A 'dipper' function for texture discrimination based on orientation variance

Variance aftereffect within and between sensory modalities for visual and auditory domains

We can grasp various features of the outside world using summary statistics efficiently. Among these statistics, variance is an index of information homogeneity or reliability. Previous research has shown that visual variance information in the context of spatial integration is encoded directly as a unique feature, and currently perceived variance can be distorted by that of the preceding stimuli. In this study, we focused on variance perception in temporal integration. We investigated whether any variance aftereffects occurred in visual size and auditory pitch. Furthermore, to examine the mechanism of cross-modal variance perception, we also investigated whether variance aftereffects occur between different modalities. Four experimental conditions (a combination of sensory modalities of adaptor and test: visual-to-visual, visual-to-auditory, auditory-to-auditory, and auditory-to-visual) were conducted. Participants observed a sequence of visual or auditory stimuli perturbed in size or pitch with certain variance and performed a variance classification task before and after the variance adaptation phase. We found that in visual size, within modality adaptation to small or large variance, resulted in a variance aftereffect, indicating that variance judgments are biased in the direction away from that of the adapting stimulus. In auditory pitch, within modality adaptation to small variance caused variance aftereffect. For cross-modal combinations, adaptation to small variance in visual size resulted in variance aftereffect. However, the effect was weak, and variance aftereffect did not occur in other conditions. These findings indicate that the variance information of sequentially presented stimuli is encoded independently in visual and auditory domains.

Mean orientation discrimination based on proximal stimuli

Ensemble perception refers to the ability to accurately and rapidly perceive summary statistical representations of specific features from a group of similar objects. However, the specific type of representation involved in this perception within a three-dimensional (3-D) environment remains unclear. In the context of perspective viewing with stereopsis, distal stimuli can be projected onto the retina as different forms of proximal stimuli based on their distances, despite sharing similar properties, such as object size and spatial frequency. This study aimed to investigate the effects of distal and proximal stimuli on the perception of summary statistical information related to orientation. In our experiment, we presented multiple Gabor patches in a stereoscopic environment, allowing us to measure the discrimination threshold of the mean orientation. The object size and spatial frequency were fixed for all patches regardless of depth. However, the physical angular size and absolute spatial frequency covaried with the depth. The results revealed the threshold elevation with depth expansion, especially when the patches formed two clusters at near and far distances, leading to large variations in their retinotopic representations. This finding indicates a minor contribution of similarity of the distal stimuli. Subsequent experiments demonstrated that the variability in physical angular size of the patches significantly influenced the threshold elevation in contrast to that of binocular disparity and absolute spatial frequency. These findings highlight the critical role of physical angular size variability in perceiving mean orientations within the 3-D space.

What is the basis of ensemble subset selection?

The visual system can rapidly calculate the ensemble statistics of a set of objects; for example, people can easily estimate an average size of apples on a tree. To accomplish this, it is not always useful to summarize all the visual information. If there are various types of objects, the visual system should select a relevant subset: only apples, not leaves and branches. Here, we ask what kind of visual information makes a "good" ensemble that can be selectively attended to provide an accurate summary estimate. We tested three candidate representations: basic features, preattentive object files, and full-fledged bound objects. In four experiments, we presented a target and several distractors' sets of differently colored objects. We found that conditions where a target ensemble had at least one unique color (basic feature) provided ensemble averaging performance comparable to the baseline displays without distractors. When the target subset was defined as a conjunction of two colors or color-shape partly shared with distractors (so that they could be differentiated only as preattentive object files), subset averaging was also possible but less accurate than in the baseline and feature conditions. Finally, performance was very poor when the target subset was defined by an exact feature relationship, such as in the spatial conjunction of two colors (spatially bound object). Overall, these results suggest that distinguishable features and, to a lesser degree, preattentive object files can serve as the representational basis of ensemble selection, while bound objects cannot.

