Abstract

We examined the effect of changing the composition of the carrier on the perception of motion in a drifting contrast envelope. Human observers were required to discriminate the direction of motion of contrast modulations of an underlying carrier as a function of temporal frequency and scaled (carrier) contrast. The carriers were modulations of both color and luminance, defined within a cardinal color space. Random-noise carriers had either binary luminance profiles or flat (gray-scale–white) or 1/f (pink) spectral power functions. Independent variables investigated were the envelope spatial frequency and temporal-drift frequency and the fundamental spatial frequency, color, and temporal-update frequency of the carrier. The results show that observers were able to discriminate correctly the direction of envelope motion for binary-noise carriers at both high (16 Hz) and low (2 Hz) temporal-drift frequencies. Changing the carrier format from binary noise to a flat (gray-scale) or 1/f amplitude profile reduced discrimination performance slightly but only in the high-temporal-frequency condition. Manipulation of the fundamental frequency of the carrier elicited no change in performance at the low temporal frequencies but produced ambiguous or reversed motion at the higher temporal frequencies as soon as the fundamental frequency was higher than the envelope modulation frequency. We found that envelope motion detection was sensitive to the structure of the carrier.

© 2001 Optical Society of America

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    [CrossRef] [PubMed]
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2000 (1)

O. I. Ukkonen, A. M. Derrington, “Motion of contrast-modulated grating is analysed by different mechanisms at low and at high contrasts,” Vision Res. 40, 3359–3371 (2000).
[CrossRef]

1999 (2)

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-defined motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2450 (1999).
[CrossRef]

A. Johnston, C. P. Benton, M. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli,” Vision Res. 39, 3849–3855 (1999).
[CrossRef]

1998 (3)

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

A. M. Derrington, M. J. Cox, “Temporal resolution of dichoptic and second-order motion mechanisms,” Vision Res. 38, 3531–3539 (1998).
[CrossRef]

S. J. Cropper, “The detection of luminance and chromatic contrast modulation by the visual system,” J. Opt. Soc. Am. A 15, 1969–1986 (1998).
[CrossRef]

1997 (5)

T. Ledgeway, A. T. Smith, “Changes in perceived speed following adaptation to first-order and second-order motion,” Vision Res. 37, 215–225 (1997).
[CrossRef] [PubMed]

S. J. Cropper, S. T. Hammett, “Adaptation to motion of a second order pattern: The motion aftereffect is not a general result,” Vision Res. 37, 2247–2259 (1997).
[CrossRef] [PubMed]

I. Kovacs, A. Feher, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1175 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artefact?” Vision Res. 37, 45–54 (1997).
[CrossRef] [PubMed]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

1996 (2)

S. J. Cropper, K. T. Mullen, D. R. Badcock, “Motion coherence across cardinal axes,” Vision Res. 36, 2475–2488 (1996).
[CrossRef] [PubMed]

S. J. Cropper, A. M. Derrington, “Detection and motion detection in chromatic and luminance beats,” J. Opt. Soc. Am. A 13, 401–407 (1996).
[CrossRef]

1995 (7)

A. T. Smith, T. Ledgeway, “Second-order motion: the carrier is crucial,” Perception 24, 28a (1995).

S. J. Cropper, D. R. Badcock, “Perceived direction of motion: It takes all orientations,” Perception 24, 106a (1995).

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings: predictions of the multi-channel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1784 (1995).
[CrossRef] [PubMed]

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

T. Ledgeway, A. T. Smith, “The perceived speed of second-order motion and its dependence on stimulus contrast,” Vision Res. 35, 1421–1434 (1995).
[CrossRef] [PubMed]

1994 (11)

H. R. Wilson, J. Kim, “Perceived motion in the vector-sum direction,” Vision Res. 34, 1835–1842 (1994).
[CrossRef] [PubMed]

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3079 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “The duration of the motion aftereffect following adaptation to first-order and second-order motion,” Perception 23, 1211–1219 (1994).
[CrossRef] [PubMed]

T. Ledgeway, “Adaptation to second-order motion results in a motion aftereffect for directionally ambiguous test stimuli.,” Vision Res. 34, 2879–2889 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, A. Hayes, “On the role of second-order signals in the perceived direction of motion of type II plaid patterns,” Vision Res. 34, 2609–2612 (1994).
[CrossRef] [PubMed]

