Underestimation Of Numerosity Research Articles

The interplay between spatial and non-spatial grouping cues over approximate number perception.

Humans and animals share the cognitive ability to quickly extract approximate number information from sets. Main psychophysical models suggest that visual approximate numerosity relies on segmented units, which can be affected by Gestalt rules. Indeed, arrays containing spatial grouping cues, such as connectedness, closure, and even symmetry, are underestimated compared to ungrouped arrays with equal low-level features. Recent evidence suggests that non-spatial cues, such as color-similarity, also trigger numerosity underestimation. However, in natural vision, several grouping cues may coexist in the scene. Notably, conjunction of grouping cues (color and closure) reduces perceived numerosity following an additive rule. To test whether the conjunction-effect holds for other Gestalt cues, we investigated the effect of connectedness and symmetry over numerosity perception both in isolation and, critically, in conjunction with luminance similarity. Participants performed a comparison-task between a reference and a test stimulus varying in numerosity. In Experiment 1, test stimuli contained two isolated groupings (connectedness or luminance), a conjunction (connectedness and luminance), and a neutral condition (no groupings). Results show that point of subjective equality was higher in both isolated grouping conditions compared to the neutral condition. Furthermore, in the conjunction condition, the biases from isolated grouping cues added linearly, resulting in a numerosity underestimation equal to the sum of the isolated biases. In Experiment 2 we found that conjunction of symmetry and luminance followed the same additive rule. These findings strongly suggest that both spatial and non-spatial isolated cues affect numerosity perception. Crucially, we show that their conjunction effect extends to symmetry and connectedness.

Exploring Sex Differences in Numerosity Perception Using Dynamic Visual Stimuli: Insights into Cognitive Processing and STEM

Exploring Sex Differences in Numerosity Perception Using Dynamic Visual Stimuli: Insights into Cognitive Processing and STEM

The symmetry-induced numerosity illusion depends on visual attention

Symmetry is an important and strong cue we rely on to organize the visual world. Although it is at the basis of objects segmentation in a visual scene, it can sometimes bias our perception. When asked to discriminate numerical quantities between symmetric and asymmetric arrays, individuals tend to underestimate the number of items in the symmetric stimuli. The reason for this underestimation is currently unknown. In this study we investigated whether the symmetry-induced numerosity underestimation depends on perceptual grouping mechanisms by depriving attentional resources. Twenty-six adults judged the numerosity of dot arrays arranged symmetrically or randomly, while ignoring a visual distractor (single task) or while simultaneously judging its color and orientation (dual-task). Diverting attention to the concurrent color–orientation conjunction task halved the symmetry-induced numerosity underestimation. Taken together these results showed that the bias in numerosity perception of symmetric arrays depends—at least partially—on attentional resources and suggested that it might originate from the recruitment of attentional dependent incremental grouping mechanisms.

Numerosity perception is tuned to salient environmental features

SummaryNumerosity perception is a key ability to guide behavior. However, current models propose that number units encode an abstract representation of numerosity regardless of the non-numerical attributes of the stimuli, suggesting rather coarse environmental tuning. Here we investigated whether numerosity systems spontaneously adapt to all visible items, or to subsets segregated by salient attributes such as color or pitch. We measured perceived numerosity after participants adapted to highly numerous stimuli with color either matched to or different from the test. Matched colors caused a 25% underestimation of numerosity, while different colors had virtually no effect. This was true both for physically different colors, and for the same colors perceived as different, via a color-assimilation illusion. A similar result occurred in the acoustic domain, where adaptation magnitude was halved when the adaptor and test differed in pitch. Taken together, our results support the idea that numerosity perception is selectively tuned to salient environmental attributes.

