The Effect of Viewing Eccentricity on Enumeration

Visual acuity and contrast sensitivity progressively diminish with increasing viewing eccentricity. Here we evaluated how visual enumeration is affected by visual eccentricity, and whether subitizing capacity, the accurate enumeration of a small number (∼3) of items, decreases with more eccentric viewing. Participants enumerated gratings whose (1) stimulus size was constant across eccentricity, and (2) whose stimulus size scaled by a cortical magnification factor across eccentricity. While we found that enumeration accuracy and precision decreased with increasing eccentricity, cortical magnification scaling of size neutralized the deleterious effects of increasing eccentricity. We found that size scaling did not affect subitizing capacities, which were nearly constant across all eccentricities. We also found that size scaling modulated the variation coefficients, a normalized metric of enumeration precision, defined as the standard deviation divided by the mean response. Our results show that the inaccuracy and imprecision associated with increasing viewing eccentricity is due to limitations in spatial resolution. Moreover, our results also support the notion that the precise number system is restricted to small numerosities (represented by the subitizing limit), while the approximate number system extends across both small and large numerosities (indexed by variation coefficients) at large eccentricities.

[1]  David Whitaker,et al.  The influence of eccentricity on position and movement acuities as revealed by spatial scaling , 1992, Vision Research.

[2]  J Rovamo,et al.  Resolution of gratings oriented along and across meridians in peripheral vision. , 1982, Investigative ophthalmology & visual science.

[3]  E. Miller,et al.  Analog Numerical Representations in Rhesus Monkeys: Evidence for Parallel Processing , 2004, Journal of Cognitive Neuroscience.

[4]  S. Dehaene.  Varieties of numerical abilities , 1992, Cognition.

[5]  D H Brainard,et al.  The Psychophysics Toolbox. , 1997, Spatial vision.

[6]  Stanislas Dehaene,et al.  PSYCHOLOGICAL SCIENCE Research Article Does Subitizing Reflect Numerical Estimation? , 2022 .

[7]  S. Klein,et al.  Detection and discrimination of the direction of motion in central and peripheral vision of normal and amblyopic observers , 1984, Vision Research.

[8]  Tracey D. Berger,et al.  Crowding and eccentricity determine reading rate. , 2007, Journal of vision.

[9]  Z. Pylyshyn,et al.  Multiple parallel access in visual attention. , 1994, Canadian journal of experimental psychology = Revue canadienne de psychologie experimentale.

[10]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[11]  Melanie Palomares,et al.  How element visibility affects visual enumeration , 2010, Vision Research.

[12]  G. Mandler,et al.  Subitizing: an analysis of its component processes. , 1982, Journal of experimental psychology. General.

[13]  Henry Railo,et al.  The role of attention in subitizing , 2008, Cognition.

[14]  Gordon D Logan,et al.  Subitizing and similarity: Toward a pattern-matching theory of enumeration , 2003, Psychonomic bulletin & review.

[15]  J. Rovamo,et al.  An estimation and application of the human cortical magnification factor , 2004, Experimental Brain Research.

[16]  Jukka Saarinen,et al.  Detection of mirror symmetry in random dot patterns at different eccentricities , 1988, Vision Research.

[17]  Bahador Bahrami,et al.  Modulating Attentional Load Affects Numerosity Estimation: Evidence against a Pre-Attentive Subitizing Mechanism , 2008, PloS one.

[18]  Dennis M. Levi,et al.  Undercounting features and missing features: evidence for a high-level deficit in strabismic amblyopia , 2000, Nature Neuroscience.

[19]  Susana T. L. Chung,et al.  Spatial-frequency and contrast properties of reading in central and peripheral vision. , 2009, Journal of vision.

[20]  Christian N. L. Olivers,et al.  Subitizing requires attention , 2008 .

[21]  Susana T. L. Chung.  The effect of letter spacing on reading speed in central and peripheral vision. , 2002, Investigative ophthalmology & visual science.

[22]  Carly J. Leonard,et al.  The role of attention in subitizing: Is the magical number 1? , 2008 .

[23]  David C Burr,et al.  Adaptation affects both high and low (subitized) numbers under conditions of high attentional load. , 2011, Seeing and perceiving.

[24]  Ingo Rentschler,et al.  Numerosity judgments in peripheral vision: Limitations of the cortical magnification hypothesis , 1984, Behavioural Brain Research.

[25]  F. Gregory Ashby,et al.  Subitizing: Magical numbers or mere superstition? , 1992, Psychological research.

[26]  D. Burr,et al.  Discrimination of spatial phase in central and peripheral vision , 1989, Vision Research.

[27]  S. Kuai,et al.  Constant contour integration in peripheral vision for stimuli with good Gestalt properties. , 2006, Journal of vision.

[28]  J. D. Balakrishnan,et al.  Is subitizing a unique numerical ability? , 1991, Perception & psychophysics.

[29]  R. Hess,et al.  Differences in the neural basis of human amblyopia: The distribution of the anomaly across the visual field , 1985, Vision Research.

[30]  David C Burr,et al.  Subitizing but not estimation of numerosity requires attentional resources. , 2010, Journal of vision.

[31]  Rochel Gelman,et al.  Variability signatures distinguish verbal from nonverbal counting for both large and small numbers , 2001, Psychonomic bulletin & review.

[32]  E. L. Kaufman,et al.  The discrimination of visual number. , 1949, The American journal of psychology.

[33]  Z. Pylyshyn,et al.  Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. , 1994, Psychological review.

[34]  S. Klein,et al.  Positional uncertainty in peripheral and amblyopic vision , 1987, Vision Research.

[35]  D. Levi,et al.  Amblyopia masks the scale invariance of normal central vision. , 2009, Journal of vision.

[36]  Bahador Bahrami,et al.  A Candidate for the Attentional Bottleneck: Set-size Specific Modulation of the Right TPJ during Attentive Enumeration , 2011, Journal of Cognitive Neuroscience.

[37]  J. B.,et al.  The Power of Numerical Discrimination , 1871, Nature.

[38]  N. Cowan.  The magical number 4 in short-term memory: A reconsideration of mental storage capacity , 2001, Behavioral and Brain Sciences.

[39]  M. Banks,et al.  Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision , 1987, Nature.

[40]  F. Campbell,et al.  The Magic Number 4 ± 0: A New Look at Visual Numerosity Judgements , 1976, Perception.

[41]  D. Pelli,et al.  Crowding is unlike ordinary masking: distinguishing feature integration from detection. , 2004, Journal of vision.

[42]  MARISA CARRASCO,et al.  Cortical Magnification Neutralizes the Eccentricity Effect in Visual Search , 1997, Vision Research.

[43]  A. Nieder.  Counting on neurons: the neurobiology of numerical competence , 2005, Nature Reviews Neuroscience.