Abstract

Lu and Sperling [Vision Res. 35, 2697 (1995)] proposed that human visual motion perception is served by three separate motion systems: a first-order system that responds to moving luminance patterns, a second-order system that responds to moving modulations of feature types—stimuli in which the expected luminance is the same everywhere but an area of higher contrast or of flicker moves, and a third-order system that computes the motion of marked locations in a “salience map,” that is, a neural representation of visual space in which the locations of important visual features (“figure”) are marked and “ground” is unmarked. Subsequently, there have been some strongly confirmatory reports: different gain-control mechanisms for first- and second-order motion, selective impairment of first- versus second- and/or third-order motion by different brain injuries, and the classification of new third-order motions, e.g., isoluminant chromatic motion. Various procedures have successfully discriminated between second- and third-order motion (when first-order motion is excluded): dual tasks, second-order reversed phi, motion competition, and selective adaptation. Meanwhile, eight apparent contradictions to the three-systems theory have been proposed. A review and reanalysis here of the new evidence, pro and con, resolves the challenges and yields a more clearly defined and significantly strengthened theory.

© 2001 Optical Society of America

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  126. Apparatus. The stimuli were presented on an achromatic 19″Nanao FlexScan 6600 monitor, driven by the internal video card in a 7500/100 Power PC Macintosh at 120 frames/sec using a C++ version of VideoToolbox.127A special circuit was used to combine two 8-bit output channels of the video card to produce 6144 distinct voltage levels (12.6 bits). A psychophysical procedure was used to generate a linear lookup table that evenly divides the entire dynamic range of the monitor (from 1 cd/m2to 53 cd/m2) into 256 levels.
  127. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
    [CrossRef] [PubMed]
  128. O. I. Ukkonen, A. M. Derrington, “Motion of contrast-modulated gratings is analyzed by different mechanisms at low and at high contrasts,” Vision Res. 40, 3359–3371 (2000).
    [CrossRef]
  129. “Feature tracking” is Ukkonen and Derrington’s128term. However, a third-order motion system is required in order to do feature tracking. The terms are not synonymous. See Section 5.A.1.
  130. F. C. Kolb, J. Braun, “Blindsight in normal observers,” Nature 377, 336–338 (1995).
    [CrossRef] [PubMed]
  131. P. Burt, G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psychol. Rev. 88, 171–195 (1981).
    [CrossRef] [PubMed]
  132. A. Baloch, S. Grossberg, E. Mingolla, C. A. M. Nogueira, “Neural model of first-order and second-order motion perception and magnocellular dynamics,” J. Opt. Soc. Am. A 16, 953–978 (1999).
    [CrossRef]
  133. M. J. Morgan, C. Chubb, “Contrast facilitation in motion detection: evidence for a Reichardt detector in human vision,” Vision Res. 39, 4217–4231 (1999).
    [CrossRef]
  134. J. Krauskopf, X. Li, “Effect of contrast on detection of motion of chromatic and luminance targets: retina-relative and object-relative movement,” Vision Res. 39, 3346–3350 (1999).
    [CrossRef]

2001 (3)

H. J. Kim, Z.-L. Lu, G. Sperling, “Rivalry motion versus depth motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 42, S736 (2001).

C. Tseng, H. Kim, J. L. Gobell, Z.-L. Lu, G. Sperling, “Motion standstill in rapidly moving stereoptic depth displays,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 42, S504, Abstract nr. 2720 (2001).

Z.-L. Lu, G. Sperling, “Sensitive calibration and measurement procedures based on the amplification principle in motion perception,” Vision Res. 41, 2355–2374 (2001).
[CrossRef] [PubMed]

2000 (6)

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

C. Tseng, J. L. Gobell, G. Sperling, “Sensitization to color: induced by search, measured by motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 41, S40, Abstr nr. 207 (2000).

S. Nishida, H. Ashida, “A hierarchical structure of motion system revealed by interocular transfer of flicker motion aftereffects,” Vision Res. 40, 265–278 (2000).
[CrossRef] [PubMed]

A. J. Schofield, M. A. Georgeson, “The temporal properties of first- and second-order vision,” Vision Res. 40, 2475–2487 (2000).
[CrossRef] [PubMed]

G. Sperling, T.-S. Kim, Z.-L. Lu, “Direction-reversal VEP’s reveal signature of first-and second-order motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 41, S334 (2000).

G. Sperling, C. E. Ho, “Third-order versus first-order and second-order motion in ambiguous stimuli: competition reveals temporal tuning functions, monocularity/binocularity, and the role of attention,” Perception 29, 83 (2000).

1999 (15)

R. Patterson, “Stereoscopic (cyclopean) motion sensing,” Vision Res. 39, 3329–3345 (1999).
[CrossRef]

E. Blaser, G. Sperling, Z.-L. Lu, “Measuring the amplification and the spatial resolution of visual attention,” Proc. Natl. Acad. Sci. USA 96, 11681–11686 (1999).
[CrossRef]

C. E. Ho, G. Sperling, “Selecting second and third-order motion pathways,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 40, S425 (1999).

Z.-L. Lu, L. Lesmes, G. Sperling, “Mechanisms of isoluminant chromatic motion perception,” Proc. Natl. Acad. Sci. USA 96, 8289–8294 (1999).
[CrossRef]

Z.-L. Lu, L. Lesmes, G. Sperling, “Perceptual motion standstill from rapidly moving chromatic displays,” Proc. Natl. Acad. Sci. USA 96, 15374–15379 (1999).
[CrossRef]

I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci. 16, 1–14 (1999).
[CrossRef]

N. E. Scott-Samuel, M. A. Georgeson, “Does early non-linearity account for second-order motion?” Vision Res. 39, 2853–2865 (1999).
[CrossRef] [PubMed]

J. A. Solomon, M. J. Morgan, “Dichoptically canceled motion,” Vision Res. 39, 2293–2297 (1999).
[CrossRef] [PubMed]

Z.-L. Lu, G. Sperling, “Second-order reversed phi,” Percept. Psychophys. 61, 1075–1088 (1999).
[CrossRef] [PubMed]

L. M. Vaina, A. Cowey, D. Kennedy, “Perception of first- and second-order motion: separable neurological mechanisms?” Hum. Brain Mapping 7, 67–77 (1999).
[CrossRef]

C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

A. Baloch, S. Grossberg, E. Mingolla, C. A. M. Nogueira, “Neural model of first-order and second-order motion perception and magnocellular dynamics,” J. Opt. Soc. Am. A 16, 953–978 (1999).
[CrossRef]

M. J. Morgan, C. Chubb, “Contrast facilitation in motion detection: evidence for a Reichardt detector in human vision,” Vision Res. 39, 4217–4231 (1999).
[CrossRef]

J. Krauskopf, X. Li, “Effect of contrast on detection of motion of chromatic and luminance targets: retina-relative and object-relative movement,” Vision Res. 39, 3346–3350 (1999).
[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]

1998 (9)

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]

L. M. Vaina, N. Makris, D. Kennedy, A. Cowey, “The selective impairment of the perception of first-order motion by unilateral cortical brain damage,” Visual Neurosci. 15, 333–348 (1998).
[CrossRef]

W. Prinzmetal, H. Amiri, K. Allen, T. Edwards, “Phenomenology of attention: I. Color, location, orientation, and spatial frequency,” J. Exp. Psychol. Hum. Percep. Perform. 24, 261–282 (1998).
[CrossRef]

C. E. Ho, “Letter recognition reveals pathways of second-order and third-order motion,” Proc. Natl. Acad. Sci. USA 95, 400–404 (1998).
[CrossRef] [PubMed]

L. P. O’Keefe, J. A. Movshon, “Processing of first- and second-order motion signals by neurons in area MT of the macaque monkey,” Visual Neurosci. 15, 305–317 (1998).

