Abstract

Fender and Julesz [ J. Opt. Soc. Am. 57, 819 ( 1967)] found that fused retinally stabilized binocular line targets could be misaligned on the two retinas in the temporalward direction by at least 30 min of arc without loss of fusion and stereopsis and that random-dot stereograms could be misaligned 2 deg before fusion was lost. To test these results in normal vision, we recorded eye motions of four observers while they viewed a random-dot stereogram that subtended about 10 deg. The observers misaligned overlaid vectograph stereo images by moving them apart in a temporalward direction until fusion was lost. They then returned the vectographs to the overlaid position. Throughout this cycle the observers reported at frequent intervals if they could perceive strong or weak depth, loss of depth, or loss of fusion. For some observers the image separation could be increased to 5 deg beyond parallel before fusion was lost. The visual axes diverged to follow the image centers and varied from overconverged to overdiverged with respect to the image centers while the observers still reported depth and fusion. We call the difference between the image separation and eye vergence the vergence error. If a vergence error persisted for at least 10 sec without loss of the percepts of fusion and depth, we postulate that neutral remapping occurred that compensated for the retinal misalignment. We found that the average maximum neural remapping was 3.0 deg. The neural remapping was greater at loss of fusion than at regaining fusion. This phenomenon corresponds to the hysteresis measured by Fender and Julesz. We obtained an average hysteresis value of 2.6 deg with a maximum value of 4.1 deg. The average value is somewhat larger than the value reported by Fender and Julesz; this might result from our use of larger targets. We recorded many vergence saccades, in both the convergent and divergent directions, associated with scanning the target. Refusion occurred after the images were briefly aligned on the retinas by a pair of vergence saccades. These saccades were initiated when the vergence error returned to the value that it had when fusion was lost, and the magnitude of the divergent saccade was such that the vergence error was reduced to zero. This may imply retention of the position of correspondence that spanned a period of nearly 1 min between loss and restoration of fusion.

© 1983 Optical Society of America

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References

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  1. D. Fender and B. Julesz, “Extension of Panum’s fusional area in binocularly stabilized vision,” J. Opt. Soc. Am. 57, 819–830 (1967).
    [Crossref] [PubMed]
  2. D. B. Diner, “Hysteresis in binocular fusion,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).
  3. B. Julesz, “Towards the automation of binocular depth perception (Automap-1),” in Proceedings of the IFIPS Congress, Munich 1962, C. M. Popplewell, ed. (North-Holland, Amsterdam, 1963).
  4. G. Sperling, “Binocular vision: a physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
    [Crossref]
  5. B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).
  6. P. Dev, “Segmentation processes in visual perception: a cooperative neural model,” (University of Massachusetts, Amherst, Mass., 1974).
  7. J. I. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
    [Crossref] [PubMed]
  8. P. Dev, “Perception of depth surfaces in random-dot stereograms: a neural model,” Int. J. Man-Machine Stud. 7, 511–528 (1975).
    [Crossref]
  9. D. Marr and T. Poggio, “Cooperative computation of stereo disparity,” Science 194, 283–287 (1976).
    [Crossref] [PubMed]
  10. J. E. W. Mayhew and J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
    [Crossref]
  11. Y. Hirai and K. Fukushima, “An inference upon the neural network finding binocular correspondence,” Trans. Inst. Electron. Commun. Eng. Jpn. J59-D, 133–140 (1976).
  12. N. Sugie and M. Suwa, “A scheme for binocular depth perception suggested by neurophysiological evidence,” Biol. Cybernetics 26, 1–15 (1977).
    [Crossref]
  13. D. Marr and T. Poggio, “A theory of human stereo vision,” Artificial Intelligence Laboratory Memo 451 (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1977).
  14. D. Marr and T. Poggio, “Theory of human stereopsis,” J. Opt. Soc. Am. 67, 1400 (A) (1977).
  15. D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
    [Crossref]
  16. A. Trehub, “Neuronal models for stereoscopic vision,” J. Theor. Biol. 71, 479–486 (1978).
    [Crossref] [PubMed]
  17. W. E. L. Grimson, From Images to Surfaces: A Computational Study of the Human Early Visual System (MIT Press, Cambridge, Mass., 1981).
  18. G. J. St-Cyr and D. H. Fender, “The interplay of drifts and flicks in binocular fixation,” Vision Res. 9, 245 (1969).
    [Crossref] [PubMed]
  19. Three of our observers seldom experienced fusion without the percept of depth. The remaining observer did have this percept, but we did not record the differential thresholds for loss of the depth percept and loss of fusion.
  20. L. A. Riggs and E. W. Niehl, “Eye movements recorded during convergence and divergence,” J. Opt. Soc. Am. 50, 913–920 (1960).
    [Crossref]
  21. E. Kowler and R. M. Steinman, “The effect of expectations on slow oculomotor control—I. Periodic target steps,” Vision Res. 19, 619–632 (1979).
    [Crossref]
  22. M. H. Clark and H. D. Crane, “Dynamic interactions in binocular vision,” in Eye Movements and the Higher Psychological Functions, J. W. Senders, D. F. Fisher, and R. A. Montey, eds. (Erlbaum, Hillsdale, N. J., 1978).
  23. P. Burt and B. Julesz, “Extended Panum’s area for dynamic random dot stereograms,” presented at Association for Research in Vision and Ophthalmology Meeting, Sarasota, Florida, April 30–May 5, 1978. For some problems of Panum’s area see also P. Burt and B. Julesz, “Modifications of the classical notion of Panum’s fusional area,” Perception 9, 671–682 (1980).
    [Crossref]
  24. Our attention has recently been drawn to R. A. Crane and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47.1, 163–199 (1979). These authors measured the disparity between nonius lines when viewing fused random-dot stereograms through baseout prisms of varying power. They show a horizontal extension of Panum’s fusional area to a maximum of about 4°. The data we present agree with this figure and adds some information on the dynamics of the fusional process.
    [Crossref]

