Abstract

The perceived direction of motion of a featureless contour inside a circular aperture is always perpendicular to the contour’s orientation, regardless of its true motion (the aperture problem). This study investigates the circumstances under which unambiguous feature motion (of line terminators, single dots, or truncations of a D6 pattern) in adjacent apertures can alter the perceived direction of such featureless contours. We find that integration mechanisms responsible for motion capture are fairly robust against misorientations and contrast manipulations of individual components, are sensitive to differences in spatial frequencies, and scale with pattern size. Motion capture is not diminished when a D6 profile is substituted for the square-pulse profile of a line and is independent of the visibility of the apertures, indicating that object interpretations and three-dimensional analyses of a scene are less important than has been postulated previously. These results have strong implications for the neuronal hardware underlying the integration of motion signals across space and provide a framework for global motion models.

© 2003 Optical Society of America

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  1. This paper is concerned with motion in the two-dimensional frontoprallel plane; the term “rigidity” (or coherence) describes the perception of a single rigid object moving in this plane.
  2. E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature 300, 523–525 (1982).
    [CrossRef] [PubMed]
  3. V. P. Ferrera, H. R. Wilson, “Perceived direction of moving two-dimensional patterns,” Vision Res. 30, 273–287 (1990).
    [CrossRef] [PubMed]
  4. L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
    [CrossRef] [PubMed]
  5. C. Yo, H. R. Wilson, “Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity,” Vision Res. 32, 135–147 (1992).
    [CrossRef] [PubMed]
  6. K. Nakayama, G. H. Silverman, “The aperture problem I. Perception of nonrigidity and motion direction in translating sinusoidal lines,” Vision Res. 28, 739–746 (1988).
    [CrossRef]
  7. M. Shiffrar, M. Pavel, “Percepts of rigid motion within and across apertures,” J. Exp. Psychol. Hum. Percept. Perform. 17, 749–761 (1991).
    [CrossRef] [PubMed]
  8. J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992).
    [CrossRef] [PubMed]
  9. H. Wallach, “Über visuell wahrgenommene Bewegungsrichtung,” Psychol. Forsch. 20, 325–380 (1935).
    [CrossRef]
  10. M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028 (1993).
  11. E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992).
    [CrossRef] [PubMed]
  12. H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).
  13. M. Shiffrar, X. Li, J. Lorenceau, “Motion integration across differing image features,” Vision Res. 35, 2137–2146 (1995).
    [CrossRef] [PubMed]
  14. F. L. Kooi, “Local direction of edge motion causes and abolishes the barberpole illusion,” Vision Res. 33, 2347–2351 (1993).
    [CrossRef] [PubMed]
  15. J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
    [CrossRef] [PubMed]
  16. W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
    [CrossRef] [PubMed]
  17. G. Loffler, H. S. Orbach, “Anisotropy in judging the absolute direction of motion,” Vision Res. 41, 3677–3692 (2001).
    [CrossRef] [PubMed]
  18. To avoid confusion, there is, of course, no “real” motion for a translating line presented on a monitor. Rather, the successive switching on and off of pixels creates the illusion of motion. So when we are talking about the real motion of a rigid line, this should be understood as the motion of the rigid object that could produce the stimulation.
  19. M. B. Ben-Av, M. Shiffrar, “Disambiguating velocity estimates across image space,” Vision Res. 35, 2889–2895 (1995).
    [CrossRef] [PubMed]
  20. S. Shimojo, G. H. Silverman, K. Nakayama, “Occlusion and the solution to the aperture problem for motion,” Vision Res. 29, 619–626 (1989).
    [CrossRef] [PubMed]
  21. S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).
