Numerosity and density judgments: Biases for area but not for volume

Abstract

Human observers can rapidly judge the number of items in a scene. This ability is underpinned by specific mechanisms encoding number or density. We investigated whether judgments of number and density are biased by a change in volume, as they are by a change in area. Stimuli were constructed using nonoverlapping black and white luminance-defined dots. An eight-mirror Wheatstone stereoscope was used to present the dots as though in a volume. Using a temporal two-alternative forced-choice (2AFC) task and the Method of Constant Stimuli (MOCS), we measured the precision and bias (PSE shift) of numerosity and density judgments, separately, for stimuli differing in area or volume. For two-dimensional (2-D) stimuli, consistent with previous literature, perceived density was biased as area increased. However, perceived number was not. For three-dimensional (3-D) stimuli, despite a vivid impression of the dots filling a cylindrical volume, there was no bias in perceived density or number as volume increased. A control experiment showed that all of our observers could easily perceive disparity in our stimuli. Our findings reveal that number and density judgments that are biased by area are not similarly biased by volume changes.

Simultaneous density contrast and binocular integration

“…If density perception is implicitly involved in size scaling, one should expect density biases in both 2D (area) and 3D (stereo-depth volume) size scaling. However, a bias only in 2D has been interpreted as supporting the idea that density is only represented in 2D (Bell et al, 2015). Note that the size scaling mentioned here is a change in the space within which the texture elements are distributed, not including changes in the size of elements and inter-dot distance, since these might also be affected after adapting to a different sized disk (Zimmermann & Fink, 2016).…”

“…A similar model that computes contrast energy has also been proposed for numerosity estimation (Morgan, Raphael, Tibber, & Dakin, 2014). In support of this idea, density is biased by area, with larger patches perceived as denser (Dakin et al, 2011;Raphael, Dillenburger, & Morgan, 2013;Raphael & Morgan, 2016;Tibber et al, 2012), but not biased by stereodepth volume (Bell et al, 2015). If density perception is implicitly involved in size scaling, one should expect density biases in both 2D (area) and 3D (stereo-depth volume) size scaling.…”

“…Some studies suggest that density information is represented at a 2D retinotopic level through planar filters of high and low spatial frequencies (Bell, Manson, Edwards, & Meso, 2015;Dakin et al, 2011). A similar model that computes contrast energy has also been proposed for numerosity estimation (Morgan, Raphael, Tibber, & Dakin, 2014).…”

Asymmetrical interference between number and item size perception provide evidence for a domain specific impairment in dyscalculia

“…In addition, our study used relatively small numbers of items, contrasting with the 808 much larger numerosities employed in some other studies (Bell et al, 2015;Dakin et al, 809 2011;Nys and Content, 2012). Behavioral evidence (Anobile et al, 2015(Anobile et al, , 2013a) supports a 810 transition between a "number" and a "density" regime governed by different psychophysical 811 laws.…”

Density discrimination with occlusions in 3D clutter

“…They also showed perceived density and number were biased by increases in area, such that larger areas were perceived as denser and more numerous. Bell, Manson, Edwards, and Meso (2015) also found that perceived density was biased by increases in area, but did not find that perceived numerosity was biased by increases in area. They also showed that neither perceived density nor numerosity were biased by increases in volume.…”