Nonsymbolic numerosity in sets with illusory-contours exploits a context-sensitive, but contrast-insensitive, visual boundary formation process

The visual mechanisms underlying approximate numerical representation are still intensely debated because numerosity information is often confounded with continuous sensory cues (e.g., texture density, area, convex hull). However, numerosity is underestimated when a few items are connected by illusory contours (ICs) lines without changing other physical cues, suggesting in turn that numerosity processing may rely on discrete visual input. Yet, in these previous works, ICs were generated by black-on-gray inducers producing an illusory brightness enhancement, which could represent a further continuous sensory confound. To rule out this possibility, we tested participants in a numerical discrimination task in which we manipulated the alignment of 0, 2, or 4 pairs of open/closed inducers and their contrast polarity. In Experiment 1, aligned open inducers had only one polarity (all black or all white) generating ICs lines brighter or darker than the gray background. In Experiment 2, open inducers had always opposite contrast polarity (one black and one white inducer) generating ICs without strong brightness enhancement. In Experiment 3, reverse-contrast inducers were aligned but closed with a line preventing ICs completion. Results showed that underestimation triggered by ICs lines was independent of inducer contrast polarity in both Experiment 1 and Experiment 2, whereas no underestimation was found in Experiment 3. Taken together, these results suggest that mere brightness enhancement is not the primary cause of the numerosity underestimation induced by ICs lines. Rather, a boundary formation mechanism insensitive to contrast polarity may drive the effect, providing further support to the idea that numerosity processing exploits discrete inputs.

The Grouping-Induced Numerosity Illusion Is Attention-Dependent.

Perceptual grouping and visual attention are two mechanisms that help to segregate visual input into meaningful objects. Here we report how perceptual grouping, which affects perceived numerosity, is reduced when visual attention is engaged in a concurrent visual task. We asked participants to judge the numerosity of clouds of dot-pairs connected by thin lines, known to cause underestimation of numerosity, while simultaneously performing a color conjunction task. Diverting attention to the concomitant visual distractor significantly reduced the grouping-induced numerosity biases. Moreover, while the magnitude of the illusion under free viewing covaried strongly with AQ-defined autistic traits, under conditions of divided attention the relationship was much reduced. These results suggest that divided attention modulates the perceptual grouping of elements by connectedness and that it is independent of the perceptual style of participants.

Increased Functional Connectivity of the Intraparietal Sulcus Underlies the Attenuation of Numerosity Estimations for Self-Generated Words.

Previous studies have shown that self-generated stimuli in auditory, visual, and somatosensory domains are attenuated, producing decreased behavioral and neural responses compared with the same stimuli that are externally generated. Yet, whether such attenuation also occurs for higher-level cognitive functions beyond sensorimotor processing remains unknown. In this study, we assessed whether cognitive functions such as numerosity estimations are subject to attenuation in 56 healthy participants (32 women). We designed a task allowing the controlled comparison of numerosity estimations for self-generated (active condition) and externally generated (passive condition) words. Our behavioral results showed a larger underestimation of self-generated compared with externally generated words, suggesting that numerosity estimations for self-generated words are attenuated. Moreover, the linear relationship between the reported and actual number of words was stronger for self-generated words, although the ability to track errors about numerosity estimations was similar across conditions. Neuroimaging results revealed that numerosity underestimation involved increased functional connectivity between the right intraparietal sulcus and an extended network (bilateral supplementary motor area, left inferior parietal lobule, and left superior temporal gyrus) when estimating the number of self-generated versus externally generated words. We interpret our results in light of two models of attenuation and discuss their perceptual versus cognitive origins.SIGNIFICANCE STATEMENT We perceive sensory events as less intense when they are self-generated compared with when they are externally generated. This phenomenon, called attenuation, enables us to distinguish sensory events from self and external origins. Here, we designed a novel fMRI paradigm to assess whether cognitive processes such as numerosity estimations are also subject to attenuation. When asking participants to estimate the number of words they had generated or passively heard, we found bigger underestimation in the former case, providing behavioral evidence of attenuation. Attenuation was associated with increased functional connectivity of the intraparietal sulcus, a region involved in numerosity processing. Together, our results indicate that the attenuation of self-generated stimuli is not limited to sensory consequences but is also impact cognitive processes such as numerosity estimations.

