Range dependent processing of visual numerosity: similarities across vision and haptics

Humans can sense small numbers of objects in a box by touch alone

Everyday experiences suggest that a container, such as a box of chocolate sprinkles, can convey pertinent information about the nature of its content. Despite the familiarity of the experience, we do not know whether people can perceive the number of objects in the container from touch alone and how accurately they can do so. In three experiments, participants handled containers holding between one and five objects and verbally estimated their number. Containers were small cardboard jewelry boxes, and objects were round beads of varying diameter and weight. Any useful visual and auditory cues were precluded. Experiment 1 demonstrated very accurate performance, provided the objects were of sufficient weight. Experiment 2 demonstrated that withholding information about the possible number of objects inside the container does not affect accuracy at a group level but does produce occasional overestimations at an individual level. Experiment 3 demonstrated that removing the weight cue leads to systematic underestimations but does not eliminate people's ability to distinguish between different numbers of objects in the container. This study contributes to a growing picture that container haptics is surprisingly capable.

Parametric Representation of Tactile Numerosity in Working Memory

Estimated numerosity perception is processed in an approximate number system (ANS) that resembles the perception of a continuous magnitude. The ANS consists of a right lateralized frontoparietal network comprising the lateral prefrontal cortex (LPFC) and the intraparietal sulcus. Although the ANS has been extensively investigated, only a few studies have focused on the mental representation of retained numerosity estimates. Specifically, the underlying mechanisms of estimated numerosity working memory (WM) is unclear. Besides numerosities, as another form of abstract quantity, vibrotactile WM studies provide initial evidence that the right LPFC takes a central role in maintaining magnitudes. In the present fMRI multivariate pattern analysis study, we designed a delayed match-to-numerosity paradigm to test what brain regions retain approximate numerosity memoranda. In line with parametric WM results, our study found numerosity-specific WM representations in the right LPFC as well as in the supplementary motor area and the left premotor cortex extending into the superior frontal gyrus, thus bridging the gap in abstract quantity WM literature.

The role of connectedness in haptic object perception

We can efficiently detect whether there is a rough object among a set of smooth objects using our sense of touch. We can also quickly determine the number of rough objects in our hand. In this study, we investigated whether the perceptual processing of rough and smooth objects is influenced if these objects are connected. In Experiment 1, participants were asked to identify whether there were exactly two rough target spheres among smooth distractor spheres, while we recorded their response times. The spheres were connected to form pairs: rough spheres were paired together and smooth spheres were paired together ('within pairs arrangement'), or a rough and a smooth sphere were connected ('between pairs arrangement'). Participants responded faster when the spheres in a pair were identical. In Experiment 2, we found that the advantage for within pairs arrangements was not driven by feature saliency. Overall our results show that haptic information is processed faster when targets were connected together compared to when targets were connected to distractors.

The effects of training on tactile enumeration

Subitizing is a fast and accurate process of enumerating small quantities. Whether subitizing carried out in the tactile modality is under debate. We previously found a moderately increasing RT slope from one to four stimuli and a large decrease in RT for five stimuli when using one hand. Yet, a high error rate was observed, making it difficult to determine if the RT pattern found was indeed subitizing. To increase accuracy, we carried out training of the tactile enumeration task using one hand for 6 days. We compared performance in the trained and additional non-trained tasks between two groups-the 6-day training group (6DT) and the non-trained controls (C)-after three periods (1 week, 1 and 6 months after the training of the 6DT group ended). Results showed an increase in accuracy rates for both groups but a decrease in RT for the 6DT group only for the trained task. This RT improvement was present even after 6 months. Importantly, the RT slope of one-hand enumeration did not change after training, showing a moderately increased slope up to four stimuli and a decrease for five stimuli. Our study shows the training long-term effect on tactile enumeration and emphasizes the embodiment of finger counting on enumeration. Two possible enumeration processes are discussed-accelerated counting and subitizing-both based on spatial cues and pattern recognition of familiarized finger-counting patterns.

Effects of Numerosity Range on Tactile and Visual Enumeration

Our study explores tactile enumeration using both hands and investigates the effects of numerosity range's (NR) on general enumeration. In Experiment 1, using custom-made vibro-tactile apparatus, we replicated results of Cohen, Naparstek, and Henik (2014, Acta Psychologica, 150C, 26-34) and again found a moderate increase in RT up to four stimuli and then a decrease for five stimuli. In Experiment 2, we used a within participants design and compared NR 1 to 5 and 1 to 10 in tactile and visual enumeration. The results showed that enumeration for NR 5 to 1 was faster than for NR 1 to 10, especially for numerosities four and five. Within NR 1 to 10, in the visual modality the subitizing range was 4, the counting range was from 5 to 9, and there was an end effect of 10 dots. In the tactile modality, when excluding one-hand arrangements, the subitizing range was 2, the counting range was from 3 to 5, there was an acceleration of counting from 5 and on, and there was an end effect for 10 stimuli that was stronger than for 10 visual stimuli. We suggest that NR influences enumeration and that number-hand association (i.e. resulting from finger counting) influences enumeration, resulting in faster counting.