1979 (2)

E. Kowler and R. M. Steinman, “The effect of expectations on slow oculomotor control—I. Periodic target steps,” Vision Res. 19, 619–632 (1979).
[Crossref]

Our attention has recently been drawn to R. A. Crane and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47.1, 163–199 (1979). These authors measured the disparity between nonius lines when viewing fused random-dot stereograms through baseout prisms of varying power. They show a horizontal extension of Panum’s fusional area to a maximum of about 4°. The data we present agree with this figure and adds some information on the dynamics of the fusional process.
[Crossref]

1978 (2)

D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
[Crossref]

A. Trehub, “Neuronal models for stereoscopic vision,” J. Theor. Biol. 71, 479–486 (1978).
[Crossref] [PubMed]

1977 (2)

N. Sugie and M. Suwa, “A scheme for binocular depth perception suggested by neurophysiological evidence,” Biol. Cybernetics 26, 1–15 (1977).
[Crossref]

D. Marr and T. Poggio, “Theory of human stereopsis,” J. Opt. Soc. Am. 67, 1400 (A) (1977).

1976 (3)

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

J. E. W. Mayhew and J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[Crossref]

Y. Hirai and K. Fukushima, “An inference upon the neural network finding binocular correspondence,” Trans. Inst. Electron. Commun. Eng. Jpn. J59-D, 133–140 (1976).

1975 (2)

J. I. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
[Crossref] [PubMed]

P. Dev, “Perception of depth surfaces in random-dot stereograms: a neural model,” Int. J. Man-Machine Stud. 7, 511–528 (1975).
[Crossref]

1970 (1)

G. Sperling, “Binocular vision: a physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
[Crossref]

1969 (1)

G. J. St-Cyr and D. H. Fender, “The interplay of drifts and flicks in binocular fixation,” Vision Res. 9, 245 (1969).
[Crossref] [PubMed]

1967 (1)

1960 (1)

Burt, P.

P. Burt and B. Julesz, “Extended Panum’s area for dynamic random dot stereograms,” presented at Association for Research in Vision and Ophthalmology Meeting, Sarasota, Florida, April 30–May 5, 1978. For some problems of Panum’s area see also P. Burt and B. Julesz, “Modifications of the classical notion of Panum’s fusional area,” Perception 9, 671–682 (1980).
[Crossref]

Clark, M. H.