Implicit visuospatial attention shapes numerosity adaptation and perception

The perception of numerical quantities is susceptible to adaptation: after inspecting a numerous dot array for a few seconds a subsequent dot array is grossly underestimated. In a recent work we showed that the mere appearance of an additional numerically neutral stimulus significantly reduces the adaptation magnitude. Here we demonstrate that this reduction is likely due to a numerosity underestimation of the adaptor caused by a change of numerosity-related attentional resources deployed on the adapting stimulus. In Experiment 1 we replicated previous findings revealing a robust reduction of numerosity adaptation when an additional adaptor (even if neutral) was displayed. In Experiment 2 we used the method of magnitude estimation to demonstrate that numerosity is underestimated whenever a second task-irrelevant numerical stimulus appears on screen. Furthermore we demonstrated that the same experimental manipulations were not effective in modulating orientation adaptation magnitude as well as orientation estimation accuracy. Our results support the hypothesis of a tight relationship between numerosity perception and implicit visuospatial attention and corroborate the notion that numerosity adaptation depends on perceived rather than physical numerosity. However the lack of an effect of visuospatial attentional deployment for orientation perception suggests that attention might differently shape adaptation aftereffects for different features along the visual hierarchy.

Grouping-Induced Numerosity Biases Vary with Autistic-Like Personality Traits

Individuals with autism spectrum disorder are thought to have a more local than global perceptual style. We used a novel paradigm to investigate how grouping-induced response biases in numerosity judgments depend on autistic-like personality traits in neurotypical adults. Participants judged the numerosity of clouds of dot-pairs connected by thin lines, known to cause underestimation of numerosity. The underestimation bias correlated strongly with autism-spectrum quotient (r = 0.72, Bayes factor > 100), being weaker for participants with high autistic traits. As connecting dots probably activates global grouping mechanisms, causing dot-pairs to be processed as an integrated whole rather than as individual dots, the results suggest that these grouping mechanisms may be weaker in individuals self-reporting high levels of autistic-like traits.

Visual illusions as a tool to hijack numerical perception: Disentangling nonsymbolic number from its continuous visual properties.

The past few years have witnessed a fervent theoretical debate about the exact visual mechanisms supporting nonsymbolic number processing. The idea that quantity information is extracted through a primitive visual segmentation algorithm has been challenged by recent models, which rather tap on low-level features confounded with numerosity (i.e., density, convex hull, or total area). Here we used an original manipulation based on visual illusions to disentangle whether visual numerosity processing operates over discrete units or rather over continuous variables. In particular, we generated a set of stimuli composed by open inducers (e.g., like a pac-man shape) that simulate physical connections with Kanizsa-like illusory contours (ICs). Test sets contained pairs of collinear open inducers items that prompted 0 IC, 2 IC, or 4 IC lines connecting 2 objects. Critically, low-level visual features were fully controlled across connectedness levels. We found a systematic underestimation as we increased the IC connections when participants had to select the larger between 2 sets of objects (Experiment 1) but not in the case of aligned closed inducers preventing illusory lines (Experiments 2A and 2B). We also found a systematic numerosity underestimation when both IC connections and continuous features (e.g., convex hull) were independently manipulated in test stimuli (Experiment 3). Finally, these results were shown to be task independent because the same effects of IC connections were replicated in an estimation task (Experiment 4). Taken together, our findings indicate that numerosity perception relies on basic visual-segmentation mechanisms, pointing out the need of new theoretical frameworks integrating both continuous and discrete perceptual number signals. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Numerosity representation in a deep convolutional neural network

Enumerating objects in the environment (i.e., “number sense”) is crucial for survival in many animal species, and foundational for the construction of more abstract and complex mathematical knowledge in humans. Perhaps surprisingly, deep convolutional neural networks (DCNNs) spontaneously emerge a similar number sense even without any explicit training for numerosity estimation. However, little is known about how the number sense emerges, and the extent to which it is comparable with human number sense. Here, we examined whether the numerosity underestimation effect, a phenomenon indicating that numerosity perception acts upon the perceptual number rather than the physical number, can be observed in DCNNs. In a typical DCNN, AlexNet, we found that number-selective units at late layers operated on the perceptual number, like humans do. More importantly, this perceptual number sense did not emerge abruptly, rather developed progressively along the hierarchy in the DCNN, shifting from the physical number sense at early layers to perceptual number sense at late layers. Our finding hence provides important implications for the neural implementation of number sense in the human brain and advocates future research to determine whether the representation of numerosity also develops gradually along the human visual stream from physical number to perceptual number.