A. T. Smith, M. W. Greenlee, K. D. Singh, F. M. Kraemer, J. Hennig, “The processing of first- and second-order motion in human visual cortex assessed by functional magnetic resonance imaging (fMRI),” J. Neurosci. 18, 3816–3830 (1998).
[PubMed]

A. E. Seiffert, P. Cavanagh, “Position displacement, not velocity, is the cue to motion detection of second-order stimuli,” Vision Res. 38, 3569–3582 (1998).
[CrossRef]

L. Zemany, C. F. Stromeyer, A. Chaparro, R. E. Kronauer, “Motion detection on stationary, flashed pedestal gratings: evidence for an opponent-motion mechanism,” Vision Res. 38, 795–812 (1998).
[CrossRef] [PubMed]

G. Sperling, Z. L. Lu, “Update on the three-motion-systems theory,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 39, S461 (1998).

1997 (6)

A. T. Smith, T. Ledgeway, “Separate detection of moving luminance and contrast modulations: fact or artifact?” Vision Res. 37, 45–62 (1997).
[CrossRef] [PubMed]

T. Carney, “Evidence for an early motion system which integrates information from the two eyes,” Vision Res. 37, 2361–2368 (1997).
[CrossRef] [PubMed]

E. Taub, J. D. Victor, M. M. Conte, “Nonlinear preprocessing in short-range motion,” Vision Res. 37, 1459–1477 (1997).
[CrossRef] [PubMed]

M. W. Greenlee, A. T. Smith, “Detection and discrimination of first- and second-order motion in patients with unilateral brain damage,” J. Neurosci. 17, 804–818 (1997).
[PubMed]

S. Nishida, T. Ledgeway, M. D. Edwards, “Multiple-scale processing for motion in the human visual system,” Vision Res. 37, 2685–2698 (1997).
[CrossRef] [PubMed]

Z.-L. Lu, G. Sperling, J. Beck, “Selective adaptation of three motion systems,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 38, 237 (1997).

1996 (4)

Z.-L. Lu, G. Sperling, “Contrast gain control in first- and second-order motion perception,” J. Opt. Soc. Am. A 13, 2305–2318 (1996).
[CrossRef]

L. M. Vaina, A. Cowey, “Impairment of the perception of second order motion but not first order motion in a patient with unilateral focal brain damage,” Proc. R. Soc. London Ser. B 263, 1225–1232 (1996).
[CrossRef]

Y.-X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

Z.-L. Lu, G. Sperling, “Three systems for visual motion perception,” Curr. Dir. Psychol. Sci. 5, 44–53 (1996).
[CrossRef]

1995 (7)

Z.-L. Lu, G. Sperling, “Attention-generated apparent motion,” Nature 377, 237–239 (1995).
[CrossRef] [PubMed]

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

N. M. Grzywacz, S. N. J. Watamaniuk, S. P. McKee, “Temporal coherence theory for the detection and measurement of visual motion,” Vision Res. 35, 3183–3203 (1995).
[CrossRef] [PubMed]

J. K. Tsotsos, S. M. Culhane, W. Y. K. Wai, Y. Lai, N. Davis, F. Nuflo, “Modeling visual attention via selective tuning,” Artif. Intell. 78, 507–545 (1995).
[CrossRef]

A. Johnston, C. W. G. Clifford, “A unified account of three apparent motion illusions,” Vision Res. 35, 1109–1123 (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, 1771–1783 (1995).
[CrossRef] [PubMed]

F. C. Kolb, J. Braun, “Blindsight in normal observers,” Nature 377, 336–338 (1995).
[CrossRef] [PubMed]

1994 (3)

J. A. Solomon, G. Sperling, “Full-wave and half-wave rectification in 2nd-order motion perception,” Vision Res. 34, 2239–2257 (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. Nowlan, T. J. Sejnowski, “Filter selection model for motion segmentation and velocity integration,” J. Opt. Soc. Am. A 11, 3177–3200 (1994).
[CrossRef]

1993 (6)

J. M. Zanker, “Theta motion: a paradoxical stimulus to explore higher order motion extraction,” Vision Res. 33, 553–569 (1993).
[CrossRef] [PubMed]

Y.-X. Zhou, C. L. B. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

P. Werkhoven, G. Sperling, C. Chubb, “Motion perception between dissimilar gratings: a single channel theory,” Vision Res. 33, 463–485 (1993).
[CrossRef] [PubMed]

G. T. Plant, K. D. Laxer, N. M. Barbaro, J. S. Schiffman, K. Nakayama, “Impaired visual motion perception in the contralateral hemifield following unilateral posterior cerebral lesions,” Brain 116, 1337–1353 (1993).
[CrossRef]

L. M. Vaina, M. Le May, N. M. Grzywacz, “Deficits of non-Fourier motion perception in a patient with normal performance on short-range motion tasks,” Soc. Neurosci. Abstract 19, 1284 (1993).

Second-order reversed phi was first reported byS. Nishida, “Spatiotemporal properties of motion perception for random-check contrast modulations,” Vision Res. 33, 633–645 (1993).
[CrossRef] [PubMed]

1992 (4)

J. Rademacher, A. M. Galaburda, D. N. Kennedy, P. A. Pilipek, V. S. Caviness, “Human cerebral cortex: localization, parcellation, and morphometry with magnetic resonance imaging,” J. Cog. Neurosci. 4, 352–374 (1992).
[CrossRef]

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (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]

A. Johnston, P. W. McOwan, H. Buxton, “A computational model of 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]

1991 (4)

P. Cavanagh, “Short-range vs long-range motion: not a valid distinction,” Spatial Vision 5, 303–309 (1991).
[CrossRef] [PubMed]

C. Chubb, G. Sperling, “Texture quilts: basic tools for studying motion-from-texture,” J. Math. Psychol. 35, 411–442 (1991).
[CrossRef]

S. J. Anderson, D. C. Burr, M. C. Morrone, “Two-dimensional spatial and spatial-frequency selectivity of motion-sensitive mechanisms in human vision,” J. Opt. Soc. Am. A 8, 1340–1351 (1991).
[CrossRef] [PubMed]

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

1989 (7)

B. A. Dosher, M. S. Landy, G. Sperling, “Kinetic depth effect and optic flow: 1. 3D shape from Fourier motion,” Vision Res. 29, 1789–1813 (1989).
[CrossRef]

K. Turano, A. Pantle, “On the mechanism that encodes the movement of contrast variations—I: velocity discrimination,” Vision Res. 29, 207–221 (1989).
[CrossRef]

J. D. Victor, M. M. Conte, “Motion mechanisms have only limited access to form information,” Vision Res. 30, 289–301 (1989).
[CrossRef]

P. Cavanagh, M. Arguin, M. von Grunau, “Interattribute apparent motion,” Vision Res. 29, 1379–1386 (1989).
[CrossRef]

C. Chubb, G. Sperling, “Two motion perception mechanisms revealed by distance driven reversal of apparent motion,” Proc. Natl. Acad. Sci. USA 86, 2985–2989 (1989).
[CrossRef]

M. A. Georgeson, T. M. Shackleton, “Monocular motion sensing, binocular motion perception,” Vision Res. 29, 1511–1523 (1989).
[CrossRef] [PubMed]

P. Cavanagh, G. Mather, “Motion: the long and the short of it,” Spatial Vision 4, 103–129 (1989).
[CrossRef]

1988 (1)

1987 (1)

1986 (1)

M. Shadlen, T. Carney, “Mechanism of human motion revealed by new cyclopean illusion,” Science 232, 95–97 (1986).
[CrossRef] [PubMed]

1985 (7)

