Weighted integration of visual position information

Characterizing motion prediction in small autonomous swarms

The use of robotic swarms has become increasingly common in research, industrial, and military domains for tasks such as collective exploration, coordinated movement, and collective localization. Despite the expanded use of robotic swarms, little is known about how swarms are perceived by human operators. To characterize human-swarm interactions, we evaluate how operators perceive swarm characteristics, including movement patterns, control schemes, and occlusion. In a series of experiments manipulating movement patterns and control schemes, participants tracked swarms on a computer screen until they were occluded from view, at which point participants were instructed to estimate the spatiotemporal dynamics of the occluded swarm by mouse click. In addition to capturing mouse click responses, eye tracking was used to capture participants eye movements while visually tracking swarms. We observed that manipulating control schemes had minimal impact on the perception of swarms, and that swarms are easier to track when they are visible compared to when they were occluded. Regarding swarm movements, a complex pattern of data emerged. For example, eye tracking indicates that participants more closely track a swarm in an arc pattern compared to sinusoid and linear movement patterns. When evaluating behavioral click-responses, data show that time is underestimated, and that spatial accuracy is reduced in complex patterns. Results suggest that measures of performance may capture different patterns of behavior, underscoring the need for multiple measures to accurately characterize performance. In addition, the lack of generalizable data across different movement patterns highlights the complexity involved in the perception of swarms of objects.

Changes in length judgments caused by rotation of the contextual distractor

In the present study, we tested the applicability of the computational model of the illusion of interrupted spatial extent (Bulatov, Marma, & Bulatova, Attention, Perception, & Psychophysics, 82, 2714-2727, 2020) to account for the psychophysical data collected with three-dot stimuli containing a cross-shaped contextual distractor. In different series of experiments, the illusion magnitude changes caused by the rotation of distractors with different values of the internal angle (45°, 75°, and 90°) were quantitatively determined. It was shown that the data obtained for all modifications of stimuli can be rather well approximated by model functions proportional to the sum of the absolute values of cosines. A good agreement between theoretical calculations and experimental results supports the suggestion that the perceptual displacement of the stimulus terminators, which occurs due to the processes of local integration of neural activity, may be one of the main causes of the illusion investigated.

On the flexibility of strategies for center estimation

When subjects are asked to indicate the center of a spatially distributed stimulus, the features that control their responses tend to vary (1) across subjects and (2) as stimulus properties are altered. Here we ask: can subjects bring these different response tendencies under top-down control? In each of three tasks, all using briefly displayed, Gaussian dot-clouds, subjects were trained to perform different center-estimation responses. In the "mass task," the target was the centroid of the dots. In the "hull task," the target was the centroid of the region circumscribed by the convex hull of the dot-cloud. In the "hull-vertex task," the target was the centroid of the vertices of the convex hull. Subjects were able to perform each of the mass- and hull-tasks accurately and reliably. However, they found the hull-vertex task more difficult; errors were substantially larger in this task, and responses tended to be closer to both of the hull- and mass-task centers. The finding that subjects can intentionally target either the centroid of the dots in the stimulus or the centroid of the stimulus convex hull suggests that individual differences in feedback-free experiments may reflect idiosyncratic decisions by different subjects about what combination of these statistics to use in responding.

Quantitative study of asymmetry in the manifestation of the wings-in and wings-out versions of the Müller-Lyer illusion

The present study investigated whether the asymmetry in magnitude between the wings-in and wings-out versions of the Müller-Lyer illusion can be explained by the manifestation of accompanying effects of the filled-space illusion. In psychophysical experiments, the three-dot stimuli were used, and in different series, a single set of the Müller-Lyer wings was attached to the left or to right terminating dot. To check whether the summation of illusory effects occurs, experiments with two sets of the wings forming the Judd figure were performed. To evaluate the standalone manifestation of the filled-space illusion, we conducted experiments with distracting cross (two sets of coinciding and oppositely oriented wings) centered on the lateral terminator of the stimulus. To interpret the experimental data, we used computational procedures of previously developed quantitative models of hypothetical visual mechanisms underlying the emergence of the Müller-Lyer illusion and the filled-space illusion. It was demonstrated that theoretical calculations adequately account for the illusion magnitude variations for all modifications of stimuli, which convincingly supports the suggestion that the concomitant manifestation of the filled-space illusion is powerful enough to be considered as one of the main reasons for the asymmetric properties of illusions of extent of the Müller-Lyer type.

