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

Abstract‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than can unstructured arrays. Previous research suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays quickly and accurately. Here, we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants can use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150 ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

Grouping strategies in numerosity perception between intrinsic and extrinsic grouping cues

The number of items in an array can be quickly and accurately estimated by dividing the array into subgroups, in a strategy termed “groupitizing.” For example, when memorizing a telephone number, it is better to do so by divide the number into several segments. Different forms of visual grouping can affect the precision of the enumeration of a large set of items. Previous studies have found that when groupitizing, enumeration precision is improved by grouping arrays using visual proximity and color similarity. Based on Gestalt theory, Palmer (Cognit Psychol 24:436, 1992) divided perceptual grouping into intrinsic (e.g., proximity, similarity) and extrinsic (e.g., connectedness, common region) principles. Studies have investigated groupitizing effects on intrinsic grouping. However, to the best of our knowledge, no study has explored groupitizing effects for extrinsic grouping cues. Therefore, this study explored whether extrinsic grouping cues differed from intrinsic grouping cues for groupitizing effects in numerosity perception. The results showed that both extrinsic and intrinsic grouping cues improved enumeration precision. However, extrinsic grouping was more accurate in terms of the sensory precision of the numerosity perception.

Daily Fluctuations in the Isotope and Elemental Composition of Tap Water in Ljubljana, Slovenia

The isotope and elemental composition of tap water reflects its multiple distinct inputs and provides a link between infrastructure and the environment over a range of scales. For example, on a local scale, they can be helpful in understanding the geological, hydrogeological, and hydrological conditions and monitor the proper functioning of the water supply system (WSS). However, despite this, studies examining the urban water system remain limited. This study sought to address this knowledge gap by performing a 24 h multiparameter analysis of tap water extracted from a region where the mixing of groundwater between two recharge areas occurs. This work included measurements of temperature and electrical conductivity, as well as pH, δ2H, δ18O, d, δ13CDIC, and 87Sr/86Sr ratios and major and trace elements at hourly intervals over a 24 h period. Although the data show only slight variations in the measured parameters, four groups were distinguishable using visual grouping, and multivariate analysis (Spearman correlation coefficient analysis, hierarchical cluster analysis, and principal components analysis). Finally, changes in the mixing ratios of the two sources were estimated using a linear mixing model. The results confirm that the relative contribution from each source varied considerably over 24 h.

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

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than unstructured arrays. Previous research on groupitizing suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays fast and accurately. Here we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants could use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

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

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than unstructured arrays. Previous research on groupitizing suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays fast and accurately. Here we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants could use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.

Ensemble perception during multiple-object tracking

Multiple-object tracking studies consistently reveal attentive tracking limits of approximately three to five items. How do factors such as visual grouping and ensemble perception impact these capacity limits? Which heuristics lead to the perception of multiple objects as a group? This work investigates the role of grouping on multiple-object tracking ability, and more specifically, in identifying the heuristics that lead to the formation and perception of ensembles within dynamic contexts. First, we show that group tracking limits are approximately four groups of objects and are independent of the number of items that compose the groups. Further, we show that group tracking performance declines as inter-object spacing increases. We also demonstrate the role of group rigidity in tracking performance in that disruptions to common fate negatively impact ensemble tracking ability. The findings from this work contribute to our overall understanding of the perception of dynamic groups of objects. They characterize the properties that determine the formation and perception of dynamic object ensembles. In addition, they inform development and design decisions considering cognitive limitations involving tracking groups of objects.

Visual Multi-Metric Grouping of Eye-Tracking Data

We present an algorithmic and visual grouping of participants and eye-tracking metrics derived from recorded eye-tracking data. Our method utilizes two well-established visualization concepts. First, parallel coordinates are used to provide an overview of the used metrics, their interactions, and similarities, which helps select suitable metrics that describe characteristics of the eye-tracking data. Furthermore, parallel coordinates plots enable an analyst to test the effects of creating a combination of a subset of metrics resulting in a newly derived eye-tracking metric. Second, a similarity matrix visualization is used to visually represent the affine combination of metrics utilizing an algorithmic grouping of subjects that leads to distinct visual groups of similar behavior. To keep the diagrams of the matrix visualization simple and understandable, we visually encode our eye- tracking data into the cells of a similarity matrix of participants. The algorithmic grouping is performed with a clustering based on the affine combination of metrics, which is also the basis for the similarity value computation of the similarity matrix. To illustrate the usefulness of our visualization, we applied it to an eye-tracking data set involving the reading behavior of metro maps of up to 40 participants. Finally, we discuss limitations and scalability issues of the approach focusing on visual and perceptual issues.