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

G. Mather, P. Cavanagh, A. M. Anstis, “A moving display which opposes short-range and long-range signals,” Perception 14, 163–166 (1985).
[CrossRef] [PubMed]

J. P. H. van Santen, G. Sperling, “Elaborated Reichardt detectors,” J. Opt. Soc. Am. A 2, 300–321 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

K. Nakayama, G. H. Silverman, “Detection and discrimination of sinusoidal grating displacements,” J. Opt. Soc. Am. A 2, 267–274 (1985).
[CrossRef] [PubMed]

C. Koch, S. Ullman, “Shifts in selective visual attention: towards the underlying neural circuitry,” Hum. Neurobiol. 4, 219–227 (1985).
[PubMed]

S. J. Anderson, D. C. Burr, “Spatial and temporal selectivity of the human motion detection system,” Vision Res. 25, 1147–1154 (1985).
[CrossRef] [PubMed]

1984 (5)

M. S. Landy, Y. Cohen, G. Sperling, “HIPS: a Unix-based image processing system,” Comput. Vis. Graph. Image Process. 25, 331–347 (1984a).
[CrossRef]

M. S. Landy, Y. Cohen, G. Sperling, “HIPS: image processing under UNIX software and applications,” Behav. Res. Methods Instrum. 16, 199–216 (1984b).
[CrossRef]

M. B. Mandler, W. Makous, “A three channel model of temporal frequency perception,” Vision Res. 24, 1881–1887 (1984).
[CrossRef] [PubMed]

A. M. M. Lelkens, J. J. Koenderink, “Illusory motion in visual displays,” Vision Res. 24, 293–300 (1984).
[CrossRef]

J. P. H. van Santen, G. Sperling, “Temporal covariance model of human motion perception,” J. Opt. Soc. Am. A 1, 451–473 (1984).
[CrossRef] [PubMed]

1981 (3)

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

K. Nakayama, C. W. Tyler, “Psychophysical isolation of movement sensitivity by removal of familiar position cues,” Vision Res. 21, 427–433 (1981).
[CrossRef] [PubMed]

P. Burt, G. Sperling, “Time, distance, and feature trade-offs in visual apparent motion,” Psychol. Rev. 88, 171–195 (1981).
[CrossRef] [PubMed]

1980 (2)

H. R. Wilson, “Spatiotemporal characterization of a transient mechanism in the human visual system,” Vision Res. 20, 443–452 (1980).
[CrossRef] [PubMed]

O. Braddick, “Low-level and high-level processes in apparent motion,” Philos. Trans. R. Soc. London, Ser. B 290, 137–151 (1980).
[CrossRef] [PubMed]

1979 (2)

C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. 9, 301–315 (1979).

D. H. Kelly, “Motion and vision: II. Stabilized spatio-temporal threshold surface,” J. Opt. Soc. Am. 69, 1340–1349 (1979).
[CrossRef] [PubMed]

1978 (1)

J. T. Petersik, K. I. Hicks, A. J. Pantle, “Apparent movement of successively generated subjective figures,” Perception 7, 371–383 (1978).
[CrossRef] [PubMed]

1976 (2)

G. Sperling, “Movement perception in computer-driven visual displays,” Behav. Res. Methods Instrum. 8, 144–151 (1976).
[CrossRef]

A. Pantle, L. Picciano, “A multistable movement display: evidence for two separate motion systems in human vision,” Science 193, 500–502 (1976).
[CrossRef] [PubMed]

1975 (1)

S. M. Anstis, B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
[CrossRef] [PubMed]

1974 (1)

O. Braddick, “A short-range process in apparent motion,” Vision Res. 14, 519–529 (1974).
[CrossRef] [PubMed]

1973 (1)

V. S. Ramachandran, M. V. Rau, T. R. Vidyasagar, “Apparent movement with subjective contours,” Vision Res. 13, 1399–1401 (1973).
[CrossRef] [PubMed]

1970 (1)

S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
[CrossRef] [PubMed]

1968 (1)

B. Julesz, R. Payne, “Difference between monocular and binocular stroboscopic motion perception,” Vision Res. 8, 433–444 (1968).
[CrossRef] [PubMed]

1957 (1)

W. Reichardt, “Autokorrelationsauswertung als funktionsprinzip des zentralnervensystems,” Z. Naturforsch. 12b, 447–457 (1957).

1956 (1)

B. Hassenstein, W. Reichardt, “Systemtheoretische analyse der zeit-, reihenfolgen- and vorzeichenauswertung bei der bewegungsperzeption des russelkafers chlorophanus,” Z. Naturforsch. 11b, 513–524 (1956).

1945 (1)

W. C. Shipley, F. A. Kenney, M. E. King, “Beta apparent movement under binocular, monocular and interocular stimulation,” Am. J. Psychol. 58, 545–549 (1945).
[CrossRef] [PubMed]

1915 (1)

A. Korte, “Kinematoskopische Untersuchungen,” Z. Psychol. 72, 193–206 (1915).

1913 (1)

F. Kenkel, “Untersuchungen ueber Zusammenhang zwischen Erscheinungsgross und Erscheinungsbewegung beim einigen sogenannten optischen Tauschungen,” Z. Psychol. 61, 358–449 (1913).

1912 (1)

M. Wertheimer, “Ueber das Sehen von Scheinbewegunen und Scheinkorpern,” Z. Psychol. 61, 161–265 (1912).

Adelson, E. H.

E. H. Adelson, J. R. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “The extraction of spatio-temporal energy in human and machine vision,” in Motion: Representation and Analysis (IEEE Workshop Proceedings), (IEEE Computer Society Press, Washington D.C., 1986) pp. 151–155.

Ahmad, S.

S. Ahmad, S. Omohundro, “Efficient visual search: a connectionist solution,” (University of California, Berkeley, Calif., 1991).

Ahumada, A. J.

A. B. Watson, A. J. Ahumada, “A look at motion in the frequency domain,” in Motion: Perception and Representation, J. K. Tsotsos, ed. (Association for Computing Machinery, New York, 1983) pp. 1–10.

Albright, T. D.

T. D. Albright, “Form-cue invariant motion processing in primate visual cortex,” Science 255, 1141–1143 (1992).
[CrossRef] [PubMed]

Allen, K.

W. Prinzmetal, H. Amiri, K. Allen, T. Edwards, “Phenomenology of attention: I. Color, location, orientation, and spatial frequency,” J. Exp. Psychol. Hum. Percep. Perform. 24, 261–282 (1998).
[CrossRef]

Amiri, H.

W. Prinzmetal, H. Amiri, K. Allen, T. Edwards, “Phenomenology of attention: I. Color, location, orientation, and spatial frequency,” J. Exp. Psychol. Hum. Percep. Perform. 24, 261–282 (1998).
[CrossRef]

Anderson, S. J.

Anstis, A. M.

G. Mather, P. Cavanagh, A. M. Anstis, “A moving display which opposes short-range and long-range signals,” Perception 14, 163–166 (1985).
[CrossRef] [PubMed]

Anstis, S. M.

S. M. Anstis, B. J. Rogers, “Illusory reversal of visual depth and movement during changes of contrast,” Vision Res. 15, 957–961 (1975).
[CrossRef] [PubMed]

S. M. Anstis, “Phi movement as a subtraction process,” Vision Res. 10, 1411–1430 (1970).
[CrossRef] [PubMed]

Arguin, M.

P. Cavanagh, M. Arguin, M. von Grunau, “Interattribute apparent motion,” Vision Res. 29, 1379–1386 (1989).
[CrossRef]

Ashida, H.

S. Nishida, H. Ashida, “A hierarchical structure of motion system revealed by interocular transfer of flicker motion aftereffects,” Vision Res. 40, 265–278 (2000).
[CrossRef] [PubMed]

Badcock, D. R.

