Abstract

We examine how local direction signals are combined to compute the focus of radial motion (FRM) in random dot patterns and examine how this process changes across the visual field. Equivalent noise analysis showed that a loss in FRM accuracy was largely attributable to an increase in local motion detector noise with little or no change in efficiency across the visual field. The minimum separation for discriminating the foci of two overlapping optic flow patterns increased in the periphery faster than predicted from the resolution for a single FRM. This behavior requires that observers average numerous local velocities to estimate the FRM, which enables resistance to internal and external noise and endows the system with the property of position invariance. However, such pooling limits the precision with which multiple looming objects can be discriminated, especially in the peripheral visual field.

© 2006 Optical Society of America

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2005

S. C. Dakin, I. Mareschal, and P. J. Bex, 'Local and global limitations on direction integration using equivalent noise analysis,' Vision Res. 45, 3027-3049 (2005).
[CrossRef] [PubMed]

P. J. Bex and S. C. Dakin, 'Spatial interference among moving targets,' Vision Res. 45, 1385-1398 (2005).
[CrossRef] [PubMed]

2004

I. Fine, C. M. Anderson, G. M. Boynton, and K. R. Dobkins, 'The invariance of directional tuning with contrast and coherence,' Vision Res. 44, 903-913 (2004).
[CrossRef] [PubMed]

2002

J. M. Harris and W. Bonas, 'Optic flow and scene structure do not always contribute to the control of human walking,' Vision Res. 42, 1619-1626 (2002).
[CrossRef] [PubMed]

C. S. Royden, 'Computing heading in the presence of moving objects: a model that uses motion-opponent operators,' Vision Res. 42, 3043-3058 (2002).
[CrossRef] [PubMed]

K. H. Britten and R. J. Van Wezel, 'Area MST and heading perception in macaque monkeys,' Cereb. Cortex 12, 692-701 (2002).
[CrossRef] [PubMed]

D. M. Levi, S. Hariharan, and S. A. Klein, 'Suppressive and facilitatory spatial interactions in peripheral vision: peripheral crowding is neither size invariant nor simple contrast masking,' J. Vision 2, 167-177 (2002).
[CrossRef]

P. J. Bex and S. C. Dakin, 'Comparison of the spatial-frequency selectivity of local and global motion detectors,' J. Opt. Soc. Am. A 19, 670-677 (2002).
[CrossRef]

2001

S. C. Dakin and P. J. Bex, 'Local and global visual grouping: tuning for spatial frequency and contrast,' J. Vision 1, 99-111 (2001).
[CrossRef]

L. Parkes, J. Lund, A. Angelucci, J. A. Solomon, and M. Morgan, 'Compulsory averaging of crowded orientation signals in human vision,' Nat. Neurosci. 4, 739-744 (2001).
[CrossRef] [PubMed]

S. T. L. Chung, D. M. Levi, and G. E. Legge, 'Spatial-frequency and contrast properties of crowding,' Vision Res. 41, 1833-1850 (2001).
[CrossRef] [PubMed]

S. C. Dakin, 'Information limit on the spatial integration of local orientation signals,' J. Opt. Soc. Am. A 18, 1016-1026 (2001).
[CrossRef]

J. M. Harris, 'The future of flow?' Trends Cogn. Sci. 5, 7-8 (2001).
[CrossRef]

J. Wann and M. Land, 'Heading in the wrong direction. Reply,' Trends Cogn. Sci. 5, 8-9 (2001).
[CrossRef]

A. T. Smith, K. D. Singh, A. L. Williams, and M. W. Greenlee, 'Estimating receptive field size from fMRI data in human striate and extrastriate visual cortex,' Cereb. Cortex 11, 1182-1190 (2001).
[CrossRef] [PubMed]

2000

M. C. Morrone, M. Tosetti, D. Montanaro, A. Fiorentini, G. Cioni, and D. C. Burr, 'A cortical area that responds specifically to optic flow, revealed by fMRI,' Nat. Neurosci. 3, 1322-1328 (2000).
[CrossRef] [PubMed]

1999

M. C. Morrone, D. C. Burr, and S. Di Pietro, 'Cardinal directions for visual optic flow,' Curr. Biol. 9, 763-766 (1999).
[CrossRef] [PubMed]

J. M. Harris and B. J. Rogers, 'Going against the flow,' Trends Cogn. Sci. 3, 449-450 (1999).
[CrossRef] [PubMed]

M. Lappe, F. Bremmer, and A. V. van ben Berg, 'Going against the flow--Reply,' Trends Cogn. Sci. 3, 450 (1999).
[CrossRef] [PubMed]

P. J. Bex, A. B. Metha, and W. Makous, 'Enhanced motion aftereffect for complex motions,' Vision Res. 39, 2229-2238 (1999).
[CrossRef] [PubMed]

1998

M. Lappe, 'A model of the combination of optic flow and extraretinal eye movement signals in primate extrastriate visual cortex--neural model of self-motion from optic flow and extraretinal cues,' Neural Networks 11, 397-414 (1998).
[CrossRef]