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

S. J. Cropper, A. M. Derrington, “Motion of chromatic stimuli: first-order or second-order?” Vision Res. 34, 49–58 (1994).
[CrossRef] [PubMed]

R. T. Eskew, C. F. Stromeyer, R. E. Kronauer, “Temporal properties of the red–green chromatic mechanism,” Vision Res. 34, 3127–3137 (1994).
[CrossRef] [PubMed]

A. T. Smith, R. F. Hess, C. L. Baker, “Direction identification thresholds for second-order motion in central and peripheral vision,” J. Opt. Soc. Am. A 11, 506–514 (1994).
[CrossRef]

S. J. Cropper, D. R. Badcock, “Discriminating smooth from sampled motion: chromatic and luminance stimuli,” J. Opt. Soc. Am. A 11, 515–530 (1994).
[CrossRef]

1993 (2)

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, G. B. Henning, “Discriminating the direction of second-order motion at short stimulus durations,” Vision Res. 33, 1785–1794 (1993).
[CrossRef] [PubMed]

1992 (5)

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

D. I. A. MacLeod, D. R. Williams, W. Makous, “A visual non-linearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (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]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model for the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

1989 (1)

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: no role for distortion products,” Vision Res. 29, 731–739 (1989).
[CrossRef] [PubMed]

1988 (2)

1987 (3)

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: a monocular capability,” Vision Res. 27, 793–797 (1987).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Further observations on errors in direction-of-motion discrimination,” Invest. Ophthalmol. Visual Sci. Suppl. 28, 298 (1987).

1986 (2)

A. M. Derrington, D. R. Badcock, “Detection of spatial beats: non-linearity or contrast increment detection?” Vision Res. 26, 343–348 (1986).
[CrossRef] [PubMed]

A. B. Watson, A. Ahumada, J. E. Farrell, “Window of visibility: a psychophysical theory of fidelity in time-sampled visual displays,” J. Opt. Soc. Am. A 3, 300–307 (1986).
[CrossRef]

1985 (3)

K. T. Mullen, “The contrast sensitivity of human color vision to red/green and blue/yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacement of periodic patterns,” Vision Res. 25, 1253–1258 (1985).
[CrossRef] [PubMed]

1984 (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

1981 (1)

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

1978 (1)

J. M. Findlay, “Estimates on probability functions: a more virulent PEST,” Percept. Psychophys. 23, 181–185 (1978).
[CrossRef]

1975 (1)

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

1973 (1)

G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
[CrossRef] [PubMed]

1969 (1)

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

1966 (1)

1956 (1)

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der zeitreihenfolgen und vorzeichenauswertung bei der Bewegungspwezeption des Rüssekafers Chlorophanus,” Z. Naturforsch. 11b, 513–524 (1956).

Ahumada, A.

Anderson, S. J.

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Badcock, D. R.

S. J. Cropper, K. T. Mullen, D. R. Badcock, “Motion coherence across cardinal axes,” Vision Res. 36, 2475–2488 (1996).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, “Perceived direction of motion: It takes all orientations,” Perception 24, 106a (1995).

S. J. Cropper, D. R. Badcock, A. Hayes, “On the role of second-order signals in the perceived direction of motion of type II plaid patterns,” Vision Res. 34, 2609–2612 (1994).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, “Discriminating smooth from sampled motion: chromatic and luminance stimuli,” J. Opt. Soc. Am. A 11, 515–530 (1994).
[CrossRef]

A. M. Derrington, D. R. Badcock, G. B. Henning, “Discriminating the direction of second-order motion at short stimulus durations,” Vision Res. 33, 1785–1794 (1993).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: no role for distortion products,” Vision Res. 29, 731–739 (1989).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: a monocular capability,” Vision Res. 27, 793–797 (1987).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, “Detection of spatial beats: non-linearity or contrast increment detection?” Vision Res. 26, 343–348 (1986).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacement of periodic patterns,” Vision Res. 25, 1253–1258 (1985).
[CrossRef] [PubMed]

Baker, C. L.

Benton, C. P.

