Occupancy model of perceived numerosity

Allïk, Jüri; Tuulmets, Tiia

doi:10.3758/bf03205986

Cited by 189 publications

(207 citation statements)

References 21 publications

(35 reference statements)

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“…Actually, in their experiment, several non-numerical parameters such as total luminance and density of the pattern were confounded with numerosity. These parameters are known to be very influential in estimation of dots arrays (Allik & Tuulmets, 1991;Frith & Frith, 1972), and this might explain why they found a value smaller than ours. More recently, Piazza et al (2004) controlled for non-numerical variables and found an internal Weber fraction of 0.17.…”

Section: Precision Of the Representation Of Numerositycontrasting

confidence: 48%

“…It is possible that participants were using a complex combination of two or more parameters to extract numerosity (such as multiplication of density by total occupied area). Indeed, such combinations might be one way by which the visual system extracts approximate numerosity from visual displays (Allik & Tuulmets, 1991;Frith & Frith, 1972).…”

Section: Psychophysical Description Of the Responses And Influence Ofmentioning

confidence: 99%

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Calibrating the mental number line

2008

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Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.

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Section: Precision Of the Representation Of Numerositycontrasting

confidence: 48%

Section: Psychophysical Description Of the Responses And Influence Ofmentioning

confidence: 99%

Calibrating the mental number line

2008

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“…It might be argued that, in the numerosity comparison task performed in the above experiments, the comparison judgment could be confounded by other perceptual attributes of the displays, such as density or area, and other local features rather than being based on the actual representation of dot numerosity (17)(18)(19)(20)(21)(22)(23)(24). We, therefore, used, instead of the comparison task, a subjective estimation task, which required observers to report the number of dots directly (19).…”

Section: Significancementioning

confidence: 99%

Topology-defined units in numerosity perception

Zhou

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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What is a number? The number sense hypothesis suggests that numerosity is "a primary visual property" like color, contrast, or orientation. However, exactly what attribute of a stimulus is the primary visual property and determines numbers in the number sense? To verify the invariant nature of numerosity perception, we manipulated the numbers of items connected/enclosed in arbitrary and irregular forms while controlling for low-level features (e.g., orientation, color, and size). Subjects performed discrimination, estimation, and equality judgment tasks in a wide range of presentation durations and across small and large numbers. Results consistently show that connecting/ enclosing items led to robust numerosity underestimation, with the extent of underestimation increasing monotonically with the number of connected/enclosed items. In contrast, grouping based on color similarity had no effect on numerosity judgment. We propose that numbers or the primitive units counted in numerosity perception are influenced by topological invariants, such as connectivity and the inside/outside relationship. Beyond the behavioral measures, neural tuning curves to numerosity in the intraparietal sulcus were obtained using functional MRI adaptation, and the tuning curves showed that numbers represented in the intraparietal sulcus were strongly influenced by topology.W hat is a number? The answer to this age-old and fundamental question of philosophy has increasingly benefited from recent scientific investigation using psychology and neuroscience. The number sense hypothesis (1, 2) suggests that a number is "a basic property of the environment" (3) and particularly, because of its remarkable adaptation effect, "a primary visual property" (2), like color, contrast, or orientation (2-8). However, exactly what attribute in the environment is the primary property and determines numbers in the number sense, or more concretely, what is counted in numerosity perception? Consider the invariant nature of numerosity perception. It is self-evident that numerosity is invariant to specific features (e.g., orientation, size, shape, and color) of individual items to be counted. In other words, the primitive units to be counted must be invariant with variation in form dimensions and other visual features (2, 3, 7, 9-11). Then, the critical question becomes how to define precisely such abstract and invariant attributes. ResultsGeneralizing Connection to a Topological Invariant: Connectivity. We designed arbitrary and irregular shapes of connecting line segments (Fig. 1A, Upper) to test the invariant effect of connection on numerosity judgement independent of the concrete forms or manners of connection (12, 13). Three conditions of connection were constructed: zero, one, and two connected pairs of dots in the test patterns (Fig. 1A). A typical numerosity discrimination task was adopted, in which two visual patterns of dots were briefly presented on opposite sides of fixation (one serving as a reference and the other one serving as a test), and subj...

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“…We were able to fit these data to an occupancy model proposed by Allik and Tuulmets (1991) that accounts for the perception of numerosity in stimuli composed of dots. This occupancy model relies on the idea that each element of the stimulus has a neural occupancy much larger than the physical size of the element itself, and that it is the total neural occupancy that defines the perceived density and not the number of elements.…”

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confidence: 99%

How long range is contour integration in human color vision?

Beaudot

Mullen

2003

Vis Neurosci

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We quantified and compared the effect of element spacing on contour integration between the achromatic (Ach), red-green (RG), and blue-yellow (BY) mechanisms. The task requires the linking of orientation across space to detect a contour in a stimulus composed of randomly oriented Gabor elements (1.5 cpd, s ϭ 0.17 deg), measured using a temporal 2AFC method. A contour of ten elements was pasted into a 10 ϫ 10 cells array, and background elements were randomly positioned within the available cells. The effect of element spacing was investigated by varying the mean interelement distance between two and six times the period of the Gabor elements (l ϭ 0.66 deg) while the total number of elements was fixed. Contour detection was measured as a function of its curvature for jagged contours and for closed contours. At all curvatures, we found that performance for chromatic mechanisms declines more steeply with the increase in element separation than does performance for the achromatic mechanism. Averaged critical element separations were 4.6 6 0.7, 3.6 6 0.4, and 2.9 6 0.2 deg for Ach, BY, and RG mechanisms, respectively. These results suggest that contour integration by the chromatic mechanisms relies more on short-range interactions in comparison to the achromatic mechanism. In a further experiment, we looked at the combined effect of element size and element separation in contour integration for the Ach mechanism. We found that the critical separation decreases linearly with the spatial frequency, from about 5 deg at low spatial frequency (larger elements) to about 1 deg at high spatial frequency (smaller elements) suggesting a scale invariance in contour integration. In both experiments we also found no differences between closed and open jagged contours detection in terms of element separation. The neuroanatomical implications of these findings relatively to area V1 are discussed.

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Occupancy model of perceived numerosity

Cited by 189 publications

References 21 publications

Calibrating the mental number line

Calibrating the mental number line

Topology-defined units in numerosity perception

How long range is contour integration in human color vision?

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