J. A. Crowell, M. S. Banks, K. V. Shenoy, and R. A. And- ersen, 'Visual self-motion perception during head turns,' Nat. Neurosci. 1, 732-737 (1998).
[CrossRef]

K. H. Britten and R. J. van Wezel, 'Electrical microstimulation of cortical area MST biases heading perception in monkeys,' Nat. Neurosci. 1, 59-63 (1998).
[CrossRef]

D. C. Burr, M. C. Morrone, and L. M. Vaina, 'Large receptive fields for optic flow detection in humans,' Vision Res. 38, 1731-1743 (1998).
[CrossRef] [PubMed]

P. J. Bex, A. B. Metha, and W. Makous, 'Psychophysical evidence for a functional hierarchy of motion processing mechanisms,' J. Opt. Soc. Am. A 15, 769-776 (1998).
[CrossRef]

S. K. Rushton, J. M. Harris, M. R. Lloyd, and J. P. Wann, 'Guidance of locomotion on foot uses perceived target location rather than optic flow,' Curr. Biol. 8, 1191-1194 (1998).
[CrossRef] [PubMed]

1997

F. Wilkinson, H. R. Wilson, and D. Ellemberg, 'Lateral interactions in peripherally viewed texture arrays,' J. Opt. Soc. Am. A 14, 2057-2068 (1997).
[CrossRef]

C. S. Royden, 'Mathematical analysis of motion-opponent mechanisms used in the determination of heading and depth,' J. Opt. Soc. Am. A 14, 2128-2143 (1997).
[CrossRef]

R. J. Snowden and A. B. Milne, 'Phantom motion aftereffects--evidence of detectors for the analysis of optic flow,' Curr. Biol. 7, 717-722 (1997).
[CrossRef] [PubMed]

P. J. Bex and W. Makous, 'Radial motion looks faster,' Vision Res. 37, 3399-3405 (1997).
[CrossRef]

J. Kim, K. Mulligan, and H. Sherk, 'Simulated optic flow and extrastriate cortex. I: Optic flow versus texture,' J. Neurophysiol. 77, 554-561 (1997).
[PubMed]

K. Mulligan, J. Kim, and H. Sherk, 'Simulated optic flow and extrastriate cortex. II: Responses to bar versus large-field stimuli,' J. Neurophysiol. 77, 562-570 (1997).
[PubMed]

H. Barlow and S. P. Tripathy, 'Correspondence noise and signal pooling in the detection of coherent visual motion,' J. Neurosci. 17, 7954-7966 (1997).
[PubMed]

D. H. Brainard, 'The Psychophysics Toolbox,' Spatial Vis. 10, 433-436 (1997).
[CrossRef]

D. G. Pelli, 'The VideoToolbox software for visual psychophysics: transforming numbers into movies,' Spatial Vis. 10, 437-442 (1997).
[CrossRef]

1996

M. O. Scase, O. J. Braddick, and J. E. Raymond, 'What is noise for the visual system?' Vision Res. 36, 2579-2586 (1996).
[CrossRef] [PubMed]

D. C. Bradley, M. Maxwell, R. A. Andersen, M. S. Banks, and K. V. Shenoy, 'Mechanisms of heading perception in primate visual cortex,' Science 273, 1544-1547 (1996).
[CrossRef] [PubMed]

M. S. Banks, S. M. Ehrlich, B. T. Backus, and J. A. Crowell, 'Estimating heading during real and simulated eye movements,' Vision Res. 36, 431-443 (1996).
[CrossRef] [PubMed]

H. G. Krapp and R. Hengstenberg, 'Estimation of self motion by optic flow processing in single visual interneurons,' Nature (London) 384, 463-466 (1996).
[CrossRef]

R. J. Snowden and A. B. Milne, 'The effects of adapting to complex motions: position invariance and tuning to spiral motions,' J. Cogn. Neurosci. 8, 435-452 (1996).
[CrossRef]

K. Gurney and M. J. Wright, 'Rotation and radial motion thresholds support a two-stage model of differential-motion analysis,' Perception 25, 5-26 (1996).
[CrossRef] [PubMed]

P. Verghese and L. S. Stone, 'Perceived visual speed constrained by image segmentation,' Nature (London) 381, 161-163 (1996).
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1995