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-defined motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2450 (1999).
[CrossRef]

A. Johnston, C. P. Benton, M. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli,” Vision Res. 39, 3849–3855 (1999).
[CrossRef]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

Blakemore, C.

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

Brady, N.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Broadbent, D. E.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Burton, G. J.

G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
[CrossRef] [PubMed]

Buxton, H.

A. Johnston, P. W. McOwan, H. Buxton, “A computational model for the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

Cavanagh, P.

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef] [PubMed]

Chaparro, A.

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

Chubb, C.

Chubb, C. F.

C. F. Chubb, Department of Cognitive Sciences, University of California, Irvine, California 92697 (personal communication, May2001).

Clifford, C. W. G.

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings: predictions of the multi-channel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1784 (1995).
[CrossRef] [PubMed]

Cox, M. J.

A. M. Derrington, M. J. Cox, “Temporal resolution of dichoptic and second-order motion mechanisms,” Vision Res. 38, 3531–3539 (1998).
[CrossRef]

Cropper, S. J.

S. J. Cropper, “The detection of luminance and chromatic contrast modulation by the visual system,” J. Opt. Soc. Am. A 15, 1969–1986 (1998).
[CrossRef]

S. J. Cropper, S. T. Hammett, “Adaptation to motion of a second order pattern: The motion aftereffect is not a general result,” Vision Res. 37, 2247–2259 (1997).
[CrossRef] [PubMed]

S. J. Cropper, A. M. Derrington, “Detection and motion detection in chromatic and luminance beats,” J. Opt. Soc. Am. A 13, 401–407 (1996).
[CrossRef]

S. J. Cropper, K. T. Mullen, D. R. Badcock, “Motion coherence across cardinal axes,” Vision Res. 36, 2475–2488 (1996).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, “Perceived direction of motion: It takes all orientations,” Perception 24, 106a (1995).

S. J. Cropper, D. R. Badcock, A. Hayes, “On the role of second-order signals in the perceived direction of motion of type II plaid patterns,” Vision Res. 34, 2609–2612 (1994).
[CrossRef] [PubMed]

S. J. Cropper, A. M. Derrington, “Motion of chromatic stimuli: first-order or second-order?” Vision Res. 34, 49–58 (1994).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, “Discriminating smooth from sampled motion: chromatic and luminance stimuli,” J. Opt. Soc. Am. A 11, 515–530 (1994).
[CrossRef]

S. J. Cropper, “Human motion detection: different patterns, different detectors?” Ph.D. dissertation (University of Newcastle upon Tyne, Newcastle upon Tyne, UK, 1992).

S. J. Cropper, A. Johnston, “The detection of the motion of chromatic and luminance contrast modulation by the visual system,” manuscript available from the authors.

Derrington, A. M.

O. I. Ukkonen, A. M. Derrington, “Motion of contrast-modulated grating is analysed by different mechanisms at low and at high contrasts,” Vision Res. 40, 3359–3371 (2000).
[CrossRef]

A. M. Derrington, M. J. Cox, “Temporal resolution of dichoptic and second-order motion mechanisms,” Vision Res. 38, 3531–3539 (1998).
[CrossRef]

S. J. Cropper, A. M. Derrington, “Detection and motion detection in chromatic and luminance beats,” J. Opt. Soc. Am. A 13, 401–407 (1996).
[CrossRef]

S. J. Cropper, A. M. Derrington, “Motion of chromatic stimuli: first-order or second-order?” Vision Res. 34, 49–58 (1994).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, G. B. Henning, “Discriminating the direction of second-order motion at short stimulus durations,” Vision Res. 33, 1785–1794 (1993).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: no role for distortion products,” Vision Res. 29, 731–739 (1989).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: a monocular capability,” Vision Res. 27, 793–797 (1987).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Further observations on errors in direction-of-motion discrimination,” Invest. Ophthalmol. Visual Sci. Suppl. 28, 298 (1987).

A. M. Derrington, D. R. Badcock, “Detection of spatial beats: non-linearity or contrast increment detection?” Vision Res. 26, 343–348 (1986).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

D. R. Badcock, A. M. Derrington, “Detecting the displacement of periodic patterns,” Vision Res. 25, 1253–1258 (1985).
[CrossRef] [PubMed]

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Eskew, R. T.

