A texture-processing model of the ‘visual sense of number’

Morgan, M.; Raphael, Sabine; Tibber, Marc S.; Dakin, Steven C.

doi:10.1098/rspb.2014.1137

Cited by 79 publications

(123 citation statements)

References 41 publications

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“…According to the energy-based models of Dakin and collaborators (e.g. Dakin et al, 2011;Morgan et al, 2014), these patterns should appear more numerous than those with isolated dots. Figure 2 shows psychometric functions for the tasks.…”

Section: Resultsmentioning

confidence: 99%

“…For example, Stoianov and Zorzi (2012) have shown that number (rather than density) emerges spontaneously within an unsupervised learning algorithm. If numerosity were a sensory by-product of density and area, as suggested by several research groups (Dakin, Tibber, Greenwood, Kingdom, & Morgan, 2011;Durgin, 2008;Morgan, Raphael, Tibber, & Dakin, 2014;Tibber, Greenwood, & Dakin, 2012;Tibber et al, 2013), sensitivity for numerosity should be predictable from the independent measures of area and density. We recently directly tested this hypothesis and showed that when subjects discriminate items varying in the space spanned by number, density and area, discrimination thresholds are far lower for number than for density of area, suggesting that number rather than density is sensed spontaneously .…”

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confidence: 97%

“…Many authors still maintain that numerosity is encoded via texture-density mechanisms, operating on the global statistics of images (Dakin et al, 2011;Durgin, 2008;Morgan et al, 2014;Tibber et al, 2012;Tibber et al, 2013). In particular, Dakin et al (2011) have proposed a theory where numerosity is not sensed directly, but calculated from the product of density and area.…”

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

et al. 2017

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How is numerosity encoded by the visual system? -directly, or derived indirectly from texture density? We recently suggested that the numerosity of sparse patterns is encoded directly by dedicated mechanisms (which have been described as the "Approximate Number System" ANS). However, at high dot densities, where items become "crowded" and difficult to segregate, "texture-density" mechanisms come into play. Here we tested the importance of item segmentation on numerosity and density perception at various stimulus densities, by measuring the effect of connecting visual objects with thin lines. The results confirmed many previous studies showing that connecting items robustly reduces the apparent numerosity of patterns of moderate density. We further showed that the apparent density of moderatedensity patterns is also reduced by connecting the dots. Crucially, we found that both these effects are strongly reduced at higher numerosities. Indeed for density judgments, the effect reverses, so connecting dots in dense patterns increases the apparent density (as expected from the physical characteristics). The results provide clear support for the three-regime framework of number perception, and suggest that for moderately sparse stimuli, numerosity -but not texture-density -is perceived directly.

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Section: Resultsmentioning

confidence: 99%

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confidence: 97%

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confidence: 99%

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

et al. 2017

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“…However, the retinotopic feature of numerosity adaptation would make it difficult to use IPS as a candidate because IPS represents numerosity quite abstractly, independently of whether the objects are distributed in space or time and independently of modality (Butterworth, 2008). In fact, it is not easy to find compelling reason to accept the idea that numerosity is an elementary quality of perception, similar to color or other primary features (Morgan, Raphael, Tibber & Dakin, 2014;Raphael & Morgan, 2015). Numerosity cognition is proposed to be accompanied by processes for a combination of surrogate features (Franconeri, Bemis, & Alvarez, 2009).…”

Section: Introductionmentioning

confidence: 99%

Numerosity adaptation along the Y-Axis affects numerosity perception along the X-Axis: does numerosity adaptation activate MNLs?

Liu

Zhang

et al. 2015

Atten Percept Psychophys

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The current study characterized the spatial selectivity of numerosity adaptation. In Experiment 1, adaptors were arranged vertically with 8 dots at the top of the visual field and 400 dots at the bottom, and participants' perceived magnitude in the left field decreased compared to that in the right, as revealed in the numerosity comparing task after adaptation. In contrast, the perceived magnitude in the right field decreased compared to that in the left with inversed adaptors (400 dots at top, 8 at bottom). In Experiment 2, adaptors were presented horizontally, and they showed no significant effect on numerosity perception, which was tested vertically. This study demonstrated that numerosity adaptation along the vertical orientation could affect numerosity perception along the horizontal orientation, and the latter was affected by the former according to a rule of associating Btop^with Bright^and Bbottom^with Bleft.^The spatial selectivity of numerosity adaptation showed distinguishing features that should function to abstract spatial relationships rather than create purely retinotopic mapping. We proposed that numerosity adaptation is based on spatial-numerical-associated codes. Vertical adaptors could activate both the vertical and horizontal Mental Number Lines (MNLs) and involve an interaction between these types of MNLs. According to behavioral data, horizontal adaptors showed no significant influence on perception along the vertical orientation, which might be due to the higher threshold required to activate the vertical MNL.

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“…According to this approach, numerosity is a principal feature of our environment that can be directly sensed, comparable to color, contrast, or brightness. A concurrent model proposes that numerosity is derived indirectly from non-numerical stimulus dimension such as density, for example (Morgan, Raphael, Tibber, & Dakin, 2014; see also Gevers, Cohen Kadosh, & Gebuis, 2016). …”

Section: Numbers and Spacementioning

confidence: 99%

Domain-general factors influencing numerical and arithmetic processing

Knops

Nuerk²,

Göbel

2017

J. Numer. Cogn.

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This special issue contains 18 articles that address the question how numerical processes interact with domain-general factors. We start the editorial with a discussion of how to define domain-general versus domain-specific factors and then discuss the contributions to this special issue grouped into two core numerical domains that are subject to domain-general influences (see Figure 1). The first group of contributions addresses the question how numbers interact with spatial factors. The second group of contributions is concerned with factors that determine and predict arithmetic understanding, performance and development. This special issue shows that domain-general (Table 1a) as well as domain-specific (Table 1b) abilities influence numerical and arithmetic performance virtually at all levels and make it clear that for the field of numerical cognition a sole focus on one or several domain-specific factors like the approximate number system or spatial-numerical associations is not sufficient. Vice versa, in most studies that included domain-general and domain-specific variables, domain-specific numerical variables predicted arithmetic performance above and beyond domain-general variables. Therefore, a sole focus on domain-general aspects such as, for example, working memory, to explain, predict and foster arithmetic learning is also not sufficient. Based on the articles in this special issue we conclude that both domain-general and domain-specific factors contribute to numerical cognition. But the how, why and when of their contribution still needs to be better understood. We hope that this special issue may be helpful to readers in constraining future theory and model building about the interplay of domain-specific and domain-general factors.Keywords: spatial-numerical associations, arithmetic, intervention studies, spatial skills, working memory, modules Numerical cognition encompasses a broad variety of cognitive and neural processes related to the perception, understanding and manipulation of numerical content. Hence, when investigating numerical cognition, we are not looking at an encapsulated cognitive module, supported by a single neural system but rather at a widespread network of interrelated cognitive processes with complex neural underpinnings. Much like human behaviour cannot be fully understood when leaving aside the social interactions and influences, we need to understand to what extent the core numerical processes are influenced and/or mediated by domain-general factors and other domains such as spatial skills and language.

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A texture-processing model of the ‘visual sense of number’

Cited by 79 publications

References 41 publications

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

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

Numerosity adaptation along the Y-Axis affects numerosity perception along the X-Axis: does numerosity adaptation activate MNLs?

Domain-general factors influencing numerical and arithmetic processing

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