M. H. Clark and H. D. Crane, “Dynamic interactions in binocular vision,” in Eye Movements and the Higher Psychological Functions, J. W. Senders, D. F. Fisher, and R. A. Montey, eds. (Erlbaum, Hillsdale, N. J., 1978).

Crane, H. D.

M. H. Clark and H. D. Crane, “Dynamic interactions in binocular vision,” in Eye Movements and the Higher Psychological Functions, J. W. Senders, D. F. Fisher, and R. A. Montey, eds. (Erlbaum, Hillsdale, N. J., 1978).

Crane, R. A.

Our attention has recently been drawn to R. A. Crane and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47.1, 163–199 (1979). These authors measured the disparity between nonius lines when viewing fused random-dot stereograms through baseout prisms of varying power. They show a horizontal extension of Panum’s fusional area to a maximum of about 4°. The data we present agree with this figure and adds some information on the dynamics of the fusional process.
[Crossref]

Dev, P.

P. Dev, “Perception of depth surfaces in random-dot stereograms: a neural model,” Int. J. Man-Machine Stud. 7, 511–528 (1975).
[Crossref]

P. Dev, “Segmentation processes in visual perception: a cooperative neural model,” (University of Massachusetts, Amherst, Mass., 1974).

Diner, D. B.

D. B. Diner, “Hysteresis in binocular fusion,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).

Fender, D.

Fender, D. H.

G. J. St-Cyr and D. H. Fender, “The interplay of drifts and flicks in binocular fixation,” Vision Res. 9, 245 (1969).
[Crossref] [PubMed]

Frisby, J. P.

J. E. W. Mayhew and J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[Crossref]

Fukushima, K.

Y. Hirai and K. Fukushima, “An inference upon the neural network finding binocular correspondence,” Trans. Inst. Electron. Commun. Eng. Jpn. J59-D, 133–140 (1976).

Grimson, W. E. L.

W. E. L. Grimson, From Images to Surfaces: A Computational Study of the Human Early Visual System (MIT Press, Cambridge, Mass., 1981).

Hardjowijoto, S.

Our attention has recently been drawn to R. A. Crane and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47.1, 163–199 (1979). These authors measured the disparity between nonius lines when viewing fused random-dot stereograms through baseout prisms of varying power. They show a horizontal extension of Panum’s fusional area to a maximum of about 4°. The data we present agree with this figure and adds some information on the dynamics of the fusional process.
[Crossref]

Hirai, Y.

Y. Hirai and K. Fukushima, “An inference upon the neural network finding binocular correspondence,” Trans. Inst. Electron. Commun. Eng. Jpn. J59-D, 133–140 (1976).

Julesz, B.

D. Fender and B. Julesz, “Extension of Panum’s fusional area in binocularly stabilized vision,” J. Opt. Soc. Am. 57, 819–830 (1967).
[Crossref] [PubMed]

B. Julesz, “Towards the automation of binocular depth perception (Automap-1),” in Proceedings of the IFIPS Congress, Munich 1962, C. M. Popplewell, ed. (North-Holland, Amsterdam, 1963).

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).

P. Burt and B. Julesz, “Extended Panum’s area for dynamic random dot stereograms,” presented at Association for Research in Vision and Ophthalmology Meeting, Sarasota, Florida, April 30–May 5, 1978. For some problems of Panum’s area see also P. Burt and B. Julesz, “Modifications of the classical notion of Panum’s fusional area,” Perception 9, 671–682 (1980).
[Crossref]

Kowler, E.

E. Kowler and R. M. Steinman, “The effect of expectations on slow oculomotor control—I. Periodic target steps,” Vision Res. 19, 619–632 (1979).
[Crossref]

Marr, D.

D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
[Crossref]

D. Marr and T. Poggio, “Theory of human stereopsis,” J. Opt. Soc. Am. 67, 1400 (A) (1977).

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

D. Marr and T. Poggio, “A theory of human stereo vision,” Artificial Intelligence Laboratory Memo 451 (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1977).

Mayhew, J. E. W.