R. T. Eskew, C. F. Stromeyer, R. E. Kronauer, “Temporal properties of the red–green chromatic mechanism,” Vision Res. 34, 3127–3137 (1994).
[CrossRef] [PubMed]

Farrell, J. E.

Feher, A.

I. Kovacs, A. Feher, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1175 (1997).
[CrossRef] [PubMed]

Ferrera, V. P.

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Field, D. J.

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

Findlay, J. M.

J. M. Findlay, “Estimates on probability functions: a more virulent PEST,” Percept. Psychophys. 23, 181–185 (1978).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Fleet, D. J.

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3079 (1994).
[CrossRef] [PubMed]

Hammett, S. T.

S. J. Cropper, S. T. Hammett, “Adaptation to motion of a second order pattern: The motion aftereffect is not a general result,” Vision Res. 37, 2247–2259 (1997).
[CrossRef] [PubMed]

Hassenstein, B.

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der zeitreihenfolgen und vorzeichenauswertung bei der Bewegungspwezeption des Rüssekafers Chlorophanus,” Z. Naturforsch. 11b, 513–524 (1956).

Hayes, A.

S. J. Cropper, D. R. Badcock, A. Hayes, “On the role of second-order signals in the perceived direction of motion of type II plaid patterns,” Vision Res. 34, 2609–2612 (1994).
[CrossRef] [PubMed]

Henning, G. B.

A. M. Derrington, D. R. Badcock, G. B. Henning, “Discriminating the direction of second-order motion at short stimulus durations,” Vision Res. 33, 1785–1794 (1993).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).
[CrossRef] [PubMed]

A. M. Derrington, G. B. Henning, “Further observations on errors in direction-of-motion discrimination,” Invest. Ophthalmol. Visual Sci. Suppl. 28, 298 (1987).

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Hertz, B. G.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

Hess, R. F.

Holliday, I. E.

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

Johnston, A.

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-defined motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2450 (1999).
[CrossRef]

A. Johnston, C. P. Benton, M. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli,” Vision Res. 39, 3849–3855 (1999).
[CrossRef]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings: predictions of the multi-channel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1784 (1995).
[CrossRef] [PubMed]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model for the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

S. J. Cropper, A. Johnston, “The detection of the motion of chromatic and luminance contrast modulation by the visual system,” manuscript available from the authors.

Kim, J.

H. R. Wilson, J. Kim, “Perceived motion in the vector-sum direction,” Vision Res. 34, 1835–1842 (1994).
[CrossRef] [PubMed]

Kovacs, I.

I. Kovacs, A. Feher, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1175 (1997).
[CrossRef] [PubMed]

Krauskopf, J.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Kronauer, R. E.

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

R. T. Eskew, C. F. Stromeyer, R. E. Kronauer, “Temporal properties of the red–green chromatic mechanism,” Vision Res. 34, 3127–3137 (1994).
[CrossRef] [PubMed]

Langley, K.

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3079 (1994).
[CrossRef] [PubMed]

Ledgeway, T.

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Changes in perceived speed following adaptation to first-order and second-order motion,” Vision Res. 37, 215–225 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artefact?” Vision Res. 37, 45–54 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Second-order motion: the carrier is crucial,” Perception 24, 28a (1995).

T. Ledgeway, A. T. Smith, “The perceived speed of second-order motion and its dependence on stimulus contrast,” Vision Res. 35, 1421–1434 (1995).
[CrossRef] [PubMed]

T. Ledgeway, “Adaptation to second-order motion results in a motion aftereffect for directionally ambiguous test stimuli.,” Vision Res. 34, 2879–2889 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “The duration of the motion aftereffect following adaptation to first-order and second-order motion,” Perception 23, 1211–1219 (1994).
[CrossRef] [PubMed]

Lennie, P.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Lu, Z.-L.

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

MacLeod, D. I. A.

D. I. A. MacLeod, D. R. Williams, W. Makous, “A visual non-linearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

Makous, W.

D. I. A. MacLeod, D. R. Williams, W. Makous, “A visual non-linearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

Marr, D.

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

McOwan, P. W.

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-defined motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2450 (1999).
[CrossRef]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model for the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Morgan, M. J.

