattern Recognition by Man and Machine, R. Watt, ed., Vol. 14 of Vision and Visual Dysfunction, J. Cronly-Dillon, gen. ed. (MacMillan, London, 1991), Chap. 7.

Knecht, W.

W. Knecht, Z. Liu, D. Kersten, “Symmetry detection for 2D projections of 3D wire objects,” in ARVO Abstracts: Investigative Ophthalmology, Vol. 34, Suppl. 4 (Association for Research in Vision and Ophthalmology, Rockville, Md., 1993), p. s1867.

Knill, D. C.

Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
[CrossRef] [PubMed]

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

D. C. Knill, D. Kersten, “Ideal perceptual observers for computation, psychophysics and neural networks,” in Pattern Recognition by Man and Machine, R. Watt, ed., Vol. 14 of Vision and Visual Dysfunction, J. Cronly-Dillon, gen. ed. (MacMillan, London, 1991), Chap. 7.

Koenderink, J. J.

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
[CrossRef] [PubMed]

Legge, G. E.

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

Leyton, M.

M. Leyton, Symmetry, Causality, Mind (MIT, Cambridge, Mass., 1992).

Liu, Z.

Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
[CrossRef] [PubMed]

Z. Liu, D. Kersten, “2D observers for human 3D object recognition?” Special issue on Models of Recognition, Vision Res. 38, 2507–2519 (1998).
[CrossRef] [PubMed]

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

Z. Liu, B. S. Tjan, “Near-bilateral symmetry impedes symmetry discrimination,” in Proceedings of the European Conference on Visual Perception, Vol. 27 (Suppl.) (Pion Ltd., London, 1998), p. 6.

W. Knecht, Z. Liu, D. Kersten, “Symmetry detection for 2D projections of 3D wire objects,” in ARVO Abstracts: Investigative Ophthalmology, Vol. 34, Suppl. 4 (Association for Research in Vision and Ophthalmology, Rockville, Md., 1993), p. s1867.

B. S. Tjan, Z. Liu, “Symmetry discrimination of faces,” in ARVO Abstracts. Investigative Ophthalmology and Visual Science, Vol. 39, Suppl. 4 (Association for Research in Vision and Ophthalmology, Fort Lauderdale, Fla., 1998), p. s170.

Locher, P. J.

D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
[CrossRef]

MacLean, C. J.

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

Møller, A. P.

A. P. Møller, R. Thornhill, “Bilateral symmetry and sexual selection: a metaanalysis,” Am. Nat. 151, 174–192 (1998).
[CrossRef]

A. P. Møller, “Female swallow preference for symmetrical male sexual ornaments,” Nature 357, 238–240 (1992).
[CrossRef] [PubMed]

Niswander, J. D.

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

Nodine, C. F.

D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
[CrossRef]

Parsons, P. A.

P. A. Parsons, “Fluctuating asymmetry: an epigenetic measure of stress,” Biol. Rev. 65, 131–145 (1990).
[CrossRef] [PubMed]

Pelli, D. G.

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Poggio, T.

T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

T. Poggio, T. Vetter, “Recognition and structure from one 2D model view: observations on prototypes, objects classes and symmetries,” (MIT, Cambridge, Mass., 1992).

Profitt, F.

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

Reeves, B. C.

H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979).
[CrossRef] [PubMed]

Rhodes, G.

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

Sinha, P.

I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
[CrossRef]

Stone, S. L.

P. Verghese, S. L. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

Sumich, A.

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, Huntington, N.Y., 1974).

Thomas, A. L. R.

A. L. R. Thomas, “The aerodynamic costs of asymmetry in the wings and tails of birds: asymmetric birds can’t fly round tight corners,” Proc. R. Soc. London Ser. B 254, 181–189 (1993).
[CrossRef]

A. L. R. Thomas, “On avian asymmetry: the evidence of natural selection for symmetrical tails and wings in birds,” Proc. R. Soc. London Ser. B 252, 245–251 (1993).
[CrossRef]

Thornhill, R.

A. P. Møller, R. Thornhill, “Bilateral symmetry and sexual selection: a metaanalysis,” Am. Nat. 151, 174–192 (1998).
[CrossRef]

R. Thornhill, S. W. Gangestad, “Human fluctuating asymmetry and sexual behavior,” Psych. Sci. 5, 297–302 (1994).

P. J. Watson, R. Thornhill, “Fluctuating asymmetry and sexual selection,” Trends Ecol. Evol. 9, 21–25 (1994).
[CrossRef] [PubMed]

K. Grammer, R. Thornhill, “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness,” J. Comp. Psychol. 108, 233–242 (1994).
[CrossRef] [PubMed]

R. Thornhill, “Fluctuating asymmetry and the mating system of the Japanese scorpionfly Panorpa japonica,” Anim. Behav. 44, 867–879 (1992).
[CrossRef]

Tjan, B. S.

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

Z. Liu, B. S. Tjan, “Near-bilateral symmetry impedes symmetry discrimination,” in Proceedings of the European Conference on Visual Perception, Vol. 27 (Suppl.) (Pion Ltd., London, 1998), p. 6.

