Enumerating the forest before the trees: The time courses of estimation-based and individuation-based numerical processing

Abstract

Ensemble perception refers to the ability to report attributes of a group of objects, rather than focusing on only one or a few individuals. An everyday example of ensemble perception is the ability to estimate the numerosity of a large number of items. The time course of ensemble processing, including that of numerical estimation, remains a matter of debate, with some studies arguing for rapid, “preattentive” processing and other studies suggesting that ensemble perception improves with longer presentation durations. We used a forward-simultaneous masking procedure that effectively controls stimulus durations to directly measure the temporal dynamics of ensemble estimation and compared it with more precise enumeration of individual objects. Our main finding was that object individuation within the subitizing range (one to four items) took about 100–150 ms to reach its typical capacity limits, whereas estimation (six or more items) showed a temporal resolution of 50 ms or less. Estimation accuracy did not improve over time. Instead, there was an increasing tendency, with longer effective durations, to underestimate the number of targets for larger set sizes (11–35 items). Overall, the time course of enumeration for one or a few single items was dramatically different from that of estimating numerosity of six or more items. These results are consistent with the idea that the temporal resolution of ensemble processing may be as rapid as, or even faster than, individuation of individual items, and support a basic distinction between the mechanisms underlying exact enumeration of small sets (one to four items) from estimation.

Introduction to the special issue on ensemble perception

“…The papers in this section represent the forefront of the field. Melcher et al (2020) report qualitatively different relationships between exposure duration and the accuracies of small and large numerosity estimates. Zhu et al (2020) explicitly probe ensemble representations of duration and provide a model for how the quality of those representations depends on the statistics of the ensemble.…”

“…Of course, the term "low-level" is loaded, and this grouping is not intended to suggest (or exclude) any particular model of visual processing; it does not preclude feedback or necessitate strict feedforward hierarchical processing. For example, ensemble numerosity (Katzin et al, 2020;Lee et al, 2021;Melcher et al, 2020;Rosenbaum et al, 2021) might be an early representation or a late one (or both). Effects of size constancy (Haberman & Suresh, 2020;Tiurina & Utochkin, 2019) might well not be strictly low-level.…”

“…More abstract perceptual dimensions may also be represented as ensembles (Leib et al, 2016;Leib et al, 2020). For example, ensemble perception of numerosity or numerical values (Brezis et al, 2015;Katzin et al, 2020;Lee et al, 2021;Melcher et al, 2020;Rosenbaum et al, 2021;Solomon & Morgan, 2018), explicit ensemble judgments of abstract aesthetic impressions (Brielmann & Pelli, 2020), and implicit ensemble perception of category prototypes (Khayat & Hochstein, 2019) even with novel image sets that have never been seen before (Khayat et al, 2021). There is also research suggesting that high level cognition and cultural factors can impinge on ensemble perception (Peng et al, 2020).…”

Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays

“…Subitizing is characterized by being fast and accurate. Its success can be tested by presenting grouped arrays for a fraction of a second (~150 ms) and measuring whether participants could accurately enumerate both dots and groups in the array (for a similar methodology, see Melcher et al, 2020).…”

Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays

“…Its success can be tested by presenting grouped arrays for a fraction of a second (~150ms) and measuring whether participants could accurately enumerate both dots and groups in the array (for a similar methodology see Melcher, Huber-Huber & Wutz, 2020).…”