A. Johnston, C. P. Benton, M. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli,” Vision Res. 39, 3849–3855 (1999).
[CrossRef]

Mullen, K. T.

S. J. Cropper, K. T. Mullen, D. R. Badcock, “Motion coherence across cardinal axes,” Vision Res. 36, 2475–2488 (1996).
[CrossRef] [PubMed]

K. T. Mullen, “The contrast sensitivity of human color vision to red/green and blue/yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Reichardt, W.

B. Hassenstein, W. Reichardt, “Systemtheoretische Analyse der zeitreihenfolgen und vorzeichenauswertung bei der Bewegungspwezeption des Rüssekafers Chlorophanus,” Z. Naturforsch. 11b, 513–524 (1956).

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).

Robson, J. G.

Smith, A. T.

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Changes in perceived speed following adaptation to first-order and second-order motion,” Vision Res. 37, 215–225 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artefact?” Vision Res. 37, 45–54 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Second-order motion: the carrier is crucial,” Perception 24, 28a (1995).

T. Ledgeway, A. T. Smith, “The perceived speed of second-order motion and its dependence on stimulus contrast,” Vision Res. 35, 1421–1434 (1995).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “The duration of the motion aftereffect following adaptation to first-order and second-order motion,” Perception 23, 1211–1219 (1994).
[CrossRef] [PubMed]

A. T. Smith, R. F. Hess, C. L. Baker, “Direction identification thresholds for second-order motion in central and peripheral vision,” J. Opt. Soc. Am. A 11, 506–514 (1994).
[CrossRef]

Sperling, G.

Z.-L. Lu, G. Sperling, “The functional architecture of human visual motion perception,” Vision Res. 35, 2697–2722 (1995).
[CrossRef] [PubMed]

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: a general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Drift-balanced random stimuli: A general basis for studying non-Fourier motion perception,” J. Opt. Soc. Am. A 5, 1986–2006 (1988).
[CrossRef] [PubMed]

Stromeyer, C. F.

R. T. Eskew, C. F. Stromeyer, R. E. Kronauer, “Temporal properties of the red–green chromatic mechanism,” Vision Res. 34, 3127–3137 (1994).
[CrossRef] [PubMed]

Stromeyer, C. F. I.

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Tolias, A.

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

Ukkonen, O. I.

O. I. Ukkonen, A. M. Derrington, “Motion of contrast-modulated grating is analysed by different mechanisms at low and at high contrasts,” Vision Res. 40, 3359–3371 (2000).
[CrossRef]

Ullman, S.

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Watson, A. B.

Werkhoven, P.

P. Werkhoven, G. Sperling, C. Chubb, “The dimensionality of texture-defined motion: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

Williams, D. R.

D. I. A. MacLeod, D. R. Williams, W. Makous, “A visual non-linearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, J. Kim, “Perceived motion in the vector-sum direction,” Vision Res. 34, 1835–1842 (1994).
[CrossRef] [PubMed]

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

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]

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]

H. R. Wilson, V. P. Ferrera, C. Yo, “A psychophysically motivated model for two-dimensional motion perception,” Visual Neurosci. 9, 79–97 (1992).
[CrossRef]

Invest. Ophthalmol. Visual Sci. Suppl. (2)

A. M. Derrington, G. B. Henning, “Further observations on errors in direction-of-motion discrimination,” Invest. Ophthalmol. Visual Sci. Suppl. 28, 298 (1987).

C. F. I. Stromeyer, A. Chaparro, A. Tolias, R. E. Kronauer, “Equiluminant settings change markedly with temporal frequency,” Invest. Ophthalmol. Visual Sci. Suppl. 36, 962 (1995).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

J. Physiol. (London) (3)

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

K. T. Mullen, “The contrast sensitivity of human color vision to red/green and blue/yellow chromatic gratings,” J. Physiol. (London) 359, 381–400 (1985).