B. S. Tjan, Z. Liu, “Symmetry discrimination of faces,” in ARVO Abstracts. Investigative Ophthalmology and Visual Science, Vol. 39, Suppl. 4 (Association for Research in Vision and Ophthalmology, Fort Lauderdale, Fla., 1998), p. s170.

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
[CrossRef] [PubMed]

Verghese, P.

P. Verghese, S. L. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

Vetter, T.

T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

T. Poggio, T. Vetter, “Recognition and structure from one 2D model view: observations on prototypes, objects classes and symmetries,” (MIT, Cambridge, Mass., 1992).

Watson, A. B.

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

Watson, P. J.

P. J. Watson, R. Thornhill, “Fluctuating asymmetry and sexual selection,” Trends Ecol. Evol. 9, 21–25 (1994).
[CrossRef] [PubMed]

Wenderoth, P.

P. Wenderoth, “The effects on bilateral-symmetry detection of multiple symmetry, near symmetry, and axis orientation,” Perception 26, 891–904 (1997).
[CrossRef] [PubMed]

Workman, P. L.

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

Am. Nat. (1)

A. P. Møller, R. Thornhill, “Bilateral symmetry and sexual selection: a metaanalysis,” Am. Nat. 151, 174–192 (1998).
[CrossRef]

Anim. Behav. (1)

R. Thornhill, “Fluctuating asymmetry and the mating system of the Japanese scorpionfly Panorpa japonica,” Anim. Behav. 44, 867–879 (1992).
[CrossRef]

Biol. Rev. (1)

P. A. Parsons, “Fluctuating asymmetry: an epigenetic measure of stress,” Biol. Rev. 65, 131–145 (1990).
[CrossRef] [PubMed]

Curr. Biol. (1)

T. Vetter, T. Poggio, H. H. Bülthoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

Hum. Biol. (1)

H. I. Bailit, P. L. Workman, J. D. Niswander, C. J. MacLean, “Dental asymmetry as an indicator of genetic and environmental conditions in human populations,” Hum. Biol. 42, 626–638 (1970).
[PubMed]

J. Comp. Psychol. (1)

K. Grammer, R. Thornhill, “Human (Homo sapiens) facial attractiveness and sexual selection: the role of symmetry and averageness,” J. Comp. Psychol. 108, 233–242 (1994).
[CrossRef] [PubMed]

J. Exp. Psychol. (1)

B. Jenkins, “Component processes in the perception of bilaterally symmetric dot textures,” J. Exp. Psychol. 9, 258–269 (1983).

Nat. Neurosci. (1)

I. Bülthoff, H. H. Bülthoff, P. Sinha, “Top-down influences on stereoscopic depth-perception,” Nat. Neurosci. 1, 254–257 (1998).
[CrossRef]

Nature (4)

M. Enquist, A. Arak, “Symmetry, beauty and evolution,” Nature 372, 169–172 (1994).
[CrossRef] [PubMed]

A. P. Møller, “Female swallow preference for symmetrical male sexual ornaments,” Nature 357, 238–240 (1992).
[CrossRef] [PubMed]

R. A. Johnstone, “Female preference for symmetrical males as a by-product of selection for mate recognition,” Nature 372, 172–175 (1994).
[CrossRef] [PubMed]

P. Verghese, S. L. Stone, “Perceived visual speed constrained by image segmentation,” Nature 381, 161–163 (1996).
[CrossRef] [PubMed]

Percept. Mot. Skills (1)

D. P. Carmody, C. F. Nodine, P. J. Locher, “Global detection of symmetry,” Percept. Mot. Skills 45, 239–249 (1977).
[CrossRef]

Percept. Psychophys. (2)

A. B. Watson, D. G. Pelli, “QUEST: a Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Pictorial surface attitude and local depth comparisons,” Percept. Psychophys. 58, 163–173 (1996).
[CrossRef] [PubMed]

Perception (2)

J. J. Koenderink, A. J. van Doorn, A. M. L. Kappers, “Depth relief,” Perception 24, 115–126 (1995).
[CrossRef] [PubMed]

P. Wenderoth, “The effects on bilateral-symmetry detection of multiple symmetry, near symmetry, and axis orientation,” Perception 26, 891–904 (1997).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (2)

A. L. R. Thomas, “On avian asymmetry: the evidence of natural selection for symmetrical tails and wings in birds,” Proc. R. Soc. London Ser. B 252, 245–251 (1993).
[CrossRef]

A. L. R. Thomas, “The aerodynamic costs of asymmetry in the wings and tails of birds: asymmetric birds can’t fly round tight corners,” Proc. R. Soc. London Ser. B 254, 181–189 (1993).
[CrossRef]

Psych. Sci. (1)

R. Thornhill, S. W. Gangestad, “Human fluctuating asymmetry and sexual behavior,” Psych. Sci. 5, 297–302 (1994).

Psychon. Bull. Rev. (1)

G. Rhodes, F. Profitt, J. M. Grady, A. Sumich, “Facial symmetry and the perception of beauty,” Psychon. Bull. Rev. 5, 150–163 (1998).