J. E. W. Mayhew and J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[Crossref]

Nelson, J. I.

J. I. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
[Crossref] [PubMed]

Niehl, E. W.

Palm, G.

D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
[Crossref]

Poggio, T.

D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
[Crossref]

D. Marr and T. Poggio, “Theory of human stereopsis,” J. Opt. Soc. Am. 67, 1400 (A) (1977).

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

D. Marr and T. Poggio, “A theory of human stereo vision,” Artificial Intelligence Laboratory Memo 451 (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1977).

Riggs, L. A.

Sperling, G.

G. Sperling, “Binocular vision: a physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
[Crossref]

St-Cyr, G. J.

G. J. St-Cyr and D. H. Fender, “The interplay of drifts and flicks in binocular fixation,” Vision Res. 9, 245 (1969).
[Crossref] [PubMed]

Steinman, R. M.

E. Kowler and R. M. Steinman, “The effect of expectations on slow oculomotor control—I. Periodic target steps,” Vision Res. 19, 619–632 (1979).
[Crossref]

Sugie, N.

N. Sugie and M. Suwa, “A scheme for binocular depth perception suggested by neurophysiological evidence,” Biol. Cybernetics 26, 1–15 (1977).
[Crossref]

Suwa, M.

N. Sugie and M. Suwa, “A scheme for binocular depth perception suggested by neurophysiological evidence,” Biol. Cybernetics 26, 1–15 (1977).
[Crossref]

Trehub, A.

A. Trehub, “Neuronal models for stereoscopic vision,” J. Theor. Biol. 71, 479–486 (1978).
[Crossref] [PubMed]

Am. J. Psychol. (1)

G. Sperling, “Binocular vision: a physical and a neural theory,” Am. J. Psychol. 83, 461–534 (1970).
[Crossref]

Biol. Cybernetics (2)

N. Sugie and M. Suwa, “A scheme for binocular depth perception suggested by neurophysiological evidence,” Biol. Cybernetics 26, 1–15 (1977).
[Crossref]

D. Marr, G. Palm, and T. Poggio, “Analysis of a cooperative stereo algorithm,” Biol. Cybernetics 28, 223–239 (1978).
[Crossref]

Doc. Ophthalmol. (1)

Our attention has recently been drawn to R. A. Crane and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47.1, 163–199 (1979). These authors measured the disparity between nonius lines when viewing fused random-dot stereograms through baseout prisms of varying power. They show a horizontal extension of Panum’s fusional area to a maximum of about 4°. The data we present agree with this figure and adds some information on the dynamics of the fusional process.
[Crossref]

Int. J. Man-Machine Stud. (1)

P. Dev, “Perception of depth surfaces in random-dot stereograms: a neural model,” Int. J. Man-Machine Stud. 7, 511–528 (1975).
[Crossref]

J. Opt. Soc. Am. (3)

J. Theor. Biol. (2)

J. I. Nelson, “Globality and stereoscopic fusion in binocular vision,” J. Theor. Biol. 49, 1–88 (1975).
[Crossref] [PubMed]

A. Trehub, “Neuronal models for stereoscopic vision,” J. Theor. Biol. 71, 479–486 (1978).
[Crossref] [PubMed]

Nature (London) (1)

J. E. W. Mayhew and J. P. Frisby, “Rivalrous texture stereograms,” Nature (London) 264, 53–56 (1976).
[Crossref]

Science (1)

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

Trans. Inst. Electron. Commun. Eng. Jpn. (1)

Y. Hirai and K. Fukushima, “An inference upon the neural network finding binocular correspondence,” Trans. Inst. Electron. Commun. Eng. Jpn. J59-D, 133–140 (1976).

Vision Res. (2)

G. J. St-Cyr and D. H. Fender, “The interplay of drifts and flicks in binocular fixation,” Vision Res. 9, 245 (1969).
[Crossref] [PubMed]

E. Kowler and R. M. Steinman, “The effect of expectations on slow oculomotor control—I. Periodic target steps,” Vision Res. 19, 619–632 (1979).
[Crossref]

Other (9)

M. H. Clark and H. D. Crane, “Dynamic interactions in binocular vision,” in Eye Movements and the Higher Psychological Functions, J. W. Senders, D. F. Fisher, and R. A. Montey, eds. (Erlbaum, Hillsdale, N. J., 1978).

