Abstract

A problem in space perception concerns how a mobile observer acquires information about the structure of objects. Earlier research derived the optic-flow equations for an eye undergoing pure rotations. It was suggested that, by utilizing three points and two views, one can recover the distance of points and the motion parameters. The radius of the eyeball was the metric unit. Yet the common view regards this problem as indeterminate. We derived a unique solution in the discrete case, which required three points and two views. However, when we observed a single bright point, a substantial amount of visual stability existed. We therefore derived a solution in the differential approach for a single point, which is based on a distinction that we made between mathematical and visual points. Both solutions were checked with a computer simulation and were found to be accurate, supporting the space perception in navigation (SPIN) theory.

© 1994 Optical Society of America

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    [CrossRef]
  2. H. C. Longuet-Higgins, “A computer algorithm for reconstruction of a scene from two projections,” Nature (London) 293, 133–135 (1981).
    [CrossRef]
  3. I. Hadani, G. Ishai, M. Gur, “Visual stability and space perception in monocular vision: mathematical model,” J. Opt. Soc. Am. 70, 60–65 (1980).
    [CrossRef] [PubMed]
  4. A. Z. Meiri, “On monocular perception of 3–D moving objects,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 582–583 (1980).
  5. H. H. Nagel, “On the derivation of 3D rigid point configurations from image sequences,” in IEEE Conference on Pattern Recognition and Image Processing (Institute of Electrical and Electronics Engineers, New York, 1981).
  6. R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of 3–D motion parameters and surface structures of rigid objects,” in Image Understanding 1985–86, W. Richards, S. Ullman, eds. (Albex, Norwood, N.J., 1985), Chap. 6, p. 141.
  7. J. J. Koenderink, “Some theoretical aspects of optic flow,” in Perception and Control of Self-Motion, R. Warren, A. H. Wertheim, eds. (Erlbaum, Hillsdale, N.J., 1990), pp. 53–68.
  8. H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal images,” Proc. R. Soc. London Ser. B 208, 385–387 (1980).
    [CrossRef]
  9. K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinear moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
    [CrossRef]
  10. S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979), p. 199.
  11. J. J. Koenderink, A. J. van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991).
    [CrossRef] [PubMed]
  12. I. Hadani, G. Ishai, B. Julesz, “The autokinetic movement and visual stability,” Invest. Ophthalmol. Vis. Sci. 32, 900 (1991).
  13. S. Jain, “Autokinesis and some conditions of fatigue,” Percept. Mot. Skills 56, 147–154 (1983).
    [CrossRef] [PubMed]
  14. H. B. Barlow, “Three theories of cortical function,” in Developmental Neurobiology of Vision, R. D. Freeman, ed. (Plenum, New York, 1979), p. 5.
  15. I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
    [CrossRef] [PubMed]
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    [CrossRef]
  18. I. Hadani, “Corneal lens goggles and visual space perception,” Appl. Opt. 30, 4136–4147 (1991).
    [CrossRef] [PubMed]
  19. J. J. Koenderink, A. J. van Doorn, “Method of stabilizing the retinal image,” Appl. Opt. 13, 955–961 (1974).
    [CrossRef] [PubMed]
  20. I. Hadani, E. Barta, “The hybrid constraint equation for motion extraction,” Image Vis. Comput. 7, 217–224 (1989).
    [CrossRef]
  21. D. H. Fender, “Torsional movements of the eyeball,” Br. J. Ophthalmol. 39, 65–72 (1956).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. I. Hadani, “Space perception with normal and prosthetic vision,” presented at the meeting of the Society for Information Display, Boston, Mass., May 17–22, 1992.
  29. B. Julesz, Dialogues on Perception (MIT Press, Cambridge, Mass., to be published), dialogue 4.
  30. G. P. Bingham, “Optical flow from eye movement with head immobilized: ‘ocular occlusion’ beyond the nose,” Vision Res. (to be published).
  31. I. Hadani, B. Julesz, “Interpupillary distance and stereoscopic depth perception,” Invest. Ophthalmol. Vis. Sci. 33, 4 (1992).
  32. Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
    [CrossRef] [PubMed]

1992

I. Hadani, B. Julesz, “Interpupillary distance and stereoscopic depth perception,” Invest. Ophthalmol. Vis. Sci. 33, 4 (1992).

