common visual metric for approximate number and density

There is considerable interest in how humans estimate the number of objects in a scene in the context of an extensive literature on how we estimate the density (i.e., spacing) of objects. Here, we show that our sense of number and our sense of density are intertwined. Presented with two patches, obs...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2011-12, Vol.108 (49), p.19552-19557
Main Authors: Dakin, Steven C, Tibber, Marc S, Greenwood, John A, Kingdom, Frederick A. A, Morgan, Michael J
Format: Article
Language:English
Subjects:
Algorithms
Cognition & reasoning
Density
Density estimation
Discrimination (Psychology) - physiology
energy
Eyes & eyesight
Form Perception - physiology
Humans
Luminance
Mental stimulation
Modeling
Models, Psychological
Numbers
Pattern Recognition, Visual - physiology
Psychological Tests
Psychometrics - methods
Psychophysics
Ratios
Research universities
Sensory discrimination
Social Sciences
spatial distribution
Task Performance and Analysis
Visual perception
Visual Perception - physiology
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Summary:There is considerable interest in how humans estimate the number of objects in a scene in the context of an extensive literature on how we estimate the density (i.e., spacing) of objects. Here, we show that our sense of number and our sense of density are intertwined. Presented with two patches, observers found it more difficult to spot differences in either density or numerosity when those patches were mismatched in overall size, and their errors were consistent with larger patches appearing both denser and more numerous. We propose that density is estimated using the relative response of mechanisms tuned to low and high spatial frequencies (SFs), because energy at high SFs is largely determined by the number of objects, whereas low SF energy depends more on the area occupied by elements. This measure is biased by overall stimulus size in the same way as human observers, and by estimating number using the same measure scaled by relative stimulus size, we can explain all of our results. This model is a simple, biologically plausible common metric for perceptual number and density.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1113195108