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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 8 — Aug. 1, 2003
  • pp: 1472–1489

Modeling the integration of motion signals across space

Gunter Loffler and Harry S. Orbach  »View Author Affiliations

JOSA A, Vol. 20, Issue 8, pp. 1472-1489 (2003)

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Experiments by Loffler and Orbach on the integration of motion signals across space [J. Opt. Soc. Am. A 20, 1461 (2003)] revealed that both three-dimensional analysis and object interpretation play a much smaller role than previously assumed. These results motivated the quantitative description of a low-level, bottom-up model presented here. Motion is computed in parallel at different spatial sites, and excitatory interactions operate between sites. The strength of these interactions is determined mainly by distance. Simulations correctly predict behavior for a variety of manipulations on multi-aperture stimuli: aligned and skewed lines, different presentation times, different inter-aperture gaps, and different spatial frequencies. However, strictly distance-dependent mechanisms are too simplistic to account for all experimental data. Mismatches for grossly misoriented lines suggest collinear facilitation as a promising extension. Once incorporated, collinear facilitation not only correctly predicts results for misoriented patterns but also accounts for the lack of motion integration between heterogeneous stimuli such as lines and dots.

© 2003 Optical Society of America

OCIS Codes
(330.4060) Vision, color, and visual optics : Vision modeling
(330.4150) Vision, color, and visual optics : Motion detection
(330.7310) Vision, color, and visual optics : Vision

Original Manuscript: October 7, 2002
Revised Manuscript: March 5, 2003
Manuscript Accepted: March 5, 2003
Published: August 1, 2003

Gunter Loffler and Harry S. Orbach, "Modeling the integration of motion signals across space," J. Opt. Soc. Am. A 20, 1472-1489 (2003)

