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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1531–1540

Imputation of direction of motion in one dimension

Miguel A. García-Pérez and Eli Peli  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1531-1540 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001531


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Abstract

Under many conditions below the Nyquist limit, a drifting grating briefly displayed on a CRT is consistently perceived as moving in the opposite direction. Taking into account the sample-and-hold operation of CRT’s, we have derived the temporal-frequency spectra of the displayed gratings and found that they have a broad range of components moving in either direction. We have measured the perceived direction of motion of over 150 different short-duration stimuli, and we have studied the relation that performance bears to narrow-band power imbalance—the normalized difference between power in the positive- and negative-frequency half-lines within a specific band. Perceived direction of motion is highly related to power imbalance in 1-Hz-wide bands centered between 10 and 15 Hz, but none of these bands alone can account for more than 84–91% of the variance of the data, and each band ostensibly fails to explain data from a subset of the stimuli. When broadband power imbalance is determined by weighting the spectrum with an inverted-U-shaped function peaking at ∼12 Hz, the explained variance increases to 91–97%. Our results suggest that the imputation of direction of motion to stimuli with complex spectra is based on broadband power imbalance determined after weighting the temporal-frequency spectrum with an inverted-U-shaped function.

© 1999 Optical Society of America

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.5510) Vision, color, and visual optics : Psychophysics
(330.7310) Vision, color, and visual optics : Vision

Citation
Miguel A. García-Pérez and Eli Peli, "Imputation of direction of motion in one dimension," J. Opt. Soc. Am. A 16, 1531-1540 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1531


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References

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  6. This description is only a convenient simplification. Line raster, phosphor response, and display bandwidth all contribute to making the actual image displayed in each frame slightly different from what we just described.
  7. A. B. Watson and K. Turano, “The optimal motion stimulus,” Vision Res. 35, 325–336 (1995).
  8. Data at the highest nominal velocity (isolated points at the right in each panel) serve as a control condition of flicker and, not surprisingly, performance is near the 50% (guessing) level in all cases. We will no longer refer to these data.
  9. As will become clear in our discussion about Fig. 8, net directional power cannot account for our results even if it is computed within the temporal-frequency bounds of the window of visibility.10
  10. A. B. Watson, A. J. Ahumada, Jr., and J. Farrell, “Window of visibility: a psychophysical theory of fidelity in time-sampled visual motion displays,” J. Opt. Soc. Am. A 3, 300–307 (1986).
  11. Recall, however, that only 16 of the 19 conditions were actually different, since one of them (constant-contrast three-frame presentations) was replicated twice and another (constant-contrast two-frame presentations) was replicated once.
  12. There are a few instances of stimuli that come out with small negative power imbalance values, but they are simply artifacts caused by our using temporal frequencies only up to 65 Hz in the computation of P and P+ in Eqs. (3) and (4).
  13. The inherent variability in the data should be taken into account for this judgment. Data from our conditions with flickering stimuli give an estimate of this variability, and these data can easily be seen in the panels of Fig. 8(c) as a string of vertically aligned points at an abscissa of 0 and around an ordinate of 50. The vertical spread of these strings gives an indication of the response variability that one has to put up with in these plots.
  14. D. J. Fleet and K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3079 (1994).
  15. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

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