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

Baker, C. L.

I. Mareschal, C. L. Baker, “Cortical processing of second-order motion,” Visual Neurosci. 16, 1–14 (1999).
[CrossRef]

C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

Y.-X. Zhou, C. L. Baker, “Spatial properties of envelope-responsive cells in area 17 and 18 neurons of the cat,” J. Neurophysiol. 75, 1038–1050 (1996).
[PubMed]

Baker, C. L. B.

Y.-X. Zhou, C. L. B. Baker, “A processing stream in mammalian visual cortex neurons for non-Fourier responses,” Science 261, 98–101 (1993).
[CrossRef] [PubMed]

Baloch, A.

Barbaro, N. M.

G. T. Plant, K. D. Laxer, N. M. Barbaro, J. S. Schiffman, K. Nakayama, “Impaired visual motion perception in the contralateral hemifield following unilateral posterior cerebral lesions,” Brain 116, 1337–1353 (1993).
[CrossRef]

Beck, J.

Z.-L. Lu, G. Sperling, J. Beck, “Selective adaptation of three motion systems,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 38, 237 (1997).

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]

Bergen, J. R.

E. H. Adelson, J. R. Bergen, “Spatio-temporal energy models for the perception of apparent motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
[CrossRef] [PubMed]

E. H. Adelson, J. R. Bergen, “The extraction of spatio-temporal energy in human and machine vision,” in Motion: Representation and Analysis (IEEE Workshop Proceedings), (IEEE Computer Society Press, Washington D.C., 1986) pp. 151–155.

Blaser, E.

E. Blaser, G. Sperling, Z.-L. Lu, “Measuring the amplification and the spatial resolution of visual attention,” Proc. Natl. Acad. Sci. USA 96, 11681–11686 (1999).
[CrossRef]

G. Sperling, A. Reeves, E. Blaser, Z.-L. Lu, E. Weichselgartner, “Two computational models of attention,” in Attention, C. Koch, J. Braun, eds. (MIT Press, Cambridge, Mass., 2001), pp. 177–214.

Boring, E. G.

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The TVC motion strength computation is not exactly a Reichardt computation, because the forward motion and the reverse motion are computed between different pairs of points rather than the same pairs of points, as in a Reichardt computation. However, because motion between all pairs of points is summed in the computations under consideration here, this subtle difference is insignificant. Further, the Taub et al.67motion computation [Eq. (3)] is a pixel-by-pixel computation; all averaging occurs in summing all the pixel-by-pixel motions. A more realistic model would incorporate some averaging (spatial filtering) before each nonlinearity (intensity compression and motion-direction extraction). Our explorations with their model showed that such enhancements, while desirable, do not fundamentally change the character of the predictions. Jonathan D. Victor, Department of Neurology and Neuroscience, Cornell University Medical College, 1300 York Avenue, New York, N.Y. 10021 (personal communication, July31, 1996).

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J. K. Tsotsos, S. M. Culhane, W. Y. K. Wai, Y. Lai, N. Davis, F. Nuflo, “Modeling visual attention via selective tuning,” Artif. Intell. 78, 507–545 (1995).
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Behav. Res. Methods Instrum. (2)

M. S. Landy, Y. Cohen, G. Sperling, “HIPS: image processing under UNIX software and applications,” Behav. Res. Methods Instrum. 16, 199–216 (1984b).
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Brain (1)

G. T. Plant, K. D. Laxer, N. M. Barbaro, J. S. Schiffman, K. Nakayama, “Impaired visual motion perception in the contralateral hemifield following unilateral posterior cerebral lesions,” Brain 116, 1337–1353 (1993).
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C. L. Fennema, W. B. Thompson, “Velocity determination in scenes containing several moving objects,” Comput. Graph. 9, 301–315 (1979).

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M. S. Landy, Y. Cohen, G. Sperling, “HIPS: a Unix-based image processing system,” Comput. Vis. Graph. Image Process. 25, 331–347 (1984a).
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G. Sperling, T.-S. Kim, Z.-L. Lu, “Direction-reversal VEP’s reveal signature of first-and second-order motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 41, S334 (2000).

Invest. Ophthalmol. Visual Sci. ARVO Suppl. (6)

C. E. Ho, G. Sperling, “Selecting second and third-order motion pathways,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 40, S425 (1999).

G. Sperling, Z. L. Lu, “Update on the three-motion-systems theory,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 39, S461 (1998).

C. Tseng, J. L. Gobell, G. Sperling, “Sensitization to color: induced by search, measured by motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 41, S40, Abstr nr. 207 (2000).

Z.-L. Lu, G. Sperling, J. Beck, “Selective adaptation of three motion systems,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 38, 237 (1997).

H. J. Kim, Z.-L. Lu, G. Sperling, “Rivalry motion versus depth motion,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 42, S736 (2001).

C. Tseng, H. Kim, J. L. Gobell, Z.-L. Lu, G. Sperling, “Motion standstill in rapidly moving stereoptic depth displays,” Invest. Ophthalmol. Visual Sci. ARVO Suppl. 42, S504, Abstract nr. 2720 (2001).

J. Cog. Neurosci. (1)

J. Rademacher, A. M. Galaburda, D. N. Kennedy, P. A. Pilipek, V. S. Caviness, “Human cerebral cortex: localization, parcellation, and morphometry with magnetic resonance imaging,” J. Cog. Neurosci. 4, 352–374 (1992).
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M. W. Greenlee, A. T. Smith, “Detection and discrimination of first- and second-order motion in patients with unilateral brain damage,” J. Neurosci. 17, 804–818 (1997).
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Other (24)

E. G. Boring, Sensation and Perception in the History of Experimental Psychology: A History of Experimental Psychology, 2nd ed. (Appleton-Century-Crofts, New York, 1942).

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).

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G. Sperling, Z.-L. Lu, “A systems analysis of human visual motion perception,” in High-Level Motion Processing, T. Watanabe, ed. (MIT Press, Cambridge, Mass., 1998), pp. 153–183.

G. Sperling, “Visual form and motion perception: psychophysics, computation, and neural networks,” presented at Fourier and Non-Fourier Perception of Motion and Orientation, meeting dedicated to the memory of the late Kvetoslav Prazdny, Boston University, Boston, Mass., March 5, 1988.

C. Chubb, G. Sperling, “Second-order motion perception: space–time separable mechanisms,” in Proceedings: Workshop on Visual Motion (IEEE Computer Society Press, Washington, D.C., 1989), pp. 126–138.

For a class of motion models consisting of a pointwise transformation T[f(x, y)]of the contrast of the input stimulus followed by a Reichardt (or equivalent motion energy) computation, this set of stimuli could potentially be used to provide the coefficients of a Taylor series expansion T[⋅]=fK(x, y),(K=1 ,…, ∞)of an early pointwise nonlinearity, and thereby to exactly define the nonlinearity if fK(x, y)(K=1,2, 3, or 4) activates only the Kthterm in the Taylor series expansion of T. This scheme is awkward because, generally, the TVC higher-order stimuli activate more than one term in T. This is probably why Taub et al.67discarded the Taylor expansion approach. On the other hand, the different terms in the Taylor expansion generate different spatial and temporal frequencies, and this could have been used to isolate and define T.

Taub et al.67use the term “motion amount” instead of the usual “motion energy” to indicate that motion is computed between pairs of points in immediately consecutive images in the stimulus, rather than, more commonly, between nearby or overlapping regions in space–time. To be consistent with the TVC model, TVC’s definition of MSTVCis used throughout this section.

