Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects

Abstract

We have recently provided evidence that the perception of number and texture density is mediated by two independent mechanisms: numerosity mechanisms at relatively low numbers, obeying Weber's law, and texture-density mechanisms at higher numerosities, following a square root law. In this study we investigated whether the switch between the two mechanisms depends on the capacity to segregate individual dots, and therefore follows similar laws to those governing visual crowding. We measured numerosity discrimination for a wide range of numerosities at three eccentricities. We found that the point where the numerosity regime (Weber's law) gave way to the density regime (square root law) depended on eccentricity. In central vision, the regime changed at 2.3 dots/°2, while at 15° eccentricity, it changed at 0.5 dots/°2, three times less dense. As a consequence, thresholds for low numerosities increased with eccentricity, while at higher numerosities thresholds remained constant. We further showed that like crowding, the regime change was independent of dot size, depending on distance between dot centers, not distance between dot edges or ink coverage. Performance was not affected by stimulus contrast or blur, indicating that the transition does not depend on low-level stimulus properties. Our results reinforce the notion that numerosity and texture are mediated by two distinct processes, depending on whether the individual elements are perceptually segregable. Which mechanism is engaged follows laws that determine crowding.

Spontaneous perception of numerosity in humans

“…The slope of the regression for area was –0.21, between constant and square root. This result reinforces previous studies showing that numerosity judgments tend to follow Weber's law, while density judgments are better described by a square root relationship3233.…”

“…The evidence for the different mechanisms comes largely from different psychophysical laws operating at different densities, Weber's law at the moderate densities where the objects can be segregated, and a square root law at higher densities22. There is also a clear dependence of eccentricity, implicating crowding-like mechanisms33.…”

Connecting visual objects reduces perceived numerosity and density for sparse but not dense patterns

“…Importantly, the selective sensitivity for numerosity over density is far less pronounced with dense stimuli, where the results are consistent with independent analyses of density and area . This is supported by several other studies showing clear differences in the psychophysical laws governing visibility at high and low densities of dot patterns (Anobile et al, 2014;Anobile et al, 2015;Cicchini et al, 2016), leading to the suggestion of two different regimes of analysis .…”

“…This result not only shows that numerosity is not derived indirectly from density, texture or other low-level features, but also casts doubts on the idea that density is a primary visual feature: rather, density seems to be derived indirectly from numerosity, reinforcing previous evidence showing that at low numerosities, density judgments are particularly unreliable and are often surrogated by number judgments . Overall our results add to a growing body of literature showing that visual numerosity is perceived directly, rather than being recalculated from area and density (Anobile, Arrighi, et al, 2016;Anobile, Castaldi, Turi, Tinelli, & Burr, 2016;Anobile et al, 2014;Anobile, Cicchini, et al, 2016;Anobile et al, 2015;Arrighi et al, 2014;Burr & Ross, 2008;Cicchini et al, 2016;DeWind et al, 2015;Hurewitz et al, 2006;Kramer, Di Bono, & Zorzi, 2011;Ross & Burr, 2010Stoianov & Zorzi, 2012).…”

“…Over the estimation range discrimination thresholds follow Weber's law, remaining proportional to numerosity (a commonly accepted signature of the Approximate Number System), while at higher numerosities thresholds follow a square-root law, as predicted by their signalto-noise ratios. These results suggest that within a certain range, when the items are sparse enough to permit spatial segregation, numerosity is encoded directly by the Approximate Number System, without involving texture-density mechanisms (Anobile, Cicchini, & Burr, 2014;Anobile, Cicchini, et al, 2016;Anobile, Turi, Cicchini, & Burr, 2015). When the ensembles become too crowded, another system seems to come into play, encoding texture-density.…”