  22. E. Peterhans, R. Von der Heydt, “Mechanisms of contour perception in monkey visual-cortex. 2. Contours bridging gaps,” J. Neurosci. 9, 1749–1763 (1989).
    [PubMed]
  23. The space constants of the fitted Gaussians are 2.8° for the D6 patterns and 2.1° for lines. The (albeit small) difference in space constants would be even further reduced by fixing the asymptotes of the Gaussians to 45° (the expected value of perpendicular motion for an isolated line segment).
  24. Obviously, this does not prove that higher-order processes cannot influence motion integration in addition to the low-level processes indicated here.
  25. One may argue that a quantitative comparison between this and previous experiments should take the distance between the dot and the closest part of the line segment as a substitute for the inter-aperture gap. However, even given this correction, the results in this experiment still show a bias that is significantly closer to the perpendicular than for line terminators.
  26. R. L. DeValois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
    [CrossRef]
  27. Note that the 1.7-cpd flanker frequency condition here (Fig. 9) is not identical to the previous experiment on D6 patterns (Fig. 7). In the previous experiment, the contrast for the central patch and the truncations were equal but had opposite signs. Here the contrasts of the three parts of the display were identical. This gives the impression of a set of aligned, but disconnected, black and white stripes, which might be predicted to appear more coherent than in the case of contrast-alternated stripes used before. The results show that this manipulation does not greatly affect observers’ judgments.
  28. E. Castet, S. Wuerger, “Perception of moving lines: interactions between local perpendicular signals and 2D motion signals,” Vision Res. 37, 705–720 (1997).
    [CrossRef] [PubMed]
  29. L. Liden, E. Mingolla, “Monocular occlusion cues alter the influence of terminator motion in the barber pole phenomenon,” Vision Res. 38, 3883–3898 (1998).
    [CrossRef]
  30. N. Rubin, S. Hochstein, “Isolating the effect of one-dimensional motion signals on the perceived direction of moving 2-dimensional objects,” Vision Res. 33, 1385–1396 (1993).
    [CrossRef] [PubMed]
  31. G. Vallortigara, P. Bressan, “Occlusion and the perception of coherent motion,” Vision Res. 31, 1967–1978 (1991).
    [CrossRef] [PubMed]
  32. Note that, although the apertures in our experiments were invisible, such “pseudoreal” aperture terminators could conceivably be classified as extrinsic. This is because the apertures are physically absent in the sense of having zero contrast, but, as the line moves, the terminators trace out the shape of the aperture. (This possibility was raised, in conversation, by Mark Georgeson). The visual system could use this information to classify the terminator as arising from a line occluded by a circular aperture and hence be extrinsic in an elaborated intrinsic/extrinsic classification. To test this, the circular apertures were replaced with invisible rectangles in a control condition. The orientation of the rectangular apertures was perpendicular to the line’s orientation. This eliminated any difference between real and pseudoreal terminators. Nonetheless, the pattern of response was indistinguishable from that presented in Fig. 3, invalidating such a hypothesized modification of the intrinsic/extrinsic rule.
  33. J. B. Mulligan, “A continuous version of the barber-pole illusion,” Invest. Ophthalmol. Visual Sci. 32, 829 (1991).
  34. G. Loffler, “The integration of motion signals across space,” Ph.D. thesis (Glasgow Caledonian University, Glasgow, UK, 1999).
  35. G. Loffler, H. S. Orbach, “Modeling the integration of motion signals across space,” J. Opt. Soc. Am. A 20, 1472–1489 (2003).
    [CrossRef]
  36. Y. Weiss, E. H. Adelson, “Integration and segmentation of nonrigid motion,” Invest. Ophthalmol. Visual Sci. 36, S228 (1995).
  37. H. S. Orbach, G. Loffler, “What determines motion integration across apertures?” Invest. Ophthalmol. Visual Sci. 41, 2889 (2000).