The density effect in centroid estimation is blind to contrast polarity

Human vision is highly efficient in estimating the centroids of spatially scattered items. However, the processes underlying this remarkable skill remain poorly understood. A salient fact is that in estimating the centroids of dot-clouds, observers underweight densely packed dots relative to isolated dots; thus, when an observer estimates the centroid of a dot cloud, the weight exerted on the subject's response by a given dot tends to be suppressed by other dots near it. The current experiment sought to determine whether dots of contrast polarity equal vs. opposite to a given dot differ in how they alter the weight it exerts. Six observers were tested in a task that used brief (180 ms), Gaussian clouds that mixed 9 white and 9 black dots on a gray background. On each trial, the observer strove to mouse-click the centroid of the stimulus cloud weighting all dots equally. The model used to describe the results allows the weight exerted on the subject's response by a given dot to depend on its peripherality in the stimulus cloud as well as on the density of same- and opposite-polarity dots surrounding it. For four observers, peripheral dots exerted lower influence than central dots on responses; the other two showed little effect of peripherality. For all observers, dots in high-density regions exerted less weight on responses than dots in low-density regions. Concerning the primary research question: dots of opposite vs. the same polarity as a given dot suppressed the weight it exerted with equal effectiveness. This suggests that the site of the interaction producing the density effect is a neural population that registers positive and negative contrast polarities in the same way.

Synergy between research on ensemble perception, data visualization, and statistics education: A tutorial review

In the age of big data, we are constantly inventing new data visualizations to consolidate massive amounts of numerical information into smaller and more digestible visual formats. These data visualizations use various visual features to convey quantitative information, such as spatial position in scatter plots, color saturation in heat maps, and area in dot maps. These data visualizations are typically composed of ensembles, or groups of related objects, that together convey information about a data set. Ensemble perception, or one's ability to perceive summary statistics from an ensemble, such as the mean, has been used as a foundation for understanding and explaining the effectiveness of certain data visualizations. However, research in data visualization has revealed some perceptual biases and conceptual difficulties people face when trying to utilize the information in these graphs. In this tutorial review, we will provide a broad overview of research conducted in ensemble perception, discuss how principles of ensemble encoding have been applied to the research in data visualization, and showcase the barriers graphs can pose to learning statistical concepts, using histograms as a specific example. The goal of this tutorial review is to highlight possible connections between three areas of research-ensemble perception, data visualization, and statistics education-and to encourage research in the practical applications of ensemble perception in solving real-world problems in statistics education.

Two-dimensional profile of the region of distractors' influence on visual length judgments

In the illusion of interrupted spatial extent (also known as the filled-space or Oppel-Kundt illusion), the stimulus spatial interval filled with some visual elements (distractors) appears larger than the unfilled interval of the same size. Despite a long history of research, there is still no consensus on the origin of this visual phenomenon. It was recently shown (Bulatov, Bulatova, Surkys, & Mickienė, Acta Neurobiologiae Experimentalis, 77, 157-167, 2017) that the illusion emergence can be associated mainly with the integration of distractor-evoked effects in regions surrounding the endpoints (terminators) of the stimulus intervals. In the present study, we investigated the two-dimensional weighting profiles of these regions of distractors' influence on the magnitude of length misjudgments. We performed psychophysical experiments with three-dot stimuli that contain distracting line segments, the position of which varied either along or perpendicular to the main stimulus axis, thus scanning the profile in two orthogonal directions. It was demonstrated that for distractors shifted along the stimulus axis, the magnitude of the illusion increases to a certain maximum value with the increase of distractors displacement and smoothly decreases to zero thereafter. For distractors shifted orthogonally to the stimulus axis, the illusion magnitude monotonically decreases with the increase of distractors displacement. In the case of the distractor rotation, the greatest illusion magnitude refers to orientations of the distracting line segment along the stimulus axis and decreases to the minimum value for the orthogonal orientation. Based on the analysis of established functional dependencies, we proposed a simple quantitative interpretation of the obtained experimental data.

