Number and density discrimination rely on a common metric: Similar psychophysical effects of size, contrast, and divided attention (original) (raw)
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Numerosity and density judgments: Biases for area but not for volume
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.
Separate Mechanisms for Perception of Numerosity and Density
Psychological Science, 2014
Despite the existence of much evidence for a number sense in humans, several researchers have questioned whether number is sensed directly or derived indirectly from texture density. Here, we provide clear evidence that numerosity and density judgments are subserved by distinct mechanisms with different psychophysical characteristics. We measured sensitivity for numerosity discrimination over a wide range of numerosities: For low densities (less than 0.25 dots/ deg 2 ), thresholds increased directly with numerosity, following Weber's law; for higher densities, thresholds increased with the square root of texture density, a steady decrease in the Weber fraction. The existence of two different psychophysical systems is inconsistent with a model in which number is derived indirectly from noisy estimates of density and area; rather, it points to the existence of separate mechanisms for estimating density and number. These results provide strong confirmation for the existence of neural mechanisms that sense number directly, rather than indirectly from texture density.
Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects
Journal of Vision, 2015
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/8 2 , while at 158 eccentricity, it changed at 0.5 dots/8 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.
Numerosity Estimation in Visual Stimuli in the Absence of Luminance-Based Cues
PLoS ONE, 2011
Background: Numerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills. It is notoriously difficult, however, to establish whether numerosity estimation is based on numerosity itself, or on one or more non-numerical cues like-in visual stimuli-spatial extent and density. Frequently, different non-numerical cues are held constant on different trials. This strategy, however, still allows numerosity estimation to be based on a combination of non-numerical cues rather than on any particular one by itself.
Perceived numerosity is reduced in peripheral vision
In four experiments we investigated the perception of numerosity in the peripheral visual field. We found that the perceived numerosity of a peripheral cloud of dots was judged to be inferior to the one of a central cloud of dots, particularly when the dots were highly clustered. Blurring the stimuli accordingly to peripheral spatial frequency sensitivity did not abolish the effect and had little impact on numerosity judgments. In a dedicated control experiment we ruled out that the reduction in peripheral perceived numerosity is secondary to a reduction of perceived stimulus size. We suggest that visual crowding might be at the origin of the observed reduction in peripheral perceived numerosity, implying that numerosity could be partly estimated through the individuation of the elements populating the array.
Numerical Perception Biased by Saliency
2022
How do people process numerosity? Do they rely on general magnitude processing (e.g. area, density, etc.) 1,2,3 ? Alternatively, do they depend on a designated module underlying numerosity judgements 4,5 ? In a 2016 paper, Cicchini and colleagues 6 show results that strongly support the latter. They demonstrated that humans automatically perceive and spontaneously use numerosity rather than other physical magnitudes (i.e. area of convex hull or density) when asked to make comparison judgments. Here we present an alternative account for their findings. We suggest that saliency of the different attributes of
PLoS ONE, 2014
A number of studies have shown strong relations between numbers and oriented spatial codes. For example, perceiving numbers causes spatial shifts of attention depending upon numbers' magnitude, in a way suggestive of a spatially oriented, mental representation of numbers. Here, we investigated whether this phenomenon extends to non-symbolic numbers, as well as to the processing of the continuous dimensions of size and brightness, exploring whether different quantitative dimensions are equally mapped onto space. After a numerical (symbolic Arabic digits or non-symbolic arrays of dots; Experiment 1) or a non-numerical cue (shapes of different size or brightness level; Experiment 2) was presented, participants' saccadic response to a target that could appear either on the left or the right side of the screen was registered using an automated eye-tracker system. Experiment 1 showed that, both in the case of Arabic digits and dot arrays, right targets were detected faster when preceded by large numbers, and left targets were detected faster when preceded by small numbers. Participants in Experiment 2 were faster at detecting right targets when cued by large-sized shapes and left targets when cued by small-sized shapes, whereas brightness cues did not modulate the detection of peripheral targets. These findings indicate that looking at a symbolic or a non-symbolic number induces attentional shifts to a peripheral region of space that is congruent with the numbers' relative position on a mental number line, and that a similar shift in visual attention is induced by looking at shapes of different size. More specifically, results suggest that, while the dimensions of number and size spontaneously map onto an oriented space, the dimension of brightness seems to be independent at a certain level of magnitude elaboration from the dimensions of spatial extent and number, indicating that not all continuous dimensions are equally mapped onto space.
A texture-processing model of the 'visual sense of number
Proceedings. Biological sciences / The Royal Society, 2014
It has been suggested that numerosity is an elementary quality of perception, similar to colour. If so (and despite considerable investigation), its mechanism remains unknown. Here, we show that observers require on average a massive difference of approximately 40% to detect a change in the number of objects that vary irrelevantly in blur, contrast and spatial separation, and that some naive observers require even more than this. We suggest that relative numerosity is a type of texture discrimination and that a simple model computing the contrast energy at fine spatial scales in the image can perform at least as well as human observers. Like some human observers, this mechanism finds it harder to discriminate relative numerosity in two patterns with different degrees of blur, but it still outpaces the human. We propose energy discrimination as a benchmark model against which more complex models and new data can be tested.
Role of chromaticity, contrast, and local orientation cues in the perception of density
Perception, 2000
Introduction Among the many features characterising the organisation of the visual scene, the spatial distribution of its elements plays an important role. The perception of density, or numerosity, reflects one aspect of this spatial distribution, indicating proximity between neighbouring elements irrespective of their individual properties. Density has been investigated as a key attribute of pre-attentive textural processing; texture discrimination clearly depends on both the spacing as well as the form of its elements, although the spacing must fall below a certain limit before elements cohere to generate the percept of a texture (
Journal of Vision, 2014
The current research examined whether peripherally presented numerical information can affect the speed of number processing. In 2 experiments, participants were presented with a target matrix flanked by a distractor matrix and were asked to perform a comparative judgment (i.e., decide whether the target was larger or smaller than the reference 5). In Experiment 1, the target was symbolic (i.e., a single digit), and in Experiment 2, it was nonsymbolic (i.e., a random presentation of dots). In both experiments, flanker matrices had 2 dimensions-numerosity and numerical value-that were manipulated orthogonally to create stimulus congruent and stimulus incongruent conditions. Incongruent trials differed in the laterality between target and flanker (i.e., their location in relation to the reference 5). When responding to symbolic targets (Experiment 1), only the flanker's numerical value affected reaction times (RTs), whereas when responding to nonsymbolic targets (Experiment 2), only the flanker's numerosity affected RTs. In addition, the pattern of flanker interference differed between targets: For symbolic targets, laterality did not affect responses, whereas for nonsymbolic targets, laterality did affect responses. These results imply both symbolic and nonsymbolic magnitudes can be automatically activated; however, this activation is contingent upon their relevance to the task at hand. Implications of these results on the efficiency of the visual processing system and on numerical cognition are further discussed.