The Neural Dynamics of Face Ensemble and Central Face Processing

Extensive work has investigated the neural processing of single faces, including the role of shape and surface properties. However, much less is known about the neural basis of face ensemble perception (e.g., simultaneously viewing several faces in a crowd). Importantly, the contribution of shape and surface properties have not been elucidated in face ensemble processing. Furthermore, how single central faces are processed within the context of an ensemble remains unclear. Here, we probe the neural dynamics of ensemble representation using pattern analyses as applied to electrophysiology data in healthy adults (seven males, nine females). Our investigation relies on a unique set of stimuli, depicting different facial identities, which vary parametrically and independently along their shape and surface properties. These stimuli were organized into ensemble displays consisting of six surround faces arranged in a circle around one central face. Overall, our results indicate that both shape and surface properties play a significant role in face ensemble encoding, with the latter demonstrating a more pronounced contribution. Importantly, we find that the neural processing of the center face precedes that of the surround faces in an ensemble. Further, the temporal profile of center face decoding is similar to that of single faces, while those of single faces and face ensembles diverge extensively from each other. Thus, our work capitalizes on a new center-surround paradigm to elucidate the neural dynamics of ensemble processing and the information that underpins it. Critically, our results serve to bridge the study of single and ensemble face perception.

A signal-detection account of item-based and ensemble-based visual change detection: A reply to Harrison, McMaster, and Bays

Growing empirical evidence shows that ensemble information (e.g., the average feature or feature variance of a set of objects) affects visual working memory for individual items. Recently, Harrison, McMaster, and Bays (2021) used a change detection task to test whether observers explicitly rely on ensemble representations to improve their memory for individual objects. They found that sensitivity to simultaneous changes in all memorized items (which also globally changed set summary statistics) rarely exceeded a level predicted by the so-called optimal summation model within the signal-detection framework. This model implies simple integration of evidence for change from all individual items and no additional evidence coming from ensemble. Here, we argue that performance at the level of optimal summation does not rule out the use of ensemble information. First, in two experiments, we show that, even if evidence from only one item is available at test, the statistics of the whole memory set affect performance. Second, we argue that optimal summation itself can be conceptually interpreted as one of the strategies of holistic, ensemble-based decision. We also redefine the reference level for the item-based strategy as the so-called "minimum rule," which predicts performance far below the optimum. We found that that both our and Harrison et al. (2021)'s observers consistently outperformed this level. We conclude that observers can rely on ensemble information when performing visual change detection. Overall, our work clarifies and refines the use of signal-detection analysis in measuring and modeling working memory.

Subcortical encoding of summary statistics in humans

Statistical encoding compresses redundant information from multiple items into a single summary metric (e.g., mean). Such statistical representation has been suggested to be automatic, but at which stage it is extracted is unknown. Here, we examined the involvement of the subcortex in the processing of summary statistics. We presented an array of circles dichoptically or monocularly while matching the number of perceived circles after binocular fusion. Experiments 1 and 2 showed that interocularly suppressed, invisible circles were automatically involved in the summary statistical representation, but only when they were presented to the same eye as the visible circles. This same-eye effect was further observed for consciously processed circles in Experiment 3, in which the estimated mean size of the circles was biased toward the information transmitted by monocular channels. Together, we provide converging evidence that the processing of summary statistics, an assumed high-level cognitive process, is mediated by subcortical structures.

Variability of dot spread is overestimated

Previous research has demonstrated that individuals exhibit a tendency to overestimate the variability of both low-level features (e.g., color, orientation) and mid-level features (e.g., size) when items are presented dynamically in a sequential order, a finding we will refer to as the variability overestimation effect. Because previous research on this bias used sequential displays, an open question is whether the effect is due to a memory-related bias or a vision-related bias. To assess whether the bias would also be apparent with static, simultaneous displays, and to examine whether the bias generalizes to spatial properties, we tested participants' perception of the variability of a cluster of dots. Results showed a consistent overestimation bias: Participants judged the dots as being more spread than they actually were. The variability overestimation effect was observed when there were 10 or 20 dots but not when there were 50 dots. Taken together, the results of the current study contribute to the ensemble perception literature by providing evidence that simultaneously presented stimuli are also susceptible to the variability overestimation effect. The use of static displays further demonstrates that this bias is present in both dynamic and static contexts, suggesting an inherent bias existent in the human visual system. A potential theoretical account-boundary effect-is discussed as a potential underlying mechanism. Moreover, the present study has implications for common visual tasks carried out in real-world scenarios, such as a radiologist making judgments about distribution of calcification in breast cancer diagnoses.