Changes in the distribution of sustained attention alter the perceived structure of visual space

Visual spatial attention is a critical process that allows for the selection and enhanced processing of relevant objects and locations. While studies have shown attentional modulations of perceived location and the representation of distance information across multiple objects, there remains disagreement regarding what influence spatial attention has on the underlying structure of visual space. The present study utilized a method of magnitude estimation in which participants must judge the location of briefly presented targets within the boundaries of their individual visual fields in the absence of any other objects or boundaries. Spatial uncertainty of target locations was used to assess perceived locations across distributed and focused attention conditions without the use of external stimuli, such as visual cues. Across two experiments we tested locations along the cardinal and 45° oblique axes. We demonstrate that focusing attention within a region of space can expand the perceived size of visual space; even in cases where doing so makes performance less accurate. Moreover, the results of the present studies show that when fixation is actively maintained, focusing attention along a visual axis leads to an asymmetrical stretching of visual space that is predominantly focused across the central half of the visual field, consistent with an expansive gradient along the focus of voluntary attention. These results demonstrate that focusing sustained attention peripherally during active fixation leads to an asymmetrical expansion of visual space within the central visual field.

Illusion of extent evoked by closed two-dimensional shapes

In the present study, we have tested the applicability of the computational model of centroid extraction to account for the data collected in experiments with stimuli comprising of closed two-dimensional shapes. The outlined or uniformly filled pie-shaped circular sectors (contextual distractors) were arranged according to the Brentano pattern, and three different stimulus parameters (either the radius or the central angle or the tilt angle of the sectors) were used as independent variables in different series of experiments. It was demonstrated that the model calculations adequately predict the variations of illusion magnitude shown by all the subjects for all independent variables and that there is no significant difference between the data obtained for stimuli with the outlined and uniformly filled distractors. A good correspondence between the computational and experimental data provides convincing evidence in support of the "centroid" explanation of illusions of extent of the Müller-Lyer type.

Transcranial direct current stimulation over posterior parietal cortex modulates visuospatial localization

Visual localization is based on the complex interplay of bottom-up and top-down processing. Based on previous work, the posterior parietal cortex (PPC) is assumed to play an essential role in this interplay. In this study, we investigated the causal role of the PPC in visual localization. Specifically, our goal was to determine whether modulation of the PPC via transcranial direct current stimulation (tDCS) could induce visual mislocalization similar to that induced by an exogenous attentional cue (Wright, Morris, & Krekelberg, 2011). We placed one stimulation electrode over the right PPC and the other over the left PPC (dual tDCS) and varied the polarity of the stimulation. We found that this manipulation altered visual localization; this supports the causal involvement of the PPC in visual localization. Notably, mislocalization was more rightward when the cathode was placed over the right PPC than when the anode was placed over the right PPC. This mislocalization was found within a few minutes of stimulation onset, it dissipated during stimulation, but then resurfaced after stimulation offset and lasted for another 10-15 min. On the assumption that excitability is reduced beneath the cathode and increased beneath the anode, these findings support the view that each hemisphere biases processing to the contralateral hemifield and that the balance of activation between the hemispheres contributes to position perception (Kinsbourne, 1977; Szczepanski, Konen, & Kastner, 2010).