P. Burt and B. Julesz, “Extended Panum’s area for dynamic random dot stereograms,” presented at Association for Research in Vision and Ophthalmology Meeting, Sarasota, Florida, April 30–May 5, 1978. For some problems of Panum’s area see also P. Burt and B. Julesz, “Modifications of the classical notion of Panum’s fusional area,” Perception 9, 671–682 (1980).
[Crossref]

Three of our observers seldom experienced fusion without the percept of depth. The remaining observer did have this percept, but we did not record the differential thresholds for loss of the depth percept and loss of fusion.

W. E. L. Grimson, From Images to Surfaces: A Computational Study of the Human Early Visual System (MIT Press, Cambridge, Mass., 1981).

D. Marr and T. Poggio, “A theory of human stereo vision,” Artificial Intelligence Laboratory Memo 451 (Massachusetts Institute of Technology, Cambridge, Massachusetts, 1977).

D. B. Diner, “Hysteresis in binocular fusion,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).

B. Julesz, “Towards the automation of binocular depth perception (Automap-1),” in Proceedings of the IFIPS Congress, Munich 1962, C. M. Popplewell, ed. (North-Holland, Amsterdam, 1963).

B. Julesz, Foundations of Cyclopean Perception (U. Chicago Press, Chicago, Ill., 1971).

P. Dev, “Segmentation processes in visual perception: a cooperative neural model,” (University of Massachusetts, Amherst, Mass., 1974).

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Figures (7)

Fig. 1
Fig. 1

Motions of the visual axes when viewing a stereo pair of vectographs. The images were slowly drawn apart, as shown in the top trace. The signal button output was quantized at three levels, H, I, and L, indicating strong fusion, intermediate, and loss of fusion.

Fig. 2
Fig. 2

Vergence and vergence error during separation of a stereo pair. The top trace shows that the visual axes diverge to follow the images. The middle trace shows vergence error. Positive values indicate that the images were separated further than the visual axes. The heavy bar marks oscillations of vergence error. Arrows refer to the button signal: w, weak depth; b, break of fusion; f, refusion. Note the divergent saccade before refusion was signaled. There were long periods of large vergence error just before loss of fusion (marked *) and also between 250 and 300 sec after refusion, when there was again a strong percept of depth, marked by a dashed bar.

Fig. 3
Fig. 3

Vergence error for Observer C, showing a vergence error that persisted from 5 to 15 sec. Strong depth was observed throughout the entire epoch portrayed. Transient movements crossing the zero line are blinks, but the other rapid changes of vergence error are caused by convergent or divergent saccades. The arrow marks an anticipatory vergence drift.

Fig. 4
Fig. 4

Vergence versus image separation for a 300-sec run. Both visual axes diverge to follow the images roughly as they are separated. Deviations from the diagonals show vergence errors (see text). Arrows show the time course of vergence as images were separated and returned. The sloping bar in the bottom diagram marks an over-convergence following loss of fusion.

Fig. 5
Fig. 5

Vergence error versus image separation for a run of 300 sec. The diagonal is the locus for which vergence error is equal to image separation—that is, the eyes converge on the original position of the images. Arrows refer to phases of a run: a, tracking; b, increasing vergence error with the visual axes overdiverged with respect to the target; c, fusion was lost when the visual axes overdiverged, marked †; d, search; e, refusion occurred at point marked ▼; f, return. These phases are shown schematically in the inset diagram. Some periods of neural remapping are marked by *.

Fig. 6
Fig. 6

Vergence error versus image separation for a different run of Observer C. Phases a–f marked as before. Fusion was lost after visual axes overconverged. Loss of tracking marked by ■; refusion marked by ▼.

Fig. 7
Fig. 7

Maximum image separation at loss of fusion versus trial number. A learning trend is evident. The letters refer to observers.

Tables (1)

Tables Icon

Table 1 Binocular Eye-Movement Parameters for Four Observers When Tracking Vectograph Stereo Images as They Were Moved Apart