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Percept. Psychophys. (1)

J. M. Findlay, “Estimates on probability functions: a more virulent PEST,” Percept. Psychophys. 23, 181–185 (1978).
[CrossRef]

Perception (3)

A. T. Smith, T. Ledgeway, “Second-order motion: the carrier is crucial,” Perception 24, 28a (1995).

S. J. Cropper, D. R. Badcock, “Perceived direction of motion: It takes all orientations,” Perception 24, 106a (1995).

T. Ledgeway, A. T. Smith, “The duration of the motion aftereffect following adaptation to first-order and second-order motion,” Perception 23, 1211–1219 (1994).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B (4)

I. E. Holliday, S. J. Anderson, “Different processes underlie the detection of second-order motion at low and high temporal frequencies,” Proc. R. Soc. London Ser. B 257, 165–173 (1994).
[CrossRef]

A. Johnston, C. P. Benton, P. W. McOwan, “Induced motion at texture-defined motion boundaries,” Proc. R. Soc. London Ser. B 266, 2441–2450 (1999).
[CrossRef]

D. Marr, S. Ullman, “Directional selectivity and its use in early visual processing,” Proc. R. Soc. London Ser. B 211, 151–180 (1981).
[CrossRef]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model for the analysis of some first-order and second-order motion patterns by simple and complex cells,” Proc. R. Soc. London Ser. B 250, 297–306 (1992).
[CrossRef]

Science (1)

P. Cavanagh, “Attention-based motion perception,” Science 257, 1563–1565 (1992).
[CrossRef] [PubMed]

Vision Res. (33)

A. M. Derrington, G. B. Henning, “Errors in direction-of-motion discrimination with complex stimuli,” Vision Res. 27, 61–75 (1987).
[CrossRef] [PubMed]

A. M. Derrington, M. J. Cox, “Temporal resolution of dichoptic and second-order motion mechanisms,” Vision Res. 38, 3531–3539 (1998).
[CrossRef]

S. J. Cropper, A. M. Derrington, “Motion of chromatic stimuli: first-order or second-order?” Vision Res. 34, 49–58 (1994).
[CrossRef] [PubMed]

S. J. Cropper, K. T. Mullen, D. R. Badcock, “Motion coherence across cardinal axes,” Vision Res. 36, 2475–2488 (1996).
[CrossRef] [PubMed]

R. T. Eskew, C. F. Stromeyer, R. E. Kronauer, “Temporal properties of the red–green chromatic mechanism,” Vision Res. 34, 3127–3137 (1994).
[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]

N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995).
[CrossRef] [PubMed]

I. Kovacs, A. Feher, “Non-Fourier information in bandpass noise patterns,” Vision Res. 37, 1167–1175 (1997).
[CrossRef] [PubMed]

A. T. Smith, T. Ledgeway, “Sensitivity to second-order motion as a function of temporal frequency and eccentricity,” Vision Res. 38, 403–410 (1998).
[CrossRef] [PubMed]

O. I. Ukkonen, A. M. Derrington, “Motion of contrast-modulated grating is analysed by different mechanisms at low and at high contrasts,” Vision Res. 40, 3359–3371 (2000).
[CrossRef]

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artefact?” Vision Res. 37, 45–54 (1997).
[CrossRef] [PubMed]

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyses spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[CrossRef] [PubMed]

S. J. Cropper, D. R. Badcock, A. Hayes, “On the role of second-order signals in the perceived direction of motion of type II plaid patterns,” Vision Res. 34, 2609–2612 (1994).
[CrossRef] [PubMed]

D. J. Fleet, K. Langley, “Computational analysis of non-Fourier motion,” Vision Res. 34, 3057–3079 (1994).
[CrossRef] [PubMed]

T. Ledgeway, “Adaptation to second-order motion results in a motion aftereffect for directionally ambiguous test stimuli.,” Vision Res. 34, 2879–2889 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “The perceived speed of second-order motion and its dependence on stimulus contrast,” Vision Res. 35, 1421–1434 (1995).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Changes in perceived speed following adaptation to first-order and second-order motion,” Vision Res. 37, 215–225 (1997).
[CrossRef] [PubMed]

G. J. Burton, “Evidence for non-linear response processes in the human visual system from measurements on the thresholds of spatial beat frequencies,” Vision Res. 13, 1211–1225 (1973).
[CrossRef] [PubMed]

D. I. A. MacLeod, D. R. Williams, W. Makous, “A visual non-linearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

S. J. Cropper, S. T. Hammett, “Adaptation to motion of a second order pattern: The motion aftereffect is not a general result,” Vision Res. 37, 2247–2259 (1997).
[CrossRef] [PubMed]