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  1. D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of the monkey striate cortex,” J. Physiol. 195, 215–243 (1968).
  2. H. Wallach, “Über visuell wahrgenommene Bewegungsrichtung,” Psychol. Forsch. 20, 325–380 (1935). [CrossRef]
  3. M. B. Ben-Av, M. Shiffrar, “When ambiguous becomes unambiguous,” Invest. Ophthalmol. Visual Sci. 34, 1028–1028 (1993).
  4. F. L. Kooi, “Local direction of edge motion causes and abolishes the barberpole illusion,” Vision Res. 33, 2347–2351 (1993). [CrossRef] [PubMed]
  5. 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]
  6. H. S. Orbach, H. R. Wilson, “Fourier and non-Fourier terminators in motion perception,” Invest. Ophthalmol. Visual Sci. 35, 1827 (1994).
  7. G. Loffler, H. S. Orbach, “Factors affecting motion integration,” J. Opt. Soc. Am. A 20, 1461–1471 (2003). [CrossRef]
  8. 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]
  9. E. Castet, V. Charton, A. Dufour, “The extrinsic/intrinsic classification of two-dimensional motion signals with barber-pole stimuli,” Vision Res. 39, 915–932 (1999). [CrossRef] [PubMed]
  10. E. Castet, S. Wuerger, “Perception of moving lines: in-teractions between local perpendicular signals and 2D motion signals,” Vision Res. 37, 705–720 (1997). [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. G. Loffler, H. S. Orbach, “Computing feature motion without feature detectors: a model for terminator motion without end-stopped cells,” Vision Res. 39, 859–871 (1999). [CrossRef] [PubMed]
  14. N. M. Grzywacz, A. L. Yuille, “Theories for the visual perception of local velocity and coherent motion,” in Computional Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 231–252.
  15. E. C. Hildreth, The Measurement of Visual Motion (MIT Press, Cambridge, Mass., 1984).
  16. 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]
  17. J. Chey, S. Grossberg, E. Mingolla, “Neural dynamics of motion grouping: from aperture ambiguity to object speed and direction,” J. Opt. Soc. Am. A 14, 2570–2594 (1997). [CrossRef]
  18. S. Grossberg, E. Mingolla, “Neural dynamics of motion perception: direction fields, apertures, and resonant grouping,” Percept. Psychophys. 53, 248–278 (1993).
  19. S. J. Nowlan, T. J. Sejnowski, “A selection model for motion processing in area MT of primates,” J. Neurosci. 15, 1195–1214 (1995). [PubMed]
  20. Z. Y. Yang, A. Shimpi, D. Purves, “A wholly empirical explanation of perceived motion,” Proc. Natl. Acad. Sci. USA 98, 5252–5257 (2001).
  21. Y. Weiss, E. P. Simoncelli, E. H. Adelson, “Motion illusions as optimal percepts,” Nat. Neurosci. 5, 598–604 (2002). [CrossRef] [PubMed]
  22. H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992). [CrossRef]
  23. W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed. (Wiley, New York, 1961), pp. 303–317.
  24. J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985). [CrossRef] [PubMed]
  25. K. I. Naka, W. A. Rushton, “S-potentials from colour units in the retina of the fish,” J. Physiol. 185, 584–599 (1966).
  26. Note that neither the inputs, Ix,y[Eq. (1)], nor the recurrent inhibition [Eq. (2)] extends over the entire range of directions (±180°) but instead are restricted to relative angles of ±120°. The only reason for this limitation is to allow the local network to signal more than one direction of motion in circumstances of transparency.27Following this argument, such a network signals transparency by a bimodality in MT pattern unit responses. However, in agreement with psychophysical data,7all global simulations presented here resulted in a single direction of motion, and the simulations never predicted transparency.
  27. H. R. Wilson, J. Kim, “Perceived motion in the vector sum direction,” Vision Res. 34, 1835–1842 (1994). [CrossRef] [PubMed]
  28. 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]
  29. J. Kim, H. R. Wilson, “Dependence of plaid motion coherence on component grating directions,” Vision Res. 33, 2479–2489 (1993). [CrossRef] [PubMed]
  30. J. Kim, H. R. Wilson, “Direction repulsion between components in motion transparency,” Vision Res. 36, 1177–1187 (1996). [CrossRef] [PubMed]
  31. H. R. Wilson, J. Kim, “A model for motion coherence and transparency,” Visual Neurosci. 11, 1205–1220 (1994). [CrossRef]
  32. To simulate the temporal dynamics of the coupled differential equations, the fast Euler method has been employed.To verify this approach, initial sample simulations were undertaken in which the Euler method was compared with the considerably slower but more stable fourth-order Runge–Kutta method. These sample simulations proved that for a sufficiently low step size of 1/4τ, the two methods give indistinguishable results, with the Euler method being faster by a factor of ∼3.
  33. D. G. Albrecht, D. B. Hamilton, “Striate cortex of monkey and cat: contrast response functions,” J. Neurophysiol. 48, 217–237 (1982). [PubMed]
  34. G. Sclar, J. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990). [CrossRef] [PubMed]
  35. 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]