The TVC motion strength computation is not exactly a Reichardt computation, because the forward motion and the reverse motion are computed between different pairs of points rather than the same pairs of points, as in a Reichardt computation. However, because motion between all pairs of points is summed in the computations under consideration here, this subtle difference is insignificant. Further, the Taub et al.67motion computation [Eq. (3)] is a pixel-by-pixel computation; all averaging occurs in summing all the pixel-by-pixel motions. A more realistic model would incorporate some averaging (spatial filtering) before each nonlinearity (intensity compression and motion-direction extraction). Our explorations with their model showed that such enhancements, while desirable, do not fundamentally change the character of the predictions. Jonathan D. Victor, Department of Neurology and Neuroscience, Cornell University Medical College, 1300 York Avenue, New York, N.Y. 10021 (personal communication, July31, 1996).

G. Sperling, A. Reeves, E. Blaser, Z.-L. Lu, E. Weichselgartner, “Two computational models of attention,” in Attention, C. Koch, J. Braun, eds. (MIT Press, Cambridge, Mass., 2001), pp. 177–214.

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M. Mozer, The Perception of Multiple Objects: a Connectionist Approach, (MIT Press, Cambridge, Mass., 1991).

S. Ahmad, S. Omohundro, “Efficient visual search: a connectionist solution,” (University of California, Berkeley, Calif., 1991).

In actual practice, because the response of the early stages of visual processing before motion detection is a linear function of—i.e., faithfully represents—the dark–light difference only when the difference is less than approximately 5%,83,84the light bars must be no more than 2.5% lighter than the mean luminance and the dark bars no more than 2.5% darker than the mean luminance.

Z.-L. Lu, G. Sperling, “Black-white asymmetry in visual perception,” (University of California, Irvine, Calif., 2001).

Apparatus. The stimuli were presented on an achromatic 19″Nanao FlexScan 6600 monitor, driven by the internal video card in a 7500/100 Power PC Macintosh at 120 frames/sec using a C++ version of VideoToolbox.127A special circuit was used to combine two 8-bit output channels of the video card to produce 6144 distinct voltage levels (12.6 bits). A psychophysical procedure was used to generate a linear lookup table that evenly divides the entire dynamic range of the monitor (from 1 cd/m2to 53 cd/m2) into 256 levels.

Stimuli were created with HIPS image-processing software119,120and displayed by using a software package (Runtime Library for Psychology Experiments, 1988) designed to drive an AT-Vista video graphics adapter installed in an IBM 486 PC-compatible computer. Stimuli were presented on a 60-Hz vertical retrace IKEGAMI DM516A (20-inch diagonal) monochrome graphics monitor with a fast, white P4-type phosphor. A special circuit that combines two output channels produces 4096 distinct gray levels (12 bits). The luminance of the monitor was 12.1 cd/m2when every pixel was assigned the lowest gray level and 325 cd/m2when every pixel was given the greatest gray level. The background luminance was set at 0.5 * (325+12.1)=169 cd/m2.A lookup table was generated by means of a psychophysical procedure that linearly divided the whole luminance range into 256 gray levels. When extremely low contrasts were required by the experiment, a simpler lookup table was generated by linearly interpolating luminance levels around the background luminance (for contrasts less than 1%).

The MathWorks, Natick, Mass., 1997.

G. Sperling, H.-J. Kim, Z.-L. Lu. (2001). “Is there interocular first-order motion?” Talk at annual meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Fla., May 2, 2001.

Why did these observers in the interocular motion experiment overlook the first-order perceptual wind when they had previously very successfully reported the motion of the wind in pedestaled luminance-modulation motion and pedestaled texture-contrast motion?41Probably because of the context of the other trials. In pedestaled motion experiments, half of the stimuli have a pedestal, so observers are alerted to look for wind motion. In the interocular motion experiment, there was no pedestal. Most of the stimuli consist of a clearly moving grating. Only at the highest frequencies is there an illusory pedestal (which is created by motion standstill in the third-order system).59In this context, the observers attempted to interpret the output of the third-order motion system, and they overlooked the first-order wind.

Zemany et al.’s71use of 28 frames was stimulated by a misstatement by Lu and Sperling41: “… preserving pseudo-linearity requires exactly one full cycle plus one extra frame…” This is correct only for four-frame cycles. See the more general formulation in the text below.

“Feature tracking” is Ukkonen and Derrington’s128term. However, a third-order motion system is required in order to do feature tracking. The terms are not synonymous. See Section 5.A.1.

R. S. Woodworth, H. Schlosberg, Experimental Psychology (Rev. ed.). (Holt, Rinehart & Winston, New York, 1954).

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Figures (27)

Fig. 1
Fig. 1

(a) Schematic functional architecture of the visual motion system. Left, first- and second-order motion systems. Right, third-order motion. L and R, signals originating in the left and the right eye, respectively. Motion-energy detectors () acting on the spatially filtered input serve monocular first-order (luminance-modulation) motion (1L and 1R). Σ indicates (possibly complex) summation/combination. The Σ-summed L and R inputs serve binocular (including interocular) first-order motion (1B). Second-order motion (2L, 2R) requires a texture grabber TG (a spatial filter followed by full-wave rectification, e.g., absolute value of each point’s difference from mean luminance) before a motion computation. × represents multiplication—the differential salience-weighting of features determined by selective attention and the selective weighting of locations in the salience field to determine which spatial locations will be subsequently processed; salience ultimately applies to all visual inputs. 3B indicates the binocular third-order motion computation based on salience values. The connecting path from summed motion energy Σ to feature weighting conveys the motion features needed to solve motion-defined motion stimuli. (b) Definition of a motion system: a computation, presumably carried out in a brain nucleus, that takes a space–time representation of the visual field as input and produces a vector flow field that represents motion strength or velocity or some combination. The example illustrates a blurred point (or line) in linear motion and an instantaneous motion-strength flow field.

Fig. 2
Fig. 2

Elaborated Reichardt detector. It computes motion direction from two inputs that sample the visual stimulus in two spatial areas A and B. SFA and SFB denote the linear spatiotemporal filters (receptive fields) that may have different spatial distributions. In the R subunit of the detector, the output of SFA at A is delayed by a temporal delay filter TF and then multiplied (×) by the direct output of SFB at B. In the L subunit of the detector, the output of SFB at B is delayed by a temporal delay filter TF and then multiplied (×) by the direct output of SFA at B. TA (temporal averaging) represents a low-pass temporal filter. The sign of the difference between the outputs of L and R subunits determines the perceived direction of motion. Outputs greater than zero indicate stimulus motion from A to B; outputs less than zero indicate stimulus motion from B to A.

Fig. 3
Fig. 3

First- and second-order motion stimuli. (a) Five consecutive frames of a first-order motion stimulus: a moving sine-wave luminance modulation. (b) Graphical representation of the sinusoidal intensity modulation of frame one in (a). (c) Five consecutive frames of a second-order motion stimulus: a moving contrast modulation of a random-texture carrier. (d) Schematic representation of one horizontal line of (c). The random function represents the carrier texture; the envelope is the modulator. To create an impression of motion, the modulators in (b) and (d) translate horizontally from frame to frame. (e) A motion-energy computation, ME, suffices to extract motion from the point-contrast function c(x, y, t) that describes the stimulus in (a). (f) Second-order contrast-modulation motion is detected by first extracting the textural features [by means of a texture grabber represented by the first three boxes in (f)], and then computing motion energy, ME, from the features (delivered by the texture grabber) in the same way as the first-order motion system computes the motion energy of its input. The texture grabber consists of three stages: an isotropic linear spatial filter, SPATIAL; a temporal bandpass filter, TEMPORAL; and rectification (absolute value or square).