Visual bias could impede diagnostic accuracy of breast cancer calcifications

Purpose: Diagnosing breast cancer based on the distribution of calcifications is a visual task and thus prone to visual biases. We tested whether a recently discovered visual bias that has implications for breast cancer diagnosis would be present in expert radiologists, thereby validating the concern of this bias for accurate diagnoses. Approach: We ran a vision experiment with expert radiologists and untrained observers to test the presence of visual bias when judging the spread of dots that resembled calcifications and when judging the spread of line orientations. We calculated visual bias scores for both groups for both tasks. Results: Participants overestimated the spread of the dots and the spread of the line orientations. This bias, referred to as the variability overestimation effect, was of similar magnitudes in both expert radiologists and untrained observers. Even though the radiologists were better at both tasks, they were similarly biased compared with the untrained observers. Conclusions: The results justify the concern of the variability overestimation effect for accurate diagnoses based on breast calcifications. Specifically, the bias is likely to lead to an increased number of false-negative results, thereby leading to delayed treatments.

Extracting Summary Statistics of Rapid Numerical Sequences

We examine the ability of observers to extract summary statistics (such as the mean and the relative-variance) from rapid numerical sequences of two digit numbers presented at a rate of 4/s. In four experiments (total N = 100), we find that the participants show a remarkable ability to extract such summary statistics and that their precision in the estimation of the sequence-mean improves with the sequence-length (subject to individual differences). Using model selection for individual participants we find that, when only the sequence-average is estimated, most participants rely on a holistic process of frequency based estimation with a minority who rely on a (rule-based and capacity limited) mid-range strategy. When both the sequence-average and the relative variance are estimated, about half of the participants rely on these two strategies. Importantly, the holistic strategy appears more efficient in terms of its precision. We discuss implications for the domains of two pathways numerical processing and decision-making.

Multivariate summary of a complex scene

The current study investigated how people summarize and represent objects with multiple features to cope with the complexity due to the number of objects and feature dimensions. We presented a set of circles whose color and size were either correlated perfectly (r = 1) or not correlated at all (r = 0). Using a membership identification task, we found that participants formed a statistical representation that included information about conjunctions as well as each color and size dimensions. In addition, we found that participants represented different set boundaries depending on the correlation between features of a set. Lastly, a pair-matching task revealed that participants predicted one feature value from the other feature value based on the correlation between features of a set. Our findings suggest that people represent a multi-feature ensemble statistically as a multivariate feature distribution, which is an efficient strategy to cope with scene complexity.

Contribution of a common ability in average and variability judgments

People can make judgments about statistical properties of visual features within groups of objects, such as the average size, size variability, or numerosity of circles. Emerging from recent work is the view that these kinds of visual estimations, collectively dubbed ensemble perception, rely on independent abilities that are specific to the statistical property being estimated (mean, variance, range, numerosity). Here we revisit evidence for the claim that different statistical judgments (i.e., average and variability) for the same object feature are based on independent abilities. We tested a large sample of people, using a pre-registered open-ended sequential design to avoid ending up with weak evidence. We estimated the shared variance in ability across different ensemble judgments, with common constraints for the different tasks. We found that the abilities to judge the average size and the size variability for an array of circles are positively correlated, even after controlling for the ability to discriminate the size of single circles. Our results refute the idea that judgments of average and variability for the same object feature rely on completely independent abilities.

Dual strategies in human confidence judgments

Although confidence is commonly believed to be an essential element in decision-making, it remains unclear what gives rise to one's sense of confidence. Recent Bayesian theories propose that confidence is computed, in part, from the degree of uncertainty in sensory evidence. Alternatively, observers can use physical properties of the stimulus as a heuristic to confidence. In the current study, we developed ideal observer models for either hypothesis and compared their predictions against human data obtained from psychophysical experiments. Participants reported the orientation of a stimulus, and their confidence in this estimate, under varying levels of internal and external noise. As predicted by the Bayesian model, we found a consistent link between confidence and behavioral variability for a given stimulus orientation. Confidence was higher when orientation estimates were more precise, for both internal and external sources of noise. However, we observed the inverse pattern when comparing between stimulus orientations: although observers gave more precise orientation estimates for cardinal orientations (a phenomenon known as the oblique effect), they were more confident about oblique orientations. We show that these results are well explained by a strategy to confidence that is based on the perceived amount of noise in the stimulus. Altogether, our results suggest that confidence is not always computed from the degree of uncertainty in one's perceptual evidence but can instead be based on visual cues that function as simple Heuristics to confidence.