  36. T. D. Albright, “Direction and orientation selectivity of neurons in visual area MT of the macaque,” J. Neurophysiol. 52, 1106–1130 (1984). [PubMed]
  37. J. H. R. Maunsell, D. C. Van Essen, “Functional properties of neurons in middle temporal visual area of the macaque monkey. I. Selectivity for stimulus direction, speed, and orientation,” J. Neurophysiol. 49, 1127–1147 (1983). [PubMed]
  38. J. A. Movshon, W. T. Newsome, “Visual response properties of striate cortical neurons projecting to area MT in macaque monkeys,” J. Neurosci. 16, 7733–7741 (1996). [PubMed]
  39. H. R. Rodman, T. D. Albright, “Single unit analysis of patter-motion selective properties in the middle temporal area (MT),” Exp. Brain Res. 75, 53–64 (1989). [CrossRef]
  40. S. Raiguel, M. M. Van Hulle, D.-K. Xiao, V. L. Marcar, G. A. Orban, “Shape and spatial distribution of receptive fields and antagonistic motion surrounds in the middle temporal area (V5) of the macaque,” Eur. J. Neurosci. 7, 2064–2082 (1995). [CrossRef] [PubMed]
  41. G. G. Blasdel, D. Fitzpatrick, “Physiological organisation of layer-4 in macaque striate cortex,” J. Neurosci. 4, 880–895 (1984). [PubMed]
  42. D. C. Van Essen, “The visual field representation in striate cortex of the macaque monkey: asymmetries, anisotropies, and individual variability,” Vision Res. 24, 429–448 (1984). [CrossRef] [PubMed]
  43. H. R. Wilson, “A model for direction selectivity in threshold motion perception,” Biol. Cybern. 51, 213–222 (1985). [CrossRef] [PubMed]
  44. H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984). [CrossRef] [PubMed]
  45. H. R. Wilson, W. A. Richards, “Curvature and separation discrimination at texture boundaries,” J. Opt. Soc. Am. A 9, 1653–1662 (1992). [CrossRef] [PubMed]
  46. H. R. Wilson, “Psychophysical models of spatial vision and hyperacuity,” in Spatial Vision, D. Regan, ed. (MacMillan, New York, 1991), pp. 64–86.
  47. There are two conceptually different ways to treat neural sites corresponding to locations of a scene without stimulation (e.g., aperture gaps). Grzywacz and Yuille14proposed a model in which lateral interactions result in motion signals at every point of the visual field regardless of whether the field was initially stimulated by a moving object. It is unclear whether this correctly reflects neurophysiology. The approach taken here is different. Spatial sites that are not initially activated by motion in their receptive field are not activated by lateral interactions; rather, they stay silent. This is consistent with the approach of relating the activity of MT pattern neurons directly to behavior48,49and noting that, behaviorally, parts of the visual field that have not been stimulated do not appear to have motion associated with them. Mathematically, this approach is achieved by modulating lateral interactions by a site’s activity: If a site does not receive any bottom-up input through its local computations, lateral excitation stays silent.
  48. C. D. Salzman, C. M. Murasugi, K. H. Britten, W. T. Newsome, “Microstimulation in visual area MT—effects on direction discrimination performance,” J. Neurosci. 12, 2331–2355 (1992). [PubMed]
  49. K. H. Britten, M. N. Shadlen, W. T. Newsome, J. A. Movshon, “The analysis of visual-motion—a comparison of neuronal and psychophysical performance,” J. Neurosci. 12, 4745–4765 (1992). [PubMed]
  50. M. B. Ben-Av, M. Shiffrar, “Disambiguating velocity estimates across image space,” Vision Res. 35, 2889–2895 (1995). [CrossRef] [PubMed]
  51. G. Loffler, “The integration of motion signals across space,” Ph.D. thesis (Glasgow Caledonian University, Cowcaddens Road, Glasgow G4 0BA, UK, 1999).
  52. R. Hess, D. Field, “Integration of contours: new insights,” Trends Cogn. Sci. 3, 480–486 (1999). [CrossRef] [PubMed]
  53. Note the difference between this term, which depends on line-segment orientation, and the motion-discontinuity term in Eq. (4), which depends on direction of motion.
  54. To simulate this condition, a small amount of (random) noise was added to the initial V1 simple cell responses. Without this noise, it would be impossible to extract a maximally excited cell, as all cells would have the same firing rate. The randomly added noise (unique to this condition) is the reason for the small capturing behavior of the network for the smallest gap which represents the average over 20 model simulations.
  55. For example, L. Liden, C. Pack, “The role of terminators and occlusion cues in motion integration and segmentation: a neural network model,” Vision Res. 39, 3301–3320 (1999). [CrossRef]
  56. M. A. Georgeson, G. S. A. Barbieri-Hesse, T. C. A. Freeman, “The primal sketch revisited: locating and representing edges in human vision via Gaussian-derivative filtering,” Perception 31, 1 (2002).
  57. A. P. Georgopoulos, M. Taira, A. Lukashin, “Cognitive neurophysiology of the motor cortex,” Science 260, 47–52 (1993). [CrossRef] [PubMed]
  58. R. A. Andersen, L. H. Snyder, C.-S. Li, B. Stricanne, “Coordinate transformations in the representation of spatial information,” Curr. Opin. Neurobiol. 3, 171–176 (1993). [CrossRef] [PubMed]
  59. C. D. Salzman, W. T. Newsome, “Neural mechanisms for forming a perceptual decision,” Science 264, 231–237 (1994). [CrossRef] [PubMed]