Trends Ecol. Evol. (1)

P. J. Watson, R. Thornhill, “Fluctuating asymmetry and sexual selection,” Trends Ecol. Evol. 9, 21–25 (1994).
[CrossRef] [PubMed]

Vision Res. (8)

H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979).
[CrossRef] [PubMed]

A. Burgess, H. B. Barlow, “The precision of numerosity discrimination in arrays of random dots,” Vision Res. 23, 811–820 (1983).
[CrossRef] [PubMed]

H. B. Barlow, “The efficiency of detecting changes of density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

R. A. Eagle, A. Blake, “Two-dimensional constraints on three-dimensional structure from motion tasks,” Vision Res. 35, 2927–2941 (1995).
[CrossRef] [PubMed]

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

B. S. Tjan, W. L. Braje, G. E. Legge, D. Kersten, “Hu-man efficiency for recognizing 3-D objects in luminance noise,” Vision Res. 35, 3053–3070 (1995).
[CrossRef] [PubMed]

Z. Liu, D. Kersten, D. C. Knill, “Dissociating stimulus information from internal representation—a case study in object recognition,” Vision Res. 39, 603–612 (1999).
[CrossRef] [PubMed]

Z. Liu, D. Kersten, “2D observers for human 3D object recognition?” Special issue on Models of Recognition, Vision Res. 38, 2507–2519 (1998).
[CrossRef] [PubMed]

Other (8)

W. Knecht, Z. Liu, D. Kersten, “Symmetry detection for 2D projections of 3D wire objects,” in ARVO Abstracts: Investigative Ophthalmology, Vol. 34, Suppl. 4 (Association for Research in Vision and Ophthalmology, Rockville, Md., 1993), p. s1867.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Krieger, Huntington, N.Y., 1974).

C. W. Tyler, ed., Human Symmetry Perception and Its Computational Analysis [VSP (VNU Science Press) BV, Utrecht, The Netherlands, 1996].

T. Poggio, T. Vetter, “Recognition and structure from one 2D model view: observations on prototypes, objects classes and symmetries,” (MIT, Cambridge, Mass., 1992).

B. S. Tjan, Z. Liu, “Symmetry discrimination of faces,” in ARVO Abstracts. Investigative Ophthalmology and Visual Science, Vol. 39, Suppl. 4 (Association for Research in Vision and Ophthalmology, Fort Lauderdale, Fla., 1998), p. s170.

Z. Liu, B. S. Tjan, “Near-bilateral symmetry impedes symmetry discrimination,” in Proceedings of the European Conference on Visual Perception, Vol. 27 (Suppl.) (Pion Ltd., London, 1998), p. 6.

D. C. Knill, D. Kersten, “Ideal perceptual observers for computation, psychophysics and neural networks,” in Pattern Recognition by Man and Machine, R. Watt, ed., Vol. 14 of Vision and Visual Dysfunction, J. Cronly-Dillon, gen. ed. (MacMillan, London, 1991), Chap. 7.

M. Leyton, Symmetry, Causality, Mind (MIT, Cambridge, Mass., 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic illustration of a physical shape subspace, where along one dimension (horizontal) the degrees of asymmetry of an object varies and along an orthogonal dimension (vertical) shape varies while symmetry is unchanged. In this paper we ask whether two shapes are equally discriminable along the two axes, respectively, if their physical difference is kept constant (by an ideal observer).

Fig. 2
Fig. 2

Three-dimensional symmetric object from multiple views by rotation around the y axis (top two rows, left to right) and then around the x axis (bottom two rows). These 11 views (the top left, second row right, and bottom right are identical) are called the learned views.

Fig. 3
Fig. 3

Example stimuli in the test stage when objects were distorted versions of the learned symmetric object. (a) Both objects were symmetric after the distortion. (b) Both were asymmetric.

Fig. 4
Fig. 4

Discrimination threshold of 12 subjects when they were correct 75% of the time. The error bars are standard errors between subjects. Note that these error bars cannot directly reflect the statistical significance, since within-subjects analysis is used (and the same for Figs. 5, 6, 7 and 9).

Fig. 5
Fig. 5

Statistical efficiencies for the symmetric versus asymmetric conditions and learned versus novel views. Note that the pattern of symmetric versus asymmetric comparison is completely reversed here in contrast to the threshold performance.

Fig. 6
Fig. 6

Discrimination thresholds for the learned and novel views of the symmetric condition in experiment 1 and of the asymmetric condition in experiment 2.

Fig. 7
Fig. 7

Statistical efficiencies of the symmetric condition in experiment 1 and of the asymmetric condition in experiment 2 for the learned and novel views.

Fig. 8
Fig. 8

Experimental stimuli in the test phase when all the objects were silhouettes.

Fig. 9
Fig. 9

Threshold comparisons between experiment 1 and the silhouette condition of experiment 3. (a) Within-subjects comparison (four subjects). (b) Between-subjects comparison (eight subjects each). There was no significant difference between the silhouette and the shaded conditions.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E=(σdI)2-σt2(σdH)2-σt2,
E=dHdI2.
σt2(σdI)2=σt2+σH2(σdH)2+σH2,

Metrics