Connectedness affects dot numerosity judgment: Implications for configural processing

He, Liang; Zhang, Jun; Zhou, Tiangang; Chen, Lin

doi:10.3758/pbr.16.3.509

Cited by 120 publications

(176 citation statements)

References 21 publications

(11 reference statements)

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“…This is in contrast to previous studies where connectivity interfered with estimation (Franconeri, Bemis, & Alvarez, 2009;He et al, 2009) or multiple object tracking performance (Scholl et al, 2001). However, subitizing differs from estimation in both quantitative range and accuracy, and neural data suggests that separate mechanisms underlie the two processes (Cutini, Scatturin, Basso Moro, & Zorzi, 2014), suggesting that connectivity may have a different impact on exact enumeration and estimation.…”

Section: # Target Itemscontrasting

confidence: 53%

“…Merely adding a connecting line between two shapes allows patients to perform a task comparing features of the shapes, which was otherwise impossible (Humphreys & Riddoch, 1993, p. 158). For these reasons we believe that our finding that parallel individuation does occur over connected object parts is not trivial, and is somewhat unexpected given the interference present in other tasks (Franconeri, Bemis, & Alvarez, 2009;He et al, 2009;Scholl et al, 2001). …”

Section: # Target Itemsmentioning

confidence: 90%

“…Franconeri, Bemis, and Alvarez (2009) found that adding task irrelevant connecting lines between target shapes caused subjects to underestimate the number of targets, suggesting that estimation relies on representations of distinct unconnected objects. A convergent study suggested that connectivity affects the initial individuation of targets to be estimated, rather than influencing the subsequent magnitude judgment (He, Zhang, Zhou, & Chen, 2009). If estimation relies on the same individuation mechanism as observed in subitizing, we would expect that in a rapid enumeration paradigm subjects would underestimate and thus perform poorly when enumerating object parts.…”

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confidence: 99%

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Visual object individuation occurs over object wholes, parts, and even holes

Porter

Mazza

Garofalo

et al. 2016

Atten Percept Psychophys

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Segmentation of the world into meaningful units has typically been described as object individuation, emphasizing the spatially disconnected quality that comes as a result of objecthood. This segmentation can occur rapidly, even in parallel for multiple objects. It remains unclear whether objecthood is a necessary requirement for parallel individuation, or whether target features in distinct locations, such as object parts, may also be individuated in parallel. In a series of six experiments, we used a rapid enumeration task to test whether subitizing, a phenomenon believed to result from parallel individuation, occurs over object parts. We found that subitizing and individuation occur over connected object parts as well as physically separate objects of varied shapes and sizes. We also observed subitizing when target items are indents, features intrinsic to the shape of the object, and when cues for occlusion were removed. The results of these studies suggest that parallel individuation is not bound to objecthood, and can occur over object parts existing in separate locations.

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Section: # Target Itemscontrasting

confidence: 53%

Section: # Target Itemsmentioning

confidence: 90%

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confidence: 99%

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Visual object individuation occurs over object wholes, parts, and even holes

Porter

Mazza

Garofalo

et al. 2016

Atten Percept Psychophys

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“…We designed arbitrary and irregular shapes of connecting line segments (Fig. 1A, Upper) to test the invariant effect of connection on numerosity judgement independent of the concrete forms or manners of connection (12,13). Three conditions of connection were constructed: zero, one, and two connected pairs of dots in the test patterns (Fig.…”

Section: Resultsmentioning

confidence: 99%

Topology-defined units in numerosity perception

Zhou

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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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.W hat is a number? The answer to this age-old and fundamental question of philosophy has increasingly benefited from recent scientific investigation using psychology and neuroscience. The number sense hypothesis (1, 2) suggests that a number is "a basic property of the environment" (3) and particularly, because of its remarkable adaptation effect, "a primary visual property" (2), like color, contrast, or orientation (2-8). However, exactly what attribute in the environment is the primary property and determines numbers in the number sense, or more concretely, what is counted in numerosity perception? Consider the invariant nature of numerosity perception. It is self-evident that numerosity is invariant to specific features (e.g., orientation, size, shape, and color) of individual items to be counted. In other words, the primitive units to be counted must be invariant with variation in form dimensions and other visual features (2, 3, 7, 9-11). Then, the critical question becomes how to define precisely such abstract and invariant attributes. ResultsGeneralizing Connection to a Topological Invariant: Connectivity. We designed arbitrary and irregular shapes of connecting line segments (Fig. 1A, Upper) to test the invariant effect of connection on numerosity judgement independent of the concrete forms or manners of connection (12, 13). Three conditions of connection were constructed: zero, one, and two connected pairs of dots in the test patterns (Fig. 1A). A typical numerosity discrimination task was adopted, in which two visual patterns of dots were briefly presented on opposite sides of fixation (one serving as a reference and the other one serving as a test), and subj...

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“…A consequence of this is that if two items are connected, simply by joining them with lines, the apparent numerosity of the connected items is greatly reduced (Franconeri, Bemis, & Alvarez, 2009;He, Zhang, Zhou, & Chen, 2009;He, Zhou, Zhou, He, & Chen, 2015) -see examples of Figure 1, and also the Supplementary Movie. In fact the lines do not need to be physically present: the effect works well with illusory contours as well (Kirjakovski & Matsumoto, 2016).…”

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confidence: 99%

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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Connectedness affects dot numerosity judgment: Implications for configural processing

Cited by 120 publications

References 21 publications

Visual object individuation occurs over object wholes, parts, and even holes

Visual object individuation occurs over object wholes, parts, and even holes

Topology-defined units in numerosity perception

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

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