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

1991

1989

I. Hadani, E. Barta, “The hybrid constraint equation for motion extraction,” Image Vis. Comput. 7, 217–224 (1989).
[CrossRef]

1984

I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
[CrossRef] [PubMed]

1983

S. Jain, “Autokinesis and some conditions of fatigue,” Percept. Mot. Skills 56, 147–154 (1983).
[CrossRef] [PubMed]

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Vis. Graphics Image Process. 21, 3–20 (1983).
[CrossRef]

1981

H. C. Longuet-Higgins, “A computer algorithm for reconstruction of a scene from two projections,” Nature (London) 293, 133–135 (1981).
[CrossRef]

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinear moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

1980

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

A. Z. Meiri, “On monocular perception of 3–D moving objects,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 582–583 (1980).

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal images,” Proc. R. Soc. London Ser. B 208, 385–387 (1980).
[CrossRef]

I. Hadani, G. Ishai, M. Gur, “Visual stability and space perception in monocular vision: mathematical model,” J. Opt. Soc. Am. 70, 60–65 (1980).
[CrossRef] [PubMed]

1974

1956

1936

S. Hecht, E. U. Mintz, “The visibility of single lines at various illuminations and the retinal basis of visual resolution,” J. Gen. Physiol. 22, 593–612 (1936).
[CrossRef]

Barlow, H. B.

H. B. Barlow, “Three theories of cortical function,” in Developmental Neurobiology of Vision, R. D. Freeman, ed. (Plenum, New York, 1979), p. 5.

Barta, E.

I. Hadani, E. Barta, “The hybrid constraint equation for motion extraction,” Image Vis. Comput. 7, 217–224 (1989).
[CrossRef]

Bingham, G. P.

G. P. Bingham, “Optical flow from eye movement with head immobilized: ‘ocular occlusion’ beyond the nose,” Vision Res. (to be published).

Bruss, A. R.

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Vis. Graphics Image Process. 21, 3–20 (1983).
[CrossRef]

Celebrini, S.

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Ditchburn, R.

R. Ditchburn, Eye Movements and Visual Perception (Clarendon, Oxford, 1973), pp. 275, 315.

Fender, D. H.

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

D. H. Fender, “Torsional movements of the eyeball,” Br. J. Ophthalmol. 39, 65–72 (1956).
[CrossRef]

Gibson, J. J.

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950), Chap. 8.

J. J. Gibson, The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, Mass., 1979), pp. 310–311.

Gur, M.

I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
[CrossRef] [PubMed]

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

I. Hadani, G. Ishai, M. Gur, “Visual stability and space perception in monocular vision: mathematical model,” J. Opt. Soc. Am. 70, 60–65 (1980).
[CrossRef] [PubMed]

Hadani, I.

I. Hadani, B. Julesz, “Interpupillary distance and stereoscopic depth perception,” Invest. Ophthalmol. Vis. Sci. 33, 4 (1992).

I. Hadani, “Corneal lens goggles and visual space perception,” Appl. Opt. 30, 4136–4147 (1991).
[CrossRef] [PubMed]

I. Hadani, G. Ishai, B. Julesz, “The autokinetic movement and visual stability,” Invest. Ophthalmol. Vis. Sci. 32, 900 (1991).

I. Hadani, E. Barta, “The hybrid constraint equation for motion extraction,” Image Vis. Comput. 7, 217–224 (1989).
[CrossRef]

I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
[CrossRef] [PubMed]

I. Hadani, G. Ishai, M. Gur, “Visual stability and space perception in monocular vision: mathematical model,” J. Opt. Soc. Am. 70, 60–65 (1980).
[CrossRef] [PubMed]

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

I. Hadani, “Space perception with normal and prosthetic vision,” presented at the meeting of the Society for Information Display, Boston, Mass., May 17–22, 1992.

Hecht, S.

S. Hecht, E. U. Mintz, “The visibility of single lines at various illuminations and the retinal basis of visual resolution,” J. Gen. Physiol. 22, 593–612 (1936).
[CrossRef]

Horn, B. K. P.

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Vis. Graphics Image Process. 21, 3–20 (1983).
[CrossRef]

Howard, I. P.