Clustering leads to underestimation of numerosity, but crowding is not the cause

Humans have the remarkable ability to rapidly estimate the number of objects in a visual scene without relying on counting, something referred to as the number sense. It has been well documented that the more clustered the elements are, the lower their perceived numerosity is. A recent account of this observation is the crowdinghypothesis, which posits that the perceived underestimation is driven by visual crowding: the inability to recognise objects in clutter. Crowding can impair individuation of the elements, which would explain the underestimation. Here, we tested the crowding hypothesis by assessing numerosity estimation and crowding for the same stimulus configurations in the same participants. Experiment 1 compared the two tasks when numerosity can be considered to be estimated directly by the visual system (reference patch density = 0.12 items/deg2), while Experiment 2 used high density stimuli (density = 0.88 items/deg2), where numerosity may be estimated indirectly. In both cases, we found that spacing and similarity between elements affected estimation and crowding tasks in markedly different ways. These results are incompatible with a crowding account of numerosity underestimation and point to separate mechanisms for object identification and number estimation, although grouping may play a moderating role in both cases.

Numerosity estimation benefits from transsaccadic information integration.

Humans achieve a stable and homogeneous representation of their visual environment, although visual processing varies across the visual field. Here we investigated the circumstances under which peripheral and foveal information is integrated for numerosity estimation across saccades. We asked our participants to judge the number of black and white dots on a screen. Information was presented either in the periphery before a saccade, in the fovea after a saccade, or in both areas consecutively to measure transsaccadic integration. In contrast to previous findings, we found an underestimation of numerosity for foveal presentation and an overestimation for peripheral presentation. We used a maximum-likelihood model to predict accuracy and reliability in the transsaccadic condition based on peripheral and foveal values. We found near-optimal integration of peripheral and foveal information, consistently with previous findings about orientation integration. In three consecutive experiments, we disrupted object continuity between the peripheral and foveal presentations to probe the limits of transsaccadic integration. Even for global changes on our numerosity stimuli, no influence of object discontinuity was observed. Overall, our results suggest that transsaccadic integration is a robust mechanism that also works for complex visual features such as numerosity and is operative despite internal or external mismatches between foveal and peripheral information. Transsaccadic integration facilitates an accurate and reliable perception of our environment.

Do You Hear More Piano or Drum Sounds? An Auditory Version of the Solitaire Illusion.

The solitaire illusion is an illusion of numerosity proposed by Frith and Frith. In the original version, an apparent number of elements was determined by the spatial arrangement of two kinds of elements (black and white marbles). In our study, an auditory version of the solitaire illusion was demonstrated. Participants were asked to judge if they perceived more drum or piano sounds. When half of the piano tones were perceived as lower in pitch than a drum sound and the other half higher, piano tones appeared to be arranged in small units, leading to numerosity underestimation. Conversely, when all piano tones were perceived to be higher in pitch than the drum sounds, they appeared to be arranged in a single large unit, leading to numerosity overestimation. Comparable to the visual version of the solitaire illusion, the clustering seems to be determined by Gestalt principles. In our auditory version, a clear reversal of the illusion (numerosity overestimation or underestimation) was observed when piano tones appeared to be arranged in a single large cluster or in several small clusters, respectively.

Effects of adaptation on numerosity decoding in the human brain

Psychophysical studies have shown that numerosity is a sensory attribute susceptible to adaptation. Neuroimaging studies have reported that, at least for relatively low numbers, numerosity can be accurately discriminated in the intra-parietal sulcus. Here we developed a novel rapid adaptation paradigm where adapting and test stimuli are separated by pauses sufficient to dissociate their BOLD activity. We used multivariate pattern recognition to classify brain activity evoked by non-symbolic numbers over a wide range (20–80), both before and after psychophysical adaptation to the highest numerosity. Adaptation caused underestimation of all lower numerosities, and decreased slightly the average BOLD responses in V1 and IPS. Using support vector machine, we showed that the BOLD response of IPS, but not in V1, classified numerosity well, both when tested before and after adaptation. However, there was no transfer from training pre-adaptation responses to testing post-adaptation, and vice versa, indicating that adaptation changes the neuronal representation of the numerosity. Interestingly, decoding was more accurate after adaptation, and the amount of improvement correlated with the amount of perceptual underestimation of numerosity across subjects. These results suggest that numerosity adaptation acts directly on IPS, rather than indirectly via other low-level stimulus parameters analysis, and that adaptation improves the capacity to discriminate numerosity.