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1994

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1992

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1991

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1990

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1989

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1988

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1987

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1986

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1983

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1980

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1978

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1976

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1973

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1970

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1969

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1968

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1966

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1965

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W. H. Warren, Jr., A. W. Blackwell, K. J. Kurtz, N. G. Hatsopoulos, and M. L. Kalish, 'On the sufficiency of the velocity field for perception of heading,' Biol. Cybern. 65, 311-320 (1991).
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J. M. Harris and W. Bonas, 'Optic flow and scene structure do not always contribute to the control of human walking,' Vision Res. 42, 1619-1626 (2002).
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H. Bouma, 'Interaction effects in parafoveal letter recognition,' Nature (London) 226, 177-178 (1970).
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M. C. Morrone, M. Tosetti, D. Montanaro, A. Fiorentini, G. Cioni, and D. C. Burr, 'A cortical area that responds specifically to optic flow, revealed by fMRI,' Nat. Neurosci. 3, 1322-1328 (2000).
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J. A. Crowell, M. S. Banks, K. V. Shenoy, and R. A. And- ersen, 'Visual self-motion perception during head turns,' Nat. Neurosci. 1, 732-737 (1998).
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J. E. Cutting, K. Springer, P. A. Braren, and S. H. Johnson, 'Wayfinding on foot from information in retinal, not optical, flow,' J. Exp. Psychol. Gen. 121, 41-72 (1992).
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P. J. Bex and S. C. Dakin, 'Spatial interference among moving targets,' Vision Res. 45, 1385-1398 (2005).
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S. C. Dakin and P. J. Bex, 'Local and global visual grouping: tuning for spatial frequency and contrast,' J. Vision 1, 99-111 (2001).
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S. C. Dakin, 'Information limit on the spatial integration of local orientation signals,' J. Opt. Soc. Am. A 18, 1016-1026 (2001).
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M. S. Banks, S. M. Ehrlich, B. T. Backus, and J. A. Crowell, 'Estimating heading during real and simulated eye movements,' Vision Res. 36, 431-443 (1996).
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M. C. Morrone, M. Tosetti, D. Montanaro, A. Fiorentini, G. Cioni, and D. C. Burr, 'A cortical area that responds specifically to optic flow, revealed by fMRI,' Nat. Neurosci. 3, 1322-1328 (2000).
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W. H. Warren, Jr., A. W. Blackwell, K. J. Kurtz, N. G. Hatsopoulos, and M. L. Kalish, 'On the sufficiency of the velocity field for perception of heading,' Biol. Cybern. 65, 311-320 (1991).
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E. C. Hildreth, H. B. Barlow, and H. C. Longuet-Higgins, 'Recovering heading for visually guided navigation in the presence of self-moving objects,' Philos. Trans. R. Soc. London, Ser. B 337, 305-313 (1992).
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H. A. Saito, M. Yukie, K. Tanaka, K. Hikosaka, Y. Fukada, and E. Iwai, 'Integration of direction signals of image motion in the superior temporal sulcus of the macaque monkey,' J. Neurosci. 6, 145-157 (1986).
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J. E. Cutting, K. Springer, P. A. Braren, and S. H. Johnson, 'Wayfinding on foot from information in retinal, not optical, flow,' J. Exp. Psychol. Gen. 121, 41-72 (1992).
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Figures (4)

Fig. 1
Fig. 1

Illustrations of the stimuli. Each image is the sum of two consecutive frames from illustrative movies from the experiments. Elements in the first frame are randomly positioned; elements in the second frame are positioned relative to those in the first frame to generate an expanding/contracting radial flow field. (a) Noiseless radial motion. In (b) the x location of each element is subject to positional noise (experiment 2). There are two foci of radial motion in (c): half the dots (at random) are displaced relative to a focus 32 pixels to the left of center, and the other half are displaced relative to a focus 32 pixels to the right of center.

Fig. 2
Fig. 2

(a) Radial plot of direction of heading accuracy as a function of retinal locus. Retinal eccentricity from the fovea is plotted in degrees from the center of the figure; the direction is coded compatibly with the visual field. Each data point shows the mean and horizontal and vertical standard deviations of five repetitions of a pointing task, relative to the intersection of the axes. (b) Mean distance between the perceived and the actual focus of radial motion (FRM) averaged across all eight retinal loci at 4 ° and 8 ° eccentricity.

Fig. 3
Fig. 3

(a)–(e) FRM discrimination thresholds as a function of horizontal positional noise (applied to each element) at three eccentricities, indicated by the legend. Error bars show 95% confidence intervals. Plots (a)–(e) each shows the data for one observer, and the mean across observers is shown in (f); error bars show 1 standard error. Curves show equivalent noise fits to the data (see the text for details). The internal noise parameter of each fit is plotted as a function of eccentricity for each observer (see the legend) in (g), and the sampling efficiency parameter is plotted in (h). The unconnected error bars on the right of each figure show the mean 95% confidence interval across observers and conditions for each parameter. The solid symbols show the mean value for each parameter across observers, and the error bars show ± 1 standard error.

Fig. 4
Fig. 4

Two foci of radial motion discrimination thresholds as a function of eccentricity for four observers, indicated by the legend. Error bars show 95% confidence intervals. The dashed line shows the threshold that is predicted from the accuracy with which one focus of radial motion can be discriminated; error bars show ± 1 standard error.

Equations (2)

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L ( x , y ) = exp ( x 2 + y 2 2 σ 2 ) ,
σ FRM = σ int 2 + σ ext 2 N ,

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