I. P. Howard, “Spatial vision within egocentric and exocentric frames of reference,” in Pictorial Communication in Virtual and Real Environments, S. R. Ellis, ed. (Taylor & Francis, London, 1991), pp. 338–358.

Huang, T. S.

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of 3–D motion parameters and surface structures of rigid objects,” in Image Understanding 1985–86, W. Richards, S. Ullman, eds. (Albex, Norwood, N.J., 1985), Chap. 6, p. 141.

Imbert, M.

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Ishai, G.

I. Hadani, G. Ishai, B. Julesz, “The autokinetic movement and visual stability,” Invest. Ophthalmol. Vis. Sci. 32, 900 (1991).

I. Hadani, G. Ishai, M. Gur, “Visual stability and space perception in monocular vision: mathematical model,” J. Opt. Soc. Am. 70, 60–65 (1980).
[CrossRef] [PubMed]

Jain, S.

S. Jain, “Autokinesis and some conditions of fatigue,” Percept. Mot. Skills 56, 147–154 (1983).
[CrossRef] [PubMed]

Julesz, B.

I. Hadani, B. Julesz, “Interpupillary distance and stereoscopic depth perception,” Invest. Ophthalmol. Vis. Sci. 33, 4 (1992).

I. Hadani, G. Ishai, B. Julesz, “The autokinetic movement and visual stability,” Invest. Ophthalmol. Vis. Sci. 32, 900 (1991).

B. Julesz, Dialogues on Perception (MIT Press, Cambridge, Mass., to be published), dialogue 4.

Koenderink, J. J.

J. J. Koenderink, A. J. van Doorn, “Affine structure from motion,” J. Opt. Soc. Am. A 8, 377–385 (1991).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Method of stabilizing the retinal image,” Appl. Opt. 13, 955–961 (1974).
[CrossRef] [PubMed]

J. J. Koenderink, “Some theoretical aspects of optic flow,” in Perception and Control of Self-Motion, R. Warren, A. H. Wertheim, eds. (Erlbaum, Hillsdale, N.J., 1990), pp. 53–68.

Longuet-Higgins, H. C.

H. C. Longuet-Higgins, “A computer algorithm for reconstruction of a scene from two projections,” Nature (London) 293, 133–135 (1981).
[CrossRef]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal images,” Proc. R. Soc. London Ser. B 208, 385–387 (1980).
[CrossRef]

Matin, L.

L. Matin, “Eye movements and perceived visual direction,” in Handbook of Sensory Physiology, D. Jamson, ed. (Springer, Berlin, 1972), Vol. VII/4, pp. 331–380.

Meiri, A. Z.

I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
[CrossRef] [PubMed]

A. Z. Meiri, “On monocular perception of 3–D moving objects,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 582–583 (1980).

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

Mintz, E. U.

S. Hecht, E. U. Mintz, “The visibility of single lines at various illuminations and the retinal basis of visual resolution,” J. Gen. Physiol. 22, 593–612 (1936).
[CrossRef]

Nagel, H. H.

H. H. Nagel, “On the derivation of 3D rigid point configurations from image sequences,” in IEEE Conference on Pattern Recognition and Image Processing (Institute of Electrical and Electronics Engineers, New York, 1981).

Prazdny, K.

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinear moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal images,” Proc. R. Soc. London Ser. B 208, 385–387 (1980).
[CrossRef]

Stricanne, B.

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Thorpe, S.

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Trotter, Y.

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Tsai, R. Y.

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of 3–D motion parameters and surface structures of rigid objects,” in Image Understanding 1985–86, W. Richards, S. Ullman, eds. (Albex, Norwood, N.J., 1985), Chap. 6, p. 141.

Ullman, S.

S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979), p. 199.

van Doorn, A. J.

von Schellng, H.

Appl. Opt.

Br. J. Ophthalmol.

D. H. Fender, “Torsional movements of the eyeball,” Br. J. Ophthalmol. 39, 65–72 (1956).
[CrossRef]

Comput. Graphics Image Process.

K. Prazdny, “Determining the instantaneous direction of motion from optical flow generated by a curvilinear moving observer,” Comput. Graphics Image Process. 17, 238–248 (1981).
[CrossRef]

Comput. Vis. Graphics Image Process.