Fig. 4
Fig. 4

Alternating-feature stimulus sequence. A square moves from left to right in successive frames. In frame 1, the square is defined by texture orientation: inside the square the texture slant is +45 deg, outside -45 deg. In frame 2, the square is defined by texture contrast: the square is composed of high-contrast texture, the background of low-contrast texture. In frame 3, the square is defined by a random-dot stereogram: the square is perceived in front of the background. In frame 4 the square is defined by isoluminant color: the square is red, the background is green. Such left-to-right motion is easily and compellingly perceived. The motion between pairs of frames is invisible to either the first- or the second-order motion system. To perceive the motion depicted here with low-level motion detectors would require a motion detector to correlate the square defined by the features in frame i with a square defined by the features in frame i+1. The alternative of computing the motion of figure from frame to frame is clearly preferable.

Fig. 5
Fig. 5

Summary of the three motion systems: their preferred stimuli, properties, and key references. Most natural stimuli excite all three systems.

Fig. 6
Fig. 6

Temporal-frequency-tuning functions for five types of motion stimuli, for one observer. Abscissa, temporal frequency (Hz) of a moving sinusoidal modulation; ordinate, threshold amplitudes of modulations required for 75% correct left–right motion discrimination. The axes are logarithmic. The curves have been vertically translated to expose their similarity in shape. ○ (LUM), luminance-modulation motion (first order) for pedestaled and for nonpedestaled stimuli (thresholds are identical); △ (CON), texture-contrast modulation motion (second order) for pedestaled and nonpedestaled stimuli (thresholds are identical); + (DEP), nonpedestaled stereoptic depth-modulation motion (third order); × (MOT), nonpedestaled motion-modulated motion (third order); ⋄ (I-O) nonpedestaled interocular luminance-modulation motion (third order). The scale value 1.00 on the ordinate represents the following modulation amplitudes: LUM 0.0014, CON 0.027, DEP 0.40 min, MOT 0.11, I-O 0.023.

Fig. 7
Fig. 7

Pedestal paradigm for first- and second-order stimuli. (a) Schematic representation of five frames of a stationary sine wave (the pedestal). The dashed vertical line indicates a stationary peak. (d) Five stimulus frames of the pedestal in a first-order (luminance-modulation) stimulus. The actual frames were 3.1×1.6 deg; only a horizontal slice is shown. Luminance varies sinusoidally as a function of space. (g) Five frames of the pedestal in a second-order texture-contrast modulation stimulus. The expected luminance is the same throughout the texture; texture contrast varies sinusoidally as a function of space. (b) Schematic representation of five frames of a rightward-moving sine wave. The slanting line indicates the rightward movement of the peak. (e) Five frames of a moving sine-wave luminance modulation (first-order motion). From top to bottom, the sinusoid traverses one period. (h) Five frames of a moving second-order texture-contrast modulation. (c) Schematic representation of a pedestal-plus-motion stimulus, summation of the modulations of (a) and (b). The pedestal has twice the amplitude of the moving sine. The dashed–dotted line indicates the peak, which wobbles back and forth 1/6 of a period. (f) A pedestaled first-order motion stimulus, the sum of the modulations of (d) and (e). (i) A pedestaled second-order stimulus, the sum of the modulations of (g) and (h). The accuracy of left–right motion discrimination for (f) equals (e) and for (i) equals (h).

Fig. 8
Fig. 8

Representation of an interocular stimulus presentation in which frames are alternately directed to the left (L) and right (R) eyes. Each successive stimulus has a spatial phase shift of 90 deg. Within an eye, the stimulus sequence, indicated on the bottom, is ambiguous as to direction of motion.

Fig. 9
Fig. 9

Alternating-feature stimulus sequences for attention-generated motion and their relation to feature salience maps. The top row (a–e) shows an alternating-feature stimulus with frames of black-dot textures plus white-dot textures (a, c, e) alternating with frames of low- and high-contrast textures (b, d). A sequence of five consecutive frames is shown; each is displaced vertically by 90 deg from the previous one. The high-contrast stripes in b and d are perceived as figure against a low-contrast background. Selective attention to black spots produces downward apparent motion, attention to white spots, upward motion. The second row (f–j) shows a depth/texture alternating feature stimulus. The depth frames (g, i) are indicated schematically. The third row shows frames f, g, and h and their associated salience maps; the most salient features are marked with Xs. In depth stimuli the near peaks are automatically the most salient. No features in the texture stimuli are automatically salient. When the observer intentionally attends to the coarse grating, the grating’s features are marked in the salience map and the direction of apparent motion is from upper left to lower right as indicated by the dotted line. There is no support for upward motion (the dashed line from lower left to upper right); perceiving upward motion in this stimulus would require attention to the fine stripes. The fourth row illustrates that third-order motion is computed directly from the salience map, which also provides guidance to other perceptual processes such as visual search and the transfer to memory.

Fig. 10
Fig. 10

Masking of sine-wave motion by sine-wave pedestals as a function of pedestal amplitude. (a) First-order stimuli. Contrast-modulation thresholds for 75% correct motion-direction judgments versus pedestal-modulation amplitudes. Both axes are logarithmic. For small pedestal amplitudes (⩽1%, ∼4× unpedestaled motion threshold), pedestaled thresholds for drifting luminance modulation do not depend on pedestal amplitude. For large pedestal amplitudes, motion threshold for drifting luminance modulation is approximately proportional to the amplitude of the pedestals (a Weber law), as indicated by the dotted line. (b) Second-order stimuli. Texture-contrast modulation thresholds for 75% correct motion-direction judgments versus pedestal-modulation amplitudes. Linear axes are used here to better display the wide range of pedestal amplitudes throughout which motion threshold for a drifting texture-contrast grating is a constant. Data from (a) for first-order motion and pedestal are shown for comparison.

Fig. 11
Fig. 11

Model of early visual processing. Suns, stationary-noise sources; rectangular boxes, linear filters; double rectangles enclose graphs of input–output relations. Triangles indicate gain-controlled amplifiers: the input (controlled signal) is the horizontal path; and the gain-controlling path is vertical. Adaptation. The visual input u passes through a separable space–time filter F1 that in combination with the gain-control filter F2 creates a receptive field of a given spatial scale (i.e., a visual channel). The gain of the amplifier k1 is determined by the spatiotemporal surround μ of the through-signal. Amplifier gain is feedforward controlled by filters F2, which have greater spatial and greater temporal extents than those of controlled signal F1. For very small inputs, the gain-control signal u is negligible and the receptive field is entirely positive (low pass) as indicated by the thick graphic plots in the double boxes. At high luminances, the receptive fields are bandpass, as indicated by the thin graphic plots. The orientation selectivity of first-order motion is represented by a spatial filter F3. Contrast-gain control of first-order motion is implemented as feedforward control by filters F4, which have a somewhat greater spatiotemporal extent (∫∫) and cover a broader range of frequencies than the through-signal filter F3. The double boxes with a “V” inside indicate full-wave rectifiers whose outputs are approximately the absolute value of their inputs. Each combination of a filter and a rectifier is a texture grabber. The summed outputs of the texture grabbers determine gain control. In the second-order motion pathway, both the input and the gain control are created by summing the outputs of texture grabbers F5. The motion-controlling signal is summed over the surrounding area (∫∫). The motion computation itself is similar to first-order (Motion I), which is represented here as a Reichardt detector. The decision process is represented as a maximum-likelihood decision between two alternatives (N, S+N). The third-order motion system is indicated only schematically by the rectangle (Motion III).