2003

2001

G. Loffler, H. S. Orbach, “Anisotropy in judging the absolute direction of motion,” Vision Res. 41, 3677–3692 (2001).
[CrossRef] [PubMed]

2000

H. S. Orbach, G. Loffler, “What determines motion integration across apertures?” Invest. Ophthalmol. Visual Sci. 41, 2889 (2000).

1998

L. Liden, E. Mingolla, “Monocular occlusion cues alter the influence of terminator motion in the barber pole phenomenon,” Vision Res. 38, 3883–3898 (1998).
[CrossRef]

1997

E. Castet, S. Wuerger, “Perception of moving lines: interactions between local perpendicular signals and 2D motion signals,” Vision Res. 37, 705–720 (1997).
[CrossRef] [PubMed]

1995

Y. Weiss, E. H. Adelson, “Integration and segmentation of nonrigid motion,” Invest. Ophthalmol. Visual Sci. 36, S228 (1995).

M. B. Ben-Av, M. Shiffrar, “Disambiguating velocity estimates across image space,” Vision Res. 35, 2889–2895 (1995).
[CrossRef] [PubMed]

M. Shiffrar, X. Li, J. Lorenceau, “Motion integration across differing image features,” Vision Res. 35, 2137–2146 (1995).
[CrossRef] [PubMed]

1994

H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).

1993

S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).

N. Rubin, S. Hochstein, “Isolating the effect of one-dimensional motion signals on the perceived direction of moving 2-dimensional objects,” Vision Res. 33, 1385–1396 (1993).
[CrossRef] [PubMed]

F. L. Kooi, “Local direction of edge motion causes and abolishes the barberpole illusion,” Vision Res. 33, 2347–2351 (1993).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
[CrossRef] [PubMed]

M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028 (1993).

1992

E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992).
[CrossRef] [PubMed]

C. Yo, H. R. Wilson, “Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity,” Vision Res. 32, 135–147 (1992).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992).
[CrossRef] [PubMed]

1991

M. Shiffrar, M. Pavel, “Percepts of rigid motion within and across apertures,” J. Exp. Psychol. Hum. Percept. Perform. 17, 749–761 (1991).
[CrossRef] [PubMed]

G. Vallortigara, P. Bressan, “Occlusion and the perception of coherent motion,” Vision Res. 31, 1967–1978 (1991).
[CrossRef] [PubMed]

J. B. Mulligan, “A continuous version of the barber-pole illusion,” Invest. Ophthalmol. Visual Sci. 32, 829 (1991).

1990

V. P. Ferrera, H. R. Wilson, “Perceived direction of moving two-dimensional patterns,” Vision Res. 30, 273–287 (1990).
[CrossRef] [PubMed]

L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
[CrossRef] [PubMed]

1989

S. Shimojo, G. H. Silverman, K. Nakayama, “Occlusion and the solution to the aperture problem for motion,” Vision Res. 29, 619–626 (1989).
[CrossRef] [PubMed]

E. Peterhans, R. Von der Heydt, “Mechanisms of contour perception in monkey visual-cortex. 2. Contours bridging gaps,” J. Neurosci. 9, 1749–1763 (1989).
[PubMed]

1988

K. Nakayama, G. H. Silverman, “The aperture problem I. Perception of nonrigidity and motion direction in translating sinusoidal lines,” Vision Res. 28, 739–746 (1988).
[CrossRef]

1984

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

1982

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature 300, 523–525 (1982).
[CrossRef] [PubMed]

R. L. DeValois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef]

1935

H. Wallach, “Über visuell wahrgenommene Bewegungsrichtung,” Psychol. Forsch. 20, 325–380 (1935).
[CrossRef]

Adelson, E. H.

Y. Weiss, E. H. Adelson, “Integration and segmentation of nonrigid motion,” Invest. Ophthalmol. Visual Sci. 36, S228 (1995).

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature 300, 523–525 (1982).
[CrossRef] [PubMed]

Ben-Av, M. B.

M. B. Ben-Av, M. Shiffrar, “Disambiguating velocity estimates across image space,” Vision Res. 35, 2889–2895 (1995).
[CrossRef] [PubMed]

M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028 (1993).

Bressan, P.

G. Vallortigara, P. Bressan, “Occlusion and the perception of coherent motion,” Vision Res. 31, 1967–1978 (1991).
[CrossRef] [PubMed]

Castet, E.

E. Castet, S. Wuerger, “Perception of moving lines: interactions between local perpendicular signals and 2D motion signals,” Vision Res. 37, 705–720 (1997).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
[CrossRef] [PubMed]

DeValois, R. L.

R. L. DeValois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef]

Ferrera, V. P.

V. P. Ferrera, H. R. Wilson, “Perceived direction of moving two-dimensional patterns,” Vision Res. 30, 273–287 (1990).
[CrossRef] [PubMed]

Giese, S. C.

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Grossberg, S.

S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).

Hepler, N.

R. L. DeValois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef]

Hochstein, S.