Emotional faces influence numerosity estimation without awareness.

It is well established that emotional information influences perceived duration. On the basis of this together with the proposition of common magnitude estimation system, we hypothesized that the presentation of emotional faces can modulate the estimation of numerical quantity as well. The present study examined this hypothesis by investigating the effects of unconsciously presented emotional faces on numerosity estimation using number bisection task. We rendered the facial images invisible by continuous flash suppression methodology in order to measure the genuine effect of emotional information by reducing the influences of a conscious effort of emotional regulation. The results have shown that the unconscious presentation of fearful faces leads to underestimation of numerosity compared to happy and neutral faces. Further experiment has shown that the participants could not detect the presence of facial expressions directly. Together, these results indicate that perceived emotion influences numerosity judgments automatically without conscious awareness, which provides novel evidence linking emotion and quantity perception.

Numerosity underestimation in sets with illusory contours

People underestimate the numerosity of collections in which a few dots are connected in pairs by task-irrelevant lines. Such configural processing suggests that visual numerosity depends on the perceived scene segments, rather than on the perceived total area occupied by a collection. However, a methodology that uses irrelevant line connections may also introduce unnecessary distraction and variety, or obscure the perception of task-relevant items, given the saliency of the lines. To avoid such potentially confounding variables, we conducted four experiments where the line-connected dots were replaced with collinear inducers of Kanizsa-type illusory contours. Our participants had to compare two simultaneously presented collections and choose the more numerous one. Displays comprised c-shaped inducers and disks (Experiment 1), c-shaped inducers only (Experiments 2 and 4), or closed inducers (Experiment 3). One display always showed a 12- (Experiments 1–3) or 48-item reference pattern (Experiment 4); the other was a test pattern with numerosity varying between 9 and 15 (Experiments 1–3) or 36–60 items (Experiment 4). By manipulating the number of illusory contours in the test patterns, the level of connectedness increased or decreased respectively. The fitted psychometric functions revealed an underestimation that increased with the number of illusory contours in Experiments 1 and 2, but was absent in Experiments 3 and 4, where illusory contours were more difficult to perceive or larger numerosities were used. Results corroborate claims that visual numerosity estimation depends on segmented inputs, but only within moderate numerical ranges.

Topology-defined units in numerosity perception

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.

Underestimation of perceived number at the time of saccades

Saccadic eye movements produce transient distortions in both space and time. Mounting evidence suggests that space and time perception are linked, and associated with the perception of another important perceptual attribute, numerosity. Here we investigate the effect of saccades on the perceived numerosity of briefly presented arrays of visual elements. We report a systematic underestimation of numerosity for stimuli flashed just before or during saccades, of about 35% of the reference numerosity. The bias is observed only for relatively large arrays of visual elements, in line with the notion that a distinct perceptual mechanism is involved with enumeration of small numerosities in the ‘subitizing’ range. This study provides further evidence for the notion that space, time and number share common neural representations, all affected by saccades.

Auditory perception of numerosity by infants

Saccadic eye movements produce transient distortions in both space and time. Mounting evidence suggests that space and time perception are linked, and associated with the perception of another important perceptual attribute, numerosity. Here we investigate the effect of saccades on the perceived numerosity of briefly presented arrays of visual elements. We report a systematic underestimation of numerosity for stimuli flashed just before or during saccades, of about 35% of the reference numerosity. The bias is observed only for relatively large arrays of visual elements, in line with the notion that a distinct perceptual mechanism is involved with enumeration of small numerosities in the ‘subitizing’ range. This study provides further evidence for the notion that space, time and number share common neural representations, all affected by saccades.