Fig. 12
Fig. 12

Phase dependence: stimuli, models, and a demonstration. The first- and second-order input signals represented at the left are physically superimposed and move at the same speed and direction. ME, motion-energy computation for extracting motion direction. (a) A two-mechanism model: First- and second-order motions are computed in separate channels; summation occurs after the two independent motion computations. Motion strength is independent of the relative phases of the two stimuli. (b) A single-channel model: first- and second-order stimuli are combined before motion computation. NL represents a possible pointwise nonlinear transformation on the combined signal. (c), (d), (e). Demonstration of phase-dependence in a single-channel theory: Two signals, (c) and (e), move together 180 out of phase. (d) is the sum of (c)+(e). Because (c) and (e) are 180 deg out of phase they cancel each other; there is no modulation in the sum (e) and therefore no stimulus for motion. Two in-phase stimuli (not shown) would reinforce each other.

Fig. 13
Fig. 13

Schematic anatomic localization of brain lesions in two patients. Left panels (patient RA): An infarct caused a first-order motion deficit in the left hemifield with sparing of second and third-order motion perception. Shown in medial view, it involves cortical parcellation units97 CALC, SCLC, CN, LG, and OP in the right hemisphere. Right panels (patient FD)96: An infarct produced a right hemifield deficit of second and/or third-order motion with sparing of first-order motion perception. Shown in lateral view, it involves cortical parcellation units SGp, AG, and TO2 in the left hemisphere. (From Vaina et al.,98 Fig. 7, p. 75, with permission of Wiley–Liss, Inc.)

Fig. 14
Fig. 14

Schematic stimulus generation principles of Taub et al.67 Stimuli are fK(x-t, y)=Λk=1,K[a+b sin(x-t+θk)] where K=1, , 4 and θk=(k-1)2π/K. Λ designates a random sample at each point (x, y, t) from one of the K sine waves. Ey is the expectation over y of fKp(x-t, y). For t=t0, and for particular values of p and K, Ey is a function of x that is shown in row p column K. (See text for details).

Fig. 15
Fig. 15

Single frames similar to stimuli of Taub et al.67 a, TVC first-order stimulus; b, TVC second-order stimulus; c, TVC “third-order” stimulus; d, TVC fourth-order stimulus; e, TVC first-order stimulus with a noise carrier. The TVC terminology to describe stimuli is quite different from the terminology used by Lu and Sperling 41 to describe motion systems. The TVC first-order stimulus is primarily a stimulus to the first-order motion system. The other TVC stimuli stimulate both second- and third-order motion systems to a degree that depends on the rectifying nonlinearity of the texture grabbers in the second-order motion system and on the figure–ground process in the third-order motion system.

Fig. 16
Fig. 16

Taub et al.67 single-channel model: The input to the motion system first goes through a pointwise half-wave compressive rectification (g=f0.5). Motion is computed from the output of the half-wave rectifier by a standard motion analyzer, SMA, which is similar to a Reichardt detector.

Fig. 17
Fig. 17

Phase dependence in the TVC single-channel model: stimuli, model, and predictions. A drifting luminance sine wave and a drifting texture-contrast modulation are produced with an amplitude ratio 1:12.4 (in order to produce equal outputs after the compressive nonlinearity). The inputs are summed with relative phase θ, then are linearly summed (+). The summed signal is transformed by a half-wave compressive pointwise nonlinearity (see Fig. 16), after which the TVC motion energy extraction algorithm computes motion strength MSTVC. MSTVC is plotted against θ, 0θπ. MSTVC for each stimulus component, individually, is also shown (square, triangle). A psychometric function (from Ref. 41) converts motion strength MSTVC to fraction correct in the motion-direction-judgment task. TVC predictions are compared with experimental data from Lu and Sperling (Ref. 41, Fig. 10a, observer ZL). The TVC single-motion-system theory obviously fails to capture these data.

Fig. 18
Fig. 18

Displays to stimulate motion systems that use half-wave rectification. Half-wave stimuli are composed of “Mexican hats:” A micropattern consists of 3×3 pixels in which the middle pixel has contrast c and the other eight pixels have a contrast -c/8, so the mean contrast of the hat micropattern is 0. c is positive for white hats and negative for black hats. a, Schematic cross sections, from top to bottom, of five frames of a half-wave stimulus moving rightward. b, The actual images (partial views). Intensity compression in early vision distorts intensity relations, producing first-order and second-order contaminations. When these are compensated (removed), the motion of the half-wave stimulus can be detected only by the third-order motion system, indicating that second-order motion uses full-wave, not half-wave, rectification.73

Fig. 19
Fig. 19

Summary of the results of Seiffert and Cavanagh69 and of Nakayama and Tyler (Ref. 104, Experiment 1, Fig. 3) determinations of displacement thresholds for back-and-forth oscillating stimuli. Seiffert and Cavanagh69 interpret data with dT/df-1 as indicating a velocity mechanism and data with dT/df0 as indicating a position mechanism. They conclude that first-order motion involves velocity sensing and second-order motion involves position sensing. Applying their criteria to their data, supplemented by Nakayama and Tyler’s data we would have to conclude that first-order motion is served by three mechanisms, a different one in each of the circled ranges. An alternative interpretation is that the shape of threshold-versus-frequency functions is determined primarily by temporal filtering before the motion computation itself. (After Ref. 69, with permission of Elsevier Science Ltd.)

Fig. 20
Fig. 20

Stimuli and results from the pedestaled motion experiments of Zemany et al.71 They measured contrast threshold for discriminating left-versus-right motion of a vertical, 1-c/deg luminance sine-wave grating a, superimposed on a 1 c/deg stationary luminance grating (b, the pedestal) with twice motion-threshold amplitude. a and b schematically illustrate the phase θ between the moving sine wave and the stationary pedestal in frame 1. d, e, f, Equal-duration motion stimulus and pedestal. Both the motion stimulus and the pedestal contain one full cycle (27 frames) of the motion stimulus plus one extra frame. The graph f shows the systematic dependence of the motion-direction threshold on the initial phase θ. g, h, i One-cycle motion stimulus, impulse pedestal. The pedestal was presented for only one frame. The motion stimulus contained 28 frames (one full cycle+one frame). i, Systematic dependence of the motion-direction threshold on the phase θ.

Fig. 21
Fig. 21

Fourier analysis of the pedestaled stimuli of Zemany et al.71 a, Space–time representation of a pedestaled motion stimulus. To minimize edge effects in Fourier analysis, zero’s are padded in the x, t space around the visual stimulus. b, Power spectrum of the pedestal+motion stimulus in a. c, Directional energy ratio for a pedestaled motion stimulus as a function of the initial angle θ between the motion component and the 2× pedestal on which it is superimposed. The subscripts 28 and 34 indicate the number of stimulus frames (27 frames is one full cycle). Direction energy E28(θ) is computed as follows: E28P+M(i, θ), the motion energy in quadrant i, is the integral of the energies of all the motion components in i. Directional energy is given by energy in quadrants 1+3 minus 2+4. E28(θ) is the ratio of directional motion energy of the pedestaled stimulus divided by that of the nonpedestaled motion stimulus, computed for each initial relative phase θ of the pedestal. Graphs show E28(θ), 1.04 cycles; and E34(θ), 1.26 cycles. E28(θ) varies greatly with phase θ, including a change in direction of motion. E34(θ) has only a small variation with θ.

Fig. 22
Fig. 22

Analytic predictions of a simplified Reichardt detector for four-frame and five-frame pedestaled (IP+M) and nonpedestaled (IM) motion stimuli. a, Simplified Reichardt detector composed of (1) a spatial separation of Δx between the left and the right detector units, (2) a temporal delay Δt that is exactly equal to the frame-to-frame time, and (3) an integration time (temporal averaging, TA) that is long relative to the duration of the stimulus. b, Data from Zemany et al.71 showing that motion threshold depends strongly on the relative phase of the pedestal and the motion stimulus. c, Theoretical prediction by the simplified Reichardt detector that matches the data of b very well. d, Theoretical prediction by the simplified Reichardt detector for a five-frame stimulus: complete pedestal immunity (matches the data of Lu and Sperling41). e, One-frame pedestal data of Zemany et al.71 f, Theoretical prediction of e by the simplified Reichardt detector.