N. Rubin, S. Hochstein, “Isolating the effect of one-dimensional motion signals on the perceived direction of moving 2-dimensional objects,” Vision Res. 33, 1385–1396 (1993).
[CrossRef] [PubMed]

Kooi, F. L.

F. L. Kooi, “Local direction of edge motion causes and abolishes the barberpole illusion,” Vision Res. 33, 2347–2351 (1993).
[CrossRef] [PubMed]

Li, X.

M. Shiffrar, X. Li, J. Lorenceau, “Motion integration across differing image features,” Vision Res. 35, 2137–2146 (1995).
[CrossRef] [PubMed]

Liden, L.

L. Liden, E. Mingolla, “Monocular occlusion cues alter the influence of terminator motion in the barber pole phenomenon,” Vision Res. 38, 3883–3898 (1998).
[CrossRef]

Loffler, G.

G. Loffler, H. S. Orbach, “Modeling the integration of motion signals across space,” J. Opt. Soc. Am. A 20, 1472–1489 (2003).
[CrossRef]

G. Loffler, H. S. Orbach, “Anisotropy in judging the absolute direction of motion,” Vision Res. 41, 3677–3692 (2001).
[CrossRef] [PubMed]

H. S. Orbach, G. Loffler, “What determines motion integration across apertures?” Invest. Ophthalmol. Visual Sci. 41, 2889 (2000).

G. Loffler, “The integration of motion signals across space,” Ph.D. thesis (Glasgow Caledonian University, Glasgow, UK, 1999).

Lorenceau, J.

M. Shiffrar, X. Li, J. Lorenceau, “Motion integration across differing image features,” Vision Res. 35, 2137–2146 (1995).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992).
[CrossRef] [PubMed]

Mingolla, E.

L. Liden, E. Mingolla, “Monocular occlusion cues alter the influence of terminator motion in the barber pole phenomenon,” Vision Res. 38, 3883–3898 (1998).
[CrossRef]

S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).

E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992).
[CrossRef] [PubMed]

Movshon, J. A.

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature 300, 523–525 (1982).
[CrossRef] [PubMed]

Mulligan, J. B.

J. B. Mulligan, “A continuous version of the barber-pole illusion,” Invest. Ophthalmol. Visual Sci. 32, 829 (1991).

L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
[CrossRef] [PubMed]

Nakayama, K.

S. Shimojo, G. H. Silverman, K. Nakayama, “Occlusion and the solution to the aperture problem for motion,” Vision Res. 29, 619–626 (1989).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “The aperture problem I. Perception of nonrigidity and motion direction in translating sinusoidal lines,” Vision Res. 28, 739–746 (1988).
[CrossRef]

Norman, J. F.

E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992).
[CrossRef] [PubMed]

Orbach, H. S.

G. Loffler, H. S. Orbach, “Modeling the integration of motion signals across space,” J. Opt. Soc. Am. A 20, 1472–1489 (2003).
[CrossRef]

G. Loffler, H. S. Orbach, “Anisotropy in judging the absolute direction of motion,” Vision Res. 41, 3677–3692 (2001).
[CrossRef] [PubMed]

H. S. Orbach, G. Loffler, “What determines motion integration across apertures?” Invest. Ophthalmol. Visual Sci. 41, 2889 (2000).

H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).

Pavel, M.

M. Shiffrar, M. Pavel, “Percepts of rigid motion within and across apertures,” J. Exp. Psychol. Hum. Percept. Perform. 17, 749–761 (1991).
[CrossRef] [PubMed]

Peterhans, E.

E. Peterhans, R. Von der Heydt, “Mechanisms of contour perception in monkey visual-cortex. 2. Contours bridging gaps,” J. Neurosci. 9, 1749–1763 (1989).
[PubMed]

Rubin, N.

N. Rubin, S. Hochstein, “Isolating the effect of one-dimensional motion signals on the perceived direction of moving 2-dimensional objects,” Vision Res. 33, 1385–1396 (1993).
[CrossRef] [PubMed]

Shiffrar, M.

M. Shiffrar, X. Li, J. Lorenceau, “Motion integration across differing image features,” Vision Res. 35, 2137–2146 (1995).
[CrossRef] [PubMed]

M. B. Ben-Av, M. Shiffrar, “Disambiguating velocity estimates across image space,” Vision Res. 35, 2889–2895 (1995).
[CrossRef] [PubMed]

M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028 (1993).