A. Johnston, C. W. G. Clifford, “Perceived motion of contrast-modulated gratings: predictions of the multi-channel gradient model and the role of full-wave rectification,” Vision Res. 35, 1771–1784 (1995).
[CrossRef] [PubMed]

A. Johnston, C. P. Benton, M. J. Morgan, “Concurrent measurement of perceived speed and speed discrimination threshold using the method of single stimuli,” Vision Res. 39, 3849–3855 (1999).
[CrossRef]

H. R. Wilson, J. Kim, “Perceived motion in the vector-sum direction,” Vision Res. 34, 1835–1842 (1994).
[CrossRef] [PubMed]

C. P. Benton, A. Johnston, “First-order motion from contrast modulated noise?” Vision Res. 37, 3073–3078 (1997).
[CrossRef]

D. R. Badcock, A. M. Derrington, “Detecting the displacement of periodic patterns,” Vision Res. 25, 1253–1258 (1985).
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D. R. Badcock, A. M. Derrington, “Detecting the displacements of spatial beats: no role for distortion products,” Vision Res. 29, 731–739 (1989).
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[CrossRef] [PubMed]

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Figures (15)

Fig. 1
Fig. 1

Schematic Fourier transforms: (a) The amplitude spectrum of an amplitude modulated grating with carrier spatial frequency b and envelope spatial frequency a. (b) When the spatial frequency of the carrier is less than the spatial frequency of the envelope, all components fall in the quadrants corresponding to motion in the same direction as that of the envelope. (c) Modulation of broadband noise results in an approximately flat spectrum, although there will be different variations in level for each instantiation of noise (not shown). Each component is shifted as in (a) and (b). (d) A lower bound can be placed on noise carriers such that for all components the relationship seen in (b) is avoided.

Fig. 2
Fig. 2

Detection thresholds for grating and noise unmodulated carriers. Mean L–M-cone contrast is plotted against the spatial frequency of the fundamental in the noise (or of the grating). The format of the carrier is indicated in the legend. Data for four observers is shown, one observer per panel. Stimuli were presented in a two-alternative forced-choice detection paradigm within a 20° disk and a raised-cosine temporal envelope, the half-width of which was 500 ms.  

Fig. 3
Fig. 3

Envelope direction-discrimination with different carrier types as a function of contrast for observer SJC. The perceived direction of envelope motion is plotted against the carrier (Michelson) contrast for low (2-Hz) and high (16-Hz) temporal envelope drift rates to illustrate the basic discrepancy in the data motivating the study. Top panel, data for a dynamic (updated at 25 Hz) carrier; bottom panel, data for a static (not-updated) carrier; additionally denoted (i) and (ii). There were at least 40 observations per point, and the error bars are ± standard error of the mean (also in all subsequent figures). Symbols denoting different carrier types are indicated in the legend. Fundamental in the noise, 0.044 cpd; spatial frequency of the envelope, 0.2 cpd; 100% modulation. This general format (with differences between the x axes and symbols and observers) is followed throughout the paper.

Fig. 4
Fig. 4

Envelope direction discrimination with different carrier types as a function of temporal frequency for observer RM. The perceived envelope direction is plotted against the temporal drift frequency of the 0.2-cpd envelope. The carrier contrast was 1.5 log units above detection threshold (Michelson peak ∼0.93) with a fundamental of 0.044 cpd. Other details as in Fig. 3.

Fig. 5
Fig. 5

Envelope direction discrimination for one-dimensional flat (gray-scale) noise carriers to examine the effect of increasing the fundamental in the noise. The perceived direction of envelope motion is plotted against the carrier contrast [(a) Michelson, SJC; (b) threshold multiples, RM and MW] for low (solid symbols, 2 Hz) and high (open symbols, 16 Hz) temporal drift rates. The fundamental is progressively increased as indicated in the legend. Open symbols, conditions in which the fundamental is at a higher spatial frequency than the envelope (0.2 cpd). Carrier contrast is 1.5 log units above threshold for observers RM and MW.

Fig. 6
Fig. 6

As in Figs. 5(a)–5(b) except that the carrier was 1/f in its amplitude profile.