Fig. 23
Fig. 23

Tuning functions for luminance-modulation and contrast-modulation motion stimuli masked by broad-spectrum white static and dynamic noise. a, Temporal tuning functions for luminance modulation motion with static noise (same as without noise)41 and with dynamic noise.81 For first-order motion, this static noise has no effect. The dynamic carrier impairs performance approximately in proportion to temporal frequency. b, Temporal tuning functions for contrast modulation motion obtained by Smith and Ledgeway (Ref. 115, Fig. 2) for a static and a dynamic carrier. The data from the static carrier are similar to those of Lu and Sperling (1995, Fig. 7).41 c, Temporal frequency channels with equal bandwidth in log frequency. d, Channels of c on a linear frequency scale. e, The expected Fourier power spectrum of a dynamic second-order carrier has equal Fourier power at all temporal frequencies within the achievable range. f, The temporal frequency channels of c contain more noise frequencies and hence more noise energy at higher frequencies. Doubling the temporal frequency doubles the amount of noise within the channel, thereby producing a loss of sensitivity that is inversely proportional to temporal frequency.

Fig. 24
Fig. 24

Contrast-modulation stimuli used to stimulate the second-order motion system. Early visual processing produces different distortion products for the three regimes: a, small carrier with small modulation; b, large carrier with small modulation, and c, large carrier with large modulation.

Fig. 25
Fig. 25

Procedure for estimating first-order contamination in the second-order stimuli.124 a, First-order (luminance modulation) motion stimulus on static-random-noise carrier with ±50% contrast. d, Psychometric function (percent correct motion-direction judgment versus luminance-modulation amplitude for stimulus a). “A” is the 75% correct motion-direction threshold. b, Moving contrast modulation imposed on the same ±50% static random carrier as in a. e, Psychometric function for b for determining the contrast-modulation amplitude B that yields 75%-correct motion-direction thresholds. c, Sandwich method124 for measuring the amount of first-order contamination C in the second-order stimulus at its threshold as determined in b. Odd frames are the same as for the 75% threshold in b. Even frames have pure luminance modulation. Direction bias (ordinate) depends on added luminance contrast in odd frames and on luminance amplitude in even frames. [On even frames, luminance modulations me of 6–8× motion threshold produce the steepest psychometric functions (greatest motion amplification124)]. Two psychometric functions are shown for two values of me. Luminance modulation C is added to odd frames to bring performance to chance (50%). The canceling modulation reveals the magnitude of the contamination product. Typically C<(1/2)A; i.e., a contrast modulation stimulus with a large static carrier and a near-threshold second-order modulation contains a first-order distortion product that is 1/2 threshold and would normally be invisible.

Fig. 26
Fig. 26

Dichoptically canceled motion.62 Five consecutive frames to either the left or the right eye produce one complete cycle of motion defined either by slant, a, or by flicker, b. Motion disappears when left- and right-eye images are physically summed. When viewed dichoptically so the left- and right-eye images are summed in a perceptual cyclopean image, the motion disappears unless it can be computed monocularly before interocular combination. Only the flicker motion is visible dichoptically (i.e., computed monocularly). (After Solomon and Morgan,62 Fig. 2, p. 2295, with permission of Elsevier Science Ltd.)

Fig. 27
Fig. 27

Motion competition.66 a, Second- versus third-order motion stimulus with orthogonal-slant patches. Four frames of a longer motion sequence of texture-defined motion stimulus are shown. Two trajectories (left, right) are shown. Along the leftward trajectory (third-order), all frames have the same slant and the same low contrast (0.2). Along the rightward trajectory (second-order), patches with contrast 0.2 alternate with patches with contrast 0.4. Attending the common feature favors the third-order direction, whereas the rightward direction has higher second-order motion energy. b, Luminance-defined motion stimulus. Four frames of a longer motion sequence in which first- and third-order motions are in opposite directions. Frames along the leftward motion trajectory (third order) have the same slant feature. The rightward trajectory has first-order motion energy. For both stimuli, below 3Hz, leftward (third-order) motion is dominant; above 3 Hz, rightward motion dominates.

Tables (1)

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Table 1 Responses of the Selected Observers of Solomon and Sperling a and of the TVC Model b to Full-Wave and Half-Wave Stimuli

Equations (36)

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P(x, y, t)=l(x, y, t)-l0l0.
T[P(x, y, t)]=P(x, y, t)αifP(x, y, t)>00otherwise.
MSTVC[P(x, y, t)]=xyt{T[P(x, y, t)]T[P(x+Δx, y, t+Δt)]-T[P(x, y, t)]T[P(x-Δx, y, t+Δt)]}
C1(x, y, t, θ1)=m1cos{2[2π(ωxx-2ωtt)]+θ1}.
C2(x, y, t, θ2)=R(x, y)m2cos[2π(ωxx-ωtt)+θ2],
l(x, y, t)=I(x+udt, y+vdt, t+dt).
dI(x, y, t)dt=u I(x, y, t)x+v I(x, y, t)y+I(x, y, t)t=0.
u0=-I(x, y, t)/tI(x, y, t)/x.
xk=k+1I(x, y, t)xk+1,tk=k+1I(x, y, t)xkt.
u=-k+1I(x, y, t)xk+1k+1I(x, y, t)xktk+1I(x, y, t)xk+1k+1I(x, y, t)xk+1=-k=0Kxktkk=0Kxk2
E(x, t+Δt)=I(x, t)I(x+Δx, t+Δt)-I(x+Δx, t)I(x, t+Δt).
E(x, t+kΔt)=I(x, t+(k-1)Δt)I(x+Δx, t+kΔt)-I(x+Δx, t+(k-1)Δt)I(x, t+kΔt).
E(x)=k=1KE(x, kΔt).
IM(x, t)=m sin(fx+ωt),
IP+M(x, t)=m sin(fx+ωt)+p sin(fx+π+θ),
IF+M(x, t)=m sin(fx+ωt)+p sin(fx+π+θ)δ(t-t0),
E4P+M=3 sin(fΔx)m2+23 mp sin34 π+θ.
E4M=3m2sin(fΔx).
3 sin(fΔx)m2+22 m2m0sin34 π+θ
=3m02sin(fΔx).
mτr(θ)=m06-23/2sin34 π+θ+48+8 sin234 π+θ1/2.
mτl(θ)=m06-23/2sin34 π-θ+48+8 sin234 π-θ1/2.
mτ(θ)=m02 [mτl(θ)+mτr(θ)].
E5P+M=4m2sin(fΔx)
E5M=4m2sin(fΔx).
E4F+M=3m2sin(fΔx)1+pmcos(θ).
3m2sin(fΔx)1+2m0mcos(θ)=3m02sin(fΔx).
mτF(θ)=16 {-2 cos(θ)+[36+4 cos2(θ)]1/2}.
ENM(i)=QiF2(INM(x, t))dωtdωx,
ENP+M(i, θ)=QiF2(INP+M(x, t, θ))dωtdωx.
ENM=[ENM(1)+ENM(3)]-[ENM(2)+ENM(4)],
ENP+M(θ)=[ENP+M(1, θ)+ENP+M(3, θ)]-[ENP+M(2, θ)+ENP+M(4, θ)].
EN(θ)=ENP+M(θ)ENM.
L(x, y, t, β, j)=L0{1.0+m sin[2π(αx+βfjt)]},
L(x, t)=L0[1+C cos(2πfcx+ϕc)×{1+m cos[2π(fmx+ωt)+ϕm]+p cos[2πfmx+ϕp]}].

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