J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
[CrossRef] [PubMed]

J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992).
[CrossRef] [PubMed]

M. Shiffrar, M. Pavel, “Percepts of rigid motion within and across apertures,” J. Exp. Psychol. Hum. Percept. Perform. 17, 749–761 (1991).
[CrossRef] [PubMed]

Shimojo, S.

S. Shimojo, G. H. Silverman, K. Nakayama, “Occlusion and the solution to the aperture problem for motion,” Vision Res. 29, 619–626 (1989).
[CrossRef] [PubMed]

Silverman, G. H.

S. Shimojo, G. H. Silverman, K. Nakayama, “Occlusion and the solution to the aperture problem for motion,” Vision Res. 29, 619–626 (1989).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “The aperture problem I. Perception of nonrigidity and motion direction in translating sinusoidal lines,” Vision Res. 28, 739–746 (1988).
[CrossRef]

Stone, L. S.

L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
[CrossRef] [PubMed]

Swanson, W. H.

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Todd, J. T.

E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992).
[CrossRef] [PubMed]

Vallortigara, G.

G. Vallortigara, P. Bressan, “Occlusion and the perception of coherent motion,” Vision Res. 31, 1967–1978 (1991).
[CrossRef] [PubMed]

Von der Heydt, R.

E. Peterhans, R. Von der Heydt, “Mechanisms of contour perception in monkey visual-cortex. 2. Contours bridging gaps,” J. Neurosci. 9, 1749–1763 (1989).
[PubMed]

Wallach, H.

H. Wallach, “Über visuell wahrgenommene Bewegungsrichtung,” Psychol. Forsch. 20, 325–380 (1935).
[CrossRef]

Watson, A. B.

L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
[CrossRef] [PubMed]

Weiss, Y.

Y. Weiss, E. H. Adelson, “Integration and segmentation of nonrigid motion,” Invest. Ophthalmol. Visual Sci. 36, S228 (1995).

Wells, N.

J. Lorenceau, M. Shiffrar, N. Wells, E. Castet, “Different motion sensitive units are involved in recovering the direction of moving lines,” Vision Res. 33, 1207–1217 (1993).
[CrossRef] [PubMed]

Wilson, H. R.

H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).

C. Yo, H. R. Wilson, “Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity,” Vision Res. 32, 135–147 (1992).
[CrossRef] [PubMed]

V. P. Ferrera, H. R. Wilson, “Perceived direction of moving two-dimensional patterns,” Vision Res. 30, 273–287 (1990).
[CrossRef] [PubMed]

W. H. Swanson, H. R. Wilson, S. C. Giese, “Contrast matching data predicted from contrast increment thresholds,” Vision Res. 24, 63–75 (1984).
[CrossRef] [PubMed]

Wuerger, S.

E. Castet, S. Wuerger, “Perception of moving lines: interactions between local perpendicular signals and 2D motion signals,” Vision Res. 37, 705–720 (1997).
[CrossRef] [PubMed]

Yo, C.

C. Yo, H. R. Wilson, “Perceived direction of moving two-dimensional patterns depends on duration, contrast and eccentricity,” Vision Res. 32, 135–147 (1992).
[CrossRef] [PubMed]

Yund, E. W.

R. L. DeValois, E. W. Yund, N. Hepler, “The orientation and direction selectivity of cells in macaque visual cortex,” Vision Res. 22, 531–544 (1982).
[CrossRef]

Invest. Ophthalmol. Visual Sci.

H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).

M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028 (1993).

J. B. Mulligan, “A continuous version of the barber-pole illusion,” Invest. Ophthalmol. Visual Sci. 32, 829 (1991).

Y. Weiss, E. H. Adelson, “Integration and segmentation of nonrigid motion,” Invest. Ophthalmol. Visual Sci. 36, S228 (1995).

H. S. Orbach, G. Loffler, “What determines motion integration across apertures?” Invest. Ophthalmol. Visual Sci. 41, 2889 (2000).