Fig. 7
Fig. 7

Similar to Figs. 5(a) and 5(b) except that the independent variable plotted on the x axis is temporal drift frequency. The carrier contrast was set at 1.5 log units above detection threshold for all observers, and the amplitude spectra were either flat [(a) RM, (b) TB] or had a 1/f profile with respect to spatial frequency [(c), (d)]. Other details as in Fig. 3.

Fig. 8
Fig. 8

As in Fig. 7(d) except that the stimulus was restricted to a 4° centrally located window. Small symbols indicate this condition; large symbols are the 20° condition replicated from Fig. 7(d).

Fig. 9
Fig. 9

Direction discrimination for an envelope (0.2 cpd) modulating a 1/f red–green noise carrier as fundamental carrier frequency increases. The perceived direction of envelope motion is plotted against the temporal drift frequency. The carrier contrast was set at a maximum of 1.3 log units above detection threshold for the three observers. Other details as in previous figures.

Fig. 10
Fig. 10

(a) Envelope direction discrimination as a function of envelope spatial frequency for a fixed fundamental frequency. Temporal drift frequency and carrier fundamental spatial frequency are indicated in the legend. Arrows on the x axis indicate the fundamental frequencies of the carriers. Open and solid arrowheads relate to open and solid symbols. (a) Data for a flat noise carrier at a contrast of 1.5 log units above threshold for observer RM. (b)–(d) As (a) except that the carrier has 1/f noise profile.

Fig. 11
Fig. 11

Envelope direction discrimination plotted against temporal drift rate at a reduced stimulus duration of 107 ms for a 1/f noise profile. All other conditions are the same as Fig. 7(c), which should be examined for comparison for observer RM. Reduced conditions allow comparison (500 ms) data to be included for observer MW in (b) [see also Fig. 7(d)].

Fig. 12
Fig. 12

Envelope direction discrimination as a function of temporal drift frequency for the fundamental alone. Details the same as Fig. 7(c), which should be taken as the comparison figure for observer RM. (a) Carrier contrast 1.5 log units above threshold for a 1/f noise carrier of the same fundamental spatial frequency. (b) Carrier contrast 0.3 log unit above threshold. See text for an explanation of the 0.362-cpd plots.

Fig. 13
Fig. 13

Direction discrimination as a function of envelope spatial frequency for a fixed fundamental frequency. Fundamental alone at a contrast of 0.3 log unit above detection threshold for the 1/f noise profile. As a comparison figure, and for other details, see Figs. 10(b) (RM) and 10(d) (MW).

Fig. 14
Fig. 14

Envelope direction discrimination for the fundamental alone (0.044 cpd, 0.3 log unit above threshold) with a noise mask superimposed on the stimulus. Perceived direction is plotted against the Michelson (peak) contrast of the noise mask. The mask may be static or dynamic and had a flat (gray-scale or binary) amplitude profile. Upper panel, drift rate of 12 Hz; lower panel, drift rate of 16 Hz.

Fig. 15
Fig. 15

Effect of carrier update rate on envelope direction discrimination for a 1/f noise carrier as a function of Michelson contrast. The perceived direction of envelope motion is plotted against the carrier contrast for low (2 Hz) and high (16 Hz) temporal envelope drift rates. The dynamic carrier is updated at 25 Hz (Fig. 3) and at 75 Hz as indicated. The main observer is SJC with supplementary observers BW and MW. Other details as in Fig. 3.

Equations (7)

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L(y,t)=Lm{1+Ccsin 2π(fcy+ϕc)×0.5[1+M cos 2π(fenvy+wenvt+ϕenv)]},
L(y,t)=Lm{1+Cc[Rand_wave(fcy+ϕ1)]×0.5[1+M cos 2π(fenvy+wenvt)]},
L(y, t)=(cos A+1)cos B,
L(y, t)=cos A cos B+cos B.
cos A cos B=1/2 [cos(A+B)+cos(A-B)],
L(x, t)=1/2 [cos(ay+wt+by)+cos(ay+wt-by)]+cos(by),
L(x, t)=1/2 {cos[(a+b)y+wt]+cos[(a-b)y+wt]}+cos(by).

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