A. R. Bruss, B. K. P. Horn, “Passive navigation,” Comput. Vis. Graphics Image Process. 21, 3–20 (1983).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

A. Z. Meiri, “On monocular perception of 3–D moving objects,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 582–583 (1980).

Image Vis. Comput.

I. Hadani, E. Barta, “The hybrid constraint equation for motion extraction,” Image Vis. Comput. 7, 217–224 (1989).
[CrossRef]

Invest. Ophthalmol. Vis. Sci.

I. Hadani, G. Ishai, B. Julesz, “The autokinetic movement and visual stability,” Invest. Ophthalmol. Vis. Sci. 32, 900 (1991).

I. Hadani, B. Julesz, “Interpupillary distance and stereoscopic depth perception,” Invest. Ophthalmol. Vis. Sci. 33, 4 (1992).

J. Gen. Physiol.

S. Hecht, E. U. Mintz, “The visibility of single lines at various illuminations and the retinal basis of visual resolution,” J. Gen. Physiol. 22, 593–612 (1936).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature (London)

H. C. Longuet-Higgins, “A computer algorithm for reconstruction of a scene from two projections,” Nature (London) 293, 133–135 (1981).
[CrossRef]

Percept. Mot. Skills

S. Jain, “Autokinesis and some conditions of fatigue,” Percept. Mot. Skills 56, 147–154 (1983).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B

H. C. Longuet-Higgins, K. Prazdny, “The interpretation of moving retinal images,” Proc. R. Soc. London Ser. B 208, 385–387 (1980).
[CrossRef]

Science

Y. Trotter, S. Celebrini, B. Stricanne, S. Thorpe, M. Imbert, “Modulation of neural stereoscopic processing in primate area V1 by the viewing distance,” Science 257, 1279–1281 (1992).
[CrossRef] [PubMed]

Vision Res.

I. Hadani, A. Z. Meiri, M. Gur, “The effects of exposure duration and luminance on the 3-dot hyperacuity task,” Vision Res. 24, 871–874 (1984).
[CrossRef] [PubMed]

I. Hadani, M. Gur, A. Z. Meiri, D. H. Fender, “Hyperacuity in the detection of absolute and differential displacements of random-dot patterns,” Vision Res. 20, 947–951 (1980).
[CrossRef]

Other

J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, Mass., 1950), Chap. 8.

J. J. Gibson, The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, Mass., 1979), pp. 310–311.

L. Matin, “Eye movements and perceived visual direction,” in Handbook of Sensory Physiology, D. Jamson, ed. (Springer, Berlin, 1972), Vol. VII/4, pp. 331–380.

I. P. Howard, “Spatial vision within egocentric and exocentric frames of reference,” in Pictorial Communication in Virtual and Real Environments, S. R. Ellis, ed. (Taylor & Francis, London, 1991), pp. 338–358.

R. Ditchburn, Eye Movements and Visual Perception (Clarendon, Oxford, 1973), pp. 275, 315.

H. B. Barlow, “Three theories of cortical function,” in Developmental Neurobiology of Vision, R. D. Freeman, ed. (Plenum, New York, 1979), p. 5.

S. Ullman, The Interpretation of Visual Motion (MIT Press, Cambridge, Mass., 1979), p. 199.

H. H. Nagel, “On the derivation of 3D rigid point configurations from image sequences,” in IEEE Conference on Pattern Recognition and Image Processing (Institute of Electrical and Electronics Engineers, New York, 1981).

R. Y. Tsai, T. S. Huang, “Uniqueness and estimation of 3–D motion parameters and surface structures of rigid objects,” in Image Understanding 1985–86, W. Richards, S. Ullman, eds. (Albex, Norwood, N.J., 1985), Chap. 6, p. 141.

J. J. Koenderink, “Some theoretical aspects of optic flow,” in Perception and Control of Self-Motion, R. Warren, A. H. Wertheim, eds. (Erlbaum, Hillsdale, N.J., 1990), pp. 53–68.

I. Hadani, “Space perception with normal and prosthetic vision,” presented at the meeting of the Society for Information Display, Boston, Mass., May 17–22, 1992.

B. Julesz, Dialogues on Perception (MIT Press, Cambridge, Mass., to be published), dialogue 4.

G. P. Bingham, “Optical flow from eye movement with head immobilized: ‘ocular occlusion’ beyond the nose,” Vision Res. (to be published).

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