J. Exp. Psychol. Hum. Percept. Perform.

M. Shiffrar, M. Pavel, “Percepts of rigid motion within and across apertures,” J. Exp. Psychol. Hum. Percept. Perform. 17, 749–761 (1991).
[CrossRef] [PubMed]

J. Neurosci.

E. Peterhans, R. Von der Heydt, “Mechanisms of contour perception in monkey visual-cortex. 2. Contours bridging gaps,” J. Neurosci. 9, 1749–1763 (1989).
[PubMed]

J. Opt. Soc. Am. A

Nature

E. H. Adelson, J. A. Movshon, “Phenomenal coherence of moving visual patterns,” Nature 300, 523–525 (1982).
[CrossRef] [PubMed]

Percept. Psychophys.

S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).

Psychol. Forsch.

H. Wallach, “Über visuell wahrgenommene Bewegungsrichtung,” Psychol. Forsch. 20, 325–380 (1935).
[CrossRef]

Vision Res.

J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992).
[CrossRef] [PubMed]

V. P. Ferrera, H. R. Wilson, “Perceived direction of moving two-dimensional patterns,” Vision Res. 30, 273–287 (1990).
[CrossRef] [PubMed]

L. S. Stone, A. B. Watson, J. B. Mulligan, “Effect of contrast on the perceived direction of a moving plaid,” Vision Res. 30, 1049–1067 (1990).
[CrossRef] [PubMed]

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Other

Note that, although the apertures in our experiments were invisible, such “pseudoreal” aperture terminators could conceivably be classified as extrinsic. This is because the apertures are physically absent in the sense of having zero contrast, but, as the line moves, the terminators trace out the shape of the aperture. (This possibility was raised, in conversation, by Mark Georgeson). The visual system could use this information to classify the terminator as arising from a line occluded by a circular aperture and hence be extrinsic in an elaborated intrinsic/extrinsic classification. To test this, the circular apertures were replaced with invisible rectangles in a control condition. The orientation of the rectangular apertures was perpendicular to the line’s orientation. This eliminated any difference between real and pseudoreal terminators. Nonetheless, the pattern of response was indistinguishable from that presented in Fig. 3, invalidating such a hypothesized modification of the intrinsic/extrinsic rule.

The space constants of the fitted Gaussians are 2.8° for the D6 patterns and 2.1° for lines. The (albeit small) difference in space constants would be even further reduced by fixing the asymptotes of the Gaussians to 45° (the expected value of perpendicular motion for an isolated line segment).

Obviously, this does not prove that higher-order processes cannot influence motion integration in addition to the low-level processes indicated here.

One may argue that a quantitative comparison between this and previous experiments should take the distance between the dot and the closest part of the line segment as a substitute for the inter-aperture gap. However, even given this correction, the results in this experiment still show a bias that is significantly closer to the perpendicular than for line terminators.

Note that the 1.7-cpd flanker frequency condition here (Fig. 9) is not identical to the previous experiment on D6 patterns (Fig. 7). In the previous experiment, the contrast for the central patch and the truncations were equal but had opposite signs. Here the contrasts of the three parts of the display were identical. This gives the impression of a set of aligned, but disconnected, black and white stripes, which might be predicted to appear more coherent than in the case of contrast-alternated stripes used before. The results show that this manipulation does not greatly affect observers’ judgments.

G. Loffler, “The integration of motion signals across space,” Ph.D. thesis (Glasgow Caledonian University, Glasgow, UK, 1999).

To avoid confusion, there is, of course, no “real” motion for a translating line presented on a monitor. Rather, the successive switching on and off of pixels creates the illusion of motion. So when we are talking about the real motion of a rigid line, this should be understood as the motion of the rigid object that could produce the stimulation.

This paper is concerned with motion in the two-dimensional frontoprallel plane; the term “rigidity” (or coherence) describes the perception of a single rigid object moving in this plane.

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Figures (10)

Fig. 1
Fig. 1

General methods. The diagram shows a 45° oriented line (width=0.25°) behind a three-aperture mask (dashed lines indicate invisible 1.6°-diameter apertures). The two outer apertures include the line terminators. The permanent fixation point was 0.93° away from the center of the central aperture, which always contained a featureless contour (here a line segment). Two absolute directions of motion (up and down) and five different inter-aperture gaps were employed in the experiments.