An explicit investigation of the roles that feature distributions play in rapid visual categorization

Ensemble representations are often described as efficient tools when summarizing features of multiple similar objects as a group. However, it can sometimes be more useful not to compute a single summary description for all of the objects if they are substantially different, for example when they belong to entirely different categories. It was proposed that the visual system can efficiently use the distributional information of ensembles to decide whether simultaneously displayed items belong to single or several different categories. Here we directly tested how the feature distribution of items in a visual array affects an ability to discriminate individual items (Experiment 1) and sets (Experiments 2-3) when participants were instructed explicitly to categorize individual objects based on the median of size distribution. We varied the width (narrow or fat) as well as the shape (smooth or two-peaked) of distributions in order to manipulate the ease of ensemble extraction from the items. We found that observers unintentionally relied on the grand mean as a natural categorical boundary and that their categorization accuracy increased as a function of the size differences among individual items and a function of their separation from the grand mean. For ensembles drawn from two-peaked size distributions, participants showed better categorization performance. They were more accurate at judging within-category ensemble properties in other dimensions (centroid and orientation) and less biased by superset statistics. This finding corroborates the idea that the two-peaked feature distributions support the "segmentability" of spatially intermixed sets of objects. Our results emphasize important roles of ensemble statistics (mean, range, distribution shape) in explicit visual categorization.

Perceiving ensemble statistics of novel image sets

Perception, representation, and memory of ensemble statistics has attracted growing interest. Studies found that, at different abstraction levels, the brain represents similar items as unified percepts. We found that global ensemble perception is automatic and unconscious, affecting later perceptual judgments regarding individual member items. Implicit effects of set mean and range for low-level feature ensembles (size, orientation, brightness) were replicated for high-level category objects. This similarity suggests that analogous mechanisms underlie these extreme levels of abstraction. Here, we bridge the span between visual features and semantic object categories using the identical implicit perception experimental paradigm for intermediate novel visual-shape categories, constructing ensemble exemplars by introducing systematic variations of a central category base or ancestor. In five experiments, with different item variability, we test automatic representation of ensemble category characteristics and its effect on a subsequent memory task. Results show that observer representation of ensembles includes the group's central shape, category ancestor (progenitor), or group mean. Observers also easily reject memory of shapes belonging to different categories, i.e. originating from different ancestors. We conclude that complex categories, like simple visual form ensembles, are represented in terms of statistics including a central object, as well as category boundaries. We refer to the model proposed by Benna and Fusi (bioRxiv 624239, 2019) that memory representation is compressed when related elements are represented by identifying their ancestor and each one's difference from it. We suggest that ensemble mean perception, like category prototype extraction, might reflect employment at different representation levels of an essential, general representation mechanism.

Variability leads to overestimation of mean summaries

Research on ensemble perception has shown that people can extract both mean and variance information, but much less is understand how these two different types of summaries interact with one another. Some research has argued that people are more erroneous in extracting the mean of displays that have greater variability. In all three experiments, we manipulated the variability in the displays. Participants reported the mean size of a set of circles (Experiment 1) and mean length of horizontally placed (Experiment 2a) and randomly oriented lines (Experiment 2b). In all experiments, we found that mean size estimations were more erroneous for higher than smaller variance displays. More critically, there was a tendency to overestimate the mean, driven by variance in both task-relevant and task-irrelevant features. We discuss these findings in relation to limitations in concurrent summarization ability and outlier discounting in ensemble perception.

Contributions of ensemble perception to outlier representation precision

It is known that the visual system can efficiently extract mean and variance information, facilitating the detection of outliers. However, no research to date has directly investigated whether ensemble perception mechanisms contribute to outlier representation precision. We specifically were interested in how the distinctiveness of outliers impacts their precision. Across two experiments, we compared how accurately viewers represented the orientation of spatial outliers that varied in distinctiveness and found that increased outlier distinctiveness resulted in greater precision. Based on comparisons of our data to simulations reflecting particular selective strategies, we eliminated the possibility that participants were selectively processing the outlier, at the expense of the ensemble. Thus, we argued that participants separately represented distinct outliers along with ensemble summaries of the remaining items in a display. We also found that outlier distinctiveness moderated the precision of how the remaining items were summarized. We discuss these findings in relation to computational capacity and constraints of ensemble perception mechanisms.