The effect of perceptual grouping on haptic numerosity perception

We used a haptic enumeration task to investigate whether enumeration can be facilitated by perceptual grouping in the haptic modality. Eight participants were asked to count tangible dots as quickly and accurately as possible, while moving their finger pad over a tactile display. In Experiment 1, we manipulated the number and organization of the dots, while keeping the total exploration area constant. The dots were either evenly distributed on a horizontal line (baseline condition) or organized into groups based on either proximity (dots placed in closer proximity to each other) or configural cues (dots placed in a geometric configuration). In Experiment 2, we varied the distance between the subsets of dots. We hypothesized that when subsets of dots can be grouped together, the enumeration time will be shorter and accuracy will be higher than in the baseline condition. The results of both experiments showed faster enumeration for the configural condition than for the baseline condition, indicating that configural grouping also facilitates haptic enumeration. In Experiment 2, faster enumeration was also observed for the proximity condition than for the baseline condition. Thus, perceptual grouping speeds up haptic enumeration by both configural and proximity cues, suggesting that similar mechanisms underlie perceptual grouping in both visual and haptic enumeration.

Tactile enumeration of small quantities using one hand

Our study explores various aspects of enumerating small quantities in the tactile modality. Fingertips of one hand were stimulated by a vibro-tactile apparatus (for 100/800 ms). Between 1 and 5 stimuli were presented to the right or the left hand and applied to neighboring (e.g., thumb-index-middle) or non-neighboring (e.g., thumb-middle-pinkie) fingers. The results showed a moderate increase in RT up to 4 stimuli and then a decrease for 5 stimuli. Right hand stimulation evoked more accurate performance than left hand stimulation only under short exposures (100 ms). Importantly, when the stimuli were presented to neighboring fingers, the accuracy rate was higher and the RT was faster than when presented to non-neighboring fingers. We discuss the results and suggest that when the stimuli are presented to one hand the subitizing range is 4 rather than 3. Furthermore, the right hand advantage and the efficiency for neighboring fingers are further support for the association between number and spatial arrangement of the fingers.

The role of pattern recognition in children's exact enumeration of small numbers

Enumeration can be accomplished by subitizing, counting, estimation, and combinations of these processes. We investigated whether the dissociation between subitizing and counting can be observed in 4- to 6-year-olds and studied whether the maximum number of elements that can be subitized changes with age. To detect a dissociation between subitizing and counting, it is tested whether task manipulations have different effects in the subitizing than in the counting range. Task manipulations concerned duration of presentation of elements (limited, unlimited) and configuration of elements (random, line, dice). In Study 1, forty-nine 4- and 5-year-olds were tested with a computerized enumeration task. Study 2 concerned data from 4-, 5-, and 6-year-olds, collected with Math Garden, a computer-adaptive application to practice math. Both task manipulations affected performance in the counting, but not the subitizing range, supporting the conclusion that children use two distinct enumeration processes in the two ranges. In all age groups, the maximum number of elements that could be subitized was three. The strong effect of configuration of elements suggests that subitizing might be based on a general ability of pattern recognition.

Subitizing Is Sensitive to the Arrangement of Objects

Subitizing is a fast and accurate enumeration process of small sets of usually less than four objects. Several models were proposed in the literature. Critically, only pattern recognition theory suggests that subitizing performance is sensitive to the arrangement of the array. In our study, arrays of dots in random or canonical arrangements were enumerated. The subitizing range was larger and the reaction time slope was less steep in the canonical arrangements. When noise was added to the canonical pattern, the reaction time slope was proportional to the amount of noise. Moreover, arrangement has a stronger effect on sets with more than four objects. These results support the pattern recognition model of subitizing.

Haptic subitizing across the fingers

Numerosity judgments of small sets of items (≤ 3) are generally fast and errorfree, while response times and error rates increase rapidly for larger numbers of items. We investigated an efficient process used for judging small numbers of items (known as subitizing) in active touch. We hypothesized that this efficient process for numerosity judgment might be related to stimulus properties that allow for efficient (parallel) search. Our results showed that subitizing was not possible forraised lines among flat surfaces, whereas this type of stimulus could be detected in parallel over the fingers. However, subitizing was possible when the number of fingers touching a surface had to be judged while the other fingers were lowered in mid-air. In the latter case, the lack of tactile input is essential, since subitizing was not enabled by differences in proprioceptive information from the fingers. Our results show that subitizing using haptic information from the fingers is possible only whensome fingers receive tactile information while other fingers do not.

The effect of feature saliency on haptic subitizing

'Subitizing' refers to fast and error-free numerosity judgment for small (<4) sets of items. For larger sets, the slower process of 'counting' is used. Counting has a serial character, whereas subitizing is believed to have a parallel character. While subitizing was initially found in vision, it has been shown to exist in touch as well. In vision, it has been demonstrated that adding distractor items to a set of target items influences numerosity judgment of the target items. Subitizing was in this case only possible if the distractor item is highly salient among the targets. In the present study, we investigated the effect of adding a distractor item on haptic judgement of a set of target items. To this end, we asked subjects to judge the number of spheres grasped in their hand. Either a cube or an ellipsoid could be added to the set. A cube among spheres has been shown to be highly salient, while an ellipsoid among spheres is not. Our results show that adding a distractor item led to an increase in the response time slopes regardless of the distractor shape. Subitizing was, however, only possible in the case of a salient distractor. This is in agreement with results from vision.