Fig. 2
Fig. 2

Perceived direction of motion for the line segment inside the central aperture as a function of inter-aperture gap for lines with 45° (A), 30° (B), and 60° (C) tilts. The arrows in the icons to the right of the graphs depict the perceived direction of motion of the line segments. Error bars are standard errors of the mean (N=32). The bold solid curves represent averaged responses. Regardless of line tilt, observer perception for small gaps was determined by the veridical signal from the terminators in the outer apertures and shifts toward the line’s orthogonal when gap size was increased.

Fig. 3
Fig. 3

Effects of scaling the stimulus by a factor of 1/3 by presenting the stimuli at a threefold increased viewing distance (240 cm). Consequently, the angle subtended by the widths of the lines (0.083°) as well as stimulus speed (1.67°/s), the aperture diameters (0.53°), and the gaps (0.13°, 0.4°, 0.67°, 1°, 1.5°) all changed. Note the similarity between the resulting curves for the data here and for experiment 1 (using appropriately scaled axes), indicating linear scaling.

Fig. 4
Fig. 4

Effect of terminator contrasts on high-contrast (97%) central segments. The data are averages across the three observers for terminator contrasts of 50%, 20%, and 5%. Error bars here represent inter-subject variability expressed as the standard error of the mean. While capture appears to be unaffected when terminator contrast is decreased to 50%, it is noticeably weakened for intermediate (20%) and completely absent for low (5%) feature contrast.

Fig. 5
Fig. 5

Effect of terminator contrasts on low-contrast (20%) central segments. The data are for terminator contrasts of 100%, 20%, and 5%. Capture between high-contrast (100%) terminators and low-contrast (20%) segments is stronger than between three contrast-matching (20%) stimuli. Unlike the results of the condition of a high-contrast central segment portrayed in Fig. 4, here even the lowest-contrast (5%) terminators are able to capture a midcontrast line segment.

Fig. 6
Fig. 6

Effect of skewing terminator orientation. The graph shows the subject-averaged data for four skews (5°, solid circles; 10°, open circles; 20°, solid squares; and 45°, open squares). Subjects tolerate skews of up to 20° before integration is significantly affected.

Fig. 7
Fig. 7

Effect of object interpretation on motion integration. The typical moving-line stimulus is replaced by a truncated stimulus exhibiting the profile of a D6 (peak spatial frequency=1.7 cpd), where the central segment is contrast reversed with respect to the flanking segments. The subject-averaged data are very close to those obtained with lines (Fig. 2) regardless of stimulus tilt (30° and 60° tilt data are not shown).

Fig. 8
Fig. 8

Influence of dots on a line segment. Results demonstrate the lack of strong interactions between such dissimilar stimuli (with one subject actually showing, for this 45° case, a weak repulsion from the physical direction of motion). This observation is independent of the tilt of the line segment (30° and 60° tilts are not shown).

Fig. 9
Fig. 9

Effect of truncation-segment spatial frequency on a 1.7-cpd central D6 segment. A small shift in frequency of the truncation (2.8 cpd) is sufficient to decrease integration noticeably. The influence of the truncations is virtually absent for a frequency of 5 cpd.

Fig. 10
Fig. 10

T-junction, “pseudoreal” intrinsic terminator, and real intrinsic terminator. A T-junction is accidentally generated by the intersection of an outlined (in this example, rectangular) aperture with a contour. If the same aperture has no visible border and is cut from a foreground that is identical to the line background inside the aperture, the intersection terminator is still accidental but is indistinguishable from a real terminator (shown on the right). Although a “pseudoreal” intrinsic and a real intrinsic terminator are visually identical, they are not identical physically, as one is the result of occlusion (albeit invisible) and the other an intrinsic part of a line. The terms “pseudoreal” intrinsic and real intrinsic aim to clarify the distinction.

Equations (3)

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f(x, y)=C exp[-(x/σx)Nx]exp[-(y/σy)Ny],
D6(x)=11515-90xσ2+60xσ4-8xσ6×exp-x2σ2.
DOG(x, y)=Cexp[-(x2+y2)/σ12]-σ1σ22exp[-(x2+y2)/σ22].

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