  60. C. C. Pack, R. T. Born, “Temporal dynamics of a neural solution to the aperture problem in visual area MT of macaque brain,” Nature 409, 1040–1042 (2001). [CrossRef] [PubMed]
  61. D. Bradley, “MT signals: better with time,” Nat. Neurosci. 4, 346–348 (2001). [CrossRef] [PubMed]
  62. J. Allman, F. Miezin, E. McGuinness, “Stimulus specific responses from beyond the classical receptive-field: neurophysiological mechanisms for local–global comparisons in visual neurons,” Annu. Rev. Neurosci. 8, 407–430 (1985). [CrossRef]
  63. R. T. Born, R. B. H. Tootell, “Segregation of global and local motion processing in primate middle temporal visual area,” Nature 357, 497–499 (1992). [CrossRef] [PubMed]
  64. K. Tanaka, K. Hikosaka, H.-A. Saito, M. Yukie, Y. Fukada, E. Iwai, “Analysis of local and wide-field movements in the superior temporal visual areas of the macaque monkey,” J. Neurosci. 6, 134–144 (1986). [PubMed]
  65. K. S. Rockland, J. S. Lund, “Widespread periodic intrinsic connections in the tree shrew visual-cortex,” Science 215, 1532–1534 (1982). [CrossRef] [PubMed]
  66. K. E. Schmidt, R. Goebel, S. Lowel, W. Singer, “The perceptual grouping criterion of collinearity is reflected by anisotropies of connections in the primary visual cortex,” Eur. J. Neurosci. 9, 1083–1089 (1997). [CrossRef] [PubMed]
  67. W. H. Bosking, Y. Zhang, B. Schofield, D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex,” J. Neurosci. 17, 2112–2127 (1997). [PubMed]
  68. R. Malach, Y. Amir, M. Harel, A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in-vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. USA 90, 10469–10473 (1993). [CrossRef]
  69. W. S. Geisler, J. S. Perry, B. J. Super, D. P. Gallogly, “Edge co-occurrence in natural images predicts contour grouping performance,” Vision Res. 41, 711–724 (2001). [CrossRef] [PubMed]
  70. U. Polat, D. Sagi, “Lateral interactions between spatial channels—suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993). [CrossRef] [PubMed]
  71. D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual-system—evidence for a local association field,” Vision Res. 33, 173–193 (1993). [CrossRef] [PubMed]
  72. R. F. Hess, W. H. A. Beaudot, K. T. Mullen, “Dynamics of contour integration,” Vision Res. 41, 1023–1037 (2001). [CrossRef] [PubMed]
  73. P. J. Bex, A. J. Simmers, S. C. Dakin, “Snakes and ladders: the role of temporal modulation in visual contour integration,” Vision Res. 41, 3775–3782 (2001). [CrossRef] [PubMed]
  74. W. Marshak, R. Sekuler, “Mutual repulsion between moving visual targets,” Science 205, 1399–1401 (1979). [CrossRef] [PubMed]
  75. G. Mather, B. Moulden, “A simultaneous shift in apparent direction: further evidence for a ‘distributional-shift’ model of direction coding,” Q. J. Exp. Psychol. 32, 325–333 (1980). [CrossRef] [PubMed]
  76. M. Nawrot, R. Sekuler, “Assimilation and contrast in motion perception—explorations in cooperativity,” Vision Res. 30, 1439–1451 (1990). [CrossRef]
  77. R. J. Snowden, “Motions in orthogonal directions are mutually suppressive,” J. Opt. Soc. Am. A 6, 1096–1101 (1989). [CrossRef]
  78. J. Kim, H. R. Wilson, “Motion integration over space: interaction of the center and surround motion,” Vision Res. 37, 991–1005 (1997). [CrossRef] [PubMed]
  79. E. Mingolla, J. T. Todd, J. F. Norman, “The perception of globally coherent motion,” Vision Res. 32, 1015–1031 (1992). [CrossRef] [PubMed]
  80. J. Lorenceau, L. Zago, “Cooperative and competitive spatial interactions in motion integration,” Vision Res. 16, 755–770 (1999).
  81. J. Lorenceau, M. Shiffrar, “The influence of terminators on motion integration across space,” Vision Res. 32, 263–273 (1992). [CrossRef] [PubMed]
  82. H. R. Wilson, J. D. Cowan, “A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue,” Kybernetik 13, 55–80 (1973). [CrossRef] [PubMed]
  83. S. Grossberg, “Contour enhancement, short-term memory and constances in reverberating neural networks,” Stud. Appl. Math. 52, 217–257 (1973).
  84. H. R. Wilson, “Hysterisis in binocular grating perception: contrast effects,” Vision Res. 17, 843–851 (1977). [CrossRef]
  85. H. R. Wilson, Spikes, Decisions, and Actions (Oxford U. Press, Oxford, UK, 1999).
  86. The nature and stability of the steady state was estimated by considering the linear terms of a Taylor expansion of the nonlinear dynamics at the equilibrium points (for details of this approach see Ref. 85). The corresponding exponentials have negative real parts, and the equilibrium is consequently stable.
  87. It is important to emphasize that this kind of undamped propagation does not necessarily result in a single direction of motion in the more complicated case of a dynamic multiobject environment. Signal propagation is strong only for adjacent or overlapping sites. As our experiments show, any gap between sites weakens propagation and allows different directions of motion for nearby objects in a scene.
  88. H. S. Orbach, G. Loffler, “Motion integration across apertures: theory and experiment,” Invest. Ophthalmol. Visual Sci. 42, 4685 (2001).

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