Perceived variability reflects the reliability of individual items

When confronted with many visual items, people can compute their variability accurately and rapidly, which facilitates efficient information processing and optimal decision making. However, how the visual system computes variability is still unclear. To investigate this, we implemented situations whereby estimates of variability based on several possible variability measures (e.g., range, standard deviation, and weighted standard deviation) could be differentiated, and then examined which best accounted for human variability perception. In three psychophysical experiments, participants watched two arrays of items with various orientations and judged which had more variable orientations. Results showed that perceived variability was most consistent with the weighted standard deviation based on the reliability of individual items. Specifically, participants gave less consideration to deviant orientations that were likely to be outliers, and greater consideration to salient orientations that were likely to be encoded precisely. This reliability-based weighted standard deviation suggests an efficient and flexible way of representing visual variability.

Differential neurodynamics and connectivity in the dorsal and ventral visual pathways during perception of emotional crowds and individuals: a MEG study

Reading the prevailing emotion of groups of people ("crowd emotion") is critical to understanding their overall intention and disposition. It alerts us to potential dangers, such as angry mobs or panicked crowds, giving us time to escape. A critical aspect of processing crowd emotion is that it must occur rapidly, because delays often are costly. Although knowing the timing of neural events is crucial for understanding how the brain guides behaviors using coherent signals from a glimpse of multiple faces, this information is currently lacking in the literature on face ensemble coding. Therefore, we used magnetoencephalography to examine the neurodynamics in the dorsal and ventral visual streams and the periamygdaloid cortex to compare perception of groups of faces versus individual faces. Forty-six participants compared two groups of four faces or two individual faces with varying emotional expressions and chose which group or individual they would avoid. We found that the dorsal stream was activated as early as 68 msec after the onset of stimuli containing groups of faces. In contrast, the ventral stream was activated later and predominantly for individual face stimuli. The latencies of the dorsal stream activation peaks correlated with participants' response times for facial crowds. We also found enhanced connectivity earlier between the periamygdaloid cortex and the dorsal stream regions for crowd emotion perception. Our findings suggest that ensemble coding of facial crowds proceeds rapidly and in parallel by engaging the dorsal stream to mediate adaptive social behaviors, via a distinct route from single face perception.

Size-distance rescaling in the ensemble representation of range: Study with binocular and monocular cues

According to numerous studies observers can rapidly and precisely evaluate mean or range of the set. Recent studies have shown that the mean size estimated based on sizes of objects rescaled to their distances (Tiurina & Utochkin, 2019). In the current study, we directly tested this rescaling mechanism on the perception of range using binocular and monocular cues. In Experiment 1, a sample set of circles with different angular sizes and in different apparent distances were stereoscopically presented. Participants had to adjust the range of the test set to match the range of the sample set. The main manipulation was the size-distance correlation for sample and test sets: in negative size-distance correlation, the apparent range had to decrease, while in positive correlation - increase. We found the highest underestimation in the condition with the negative sample correlation and positive test correlation, which could be explained only if ensemble summary statistics were estimated after the item's rescaling. In Experiment 2, we used Ponzo-like illusion and spatial positions as a depth cue. Sets were presented with positive, negative or without size-distance correlation on a grey background or the background with Ponzo-like illusion. We found that the range was underestimated in negative correlation and overestimated in positive correlation. Thus, items of ensemble could be automatically rescaled according to their distance, based on both binocular and monocular cues, and ensemble summary statistics estimation is based on perceived sizes.

Global and local interference effects in ensemble encoding are best explained by interactions between summary representations of the mean and the range

Through ensemble encoding, the visual system compresses redundant statistical properties from multiple items into a single summary metric (e.g., average size). Numerous studies have shown that global summary information is extracted quickly, does not require access to single-item representations, and often interferes with reports of single items from the set. Yet a thorough understanding of ensemble processing would benefit from a more extensive investigation at the local level. Thus, the purpose of this study was to provide a more critical inspection of global-local processing in ensemble perception. Taking inspiration from Navon (Cognitive Psychology, 9(3), 353-383, 1977), we employed a novel paradigm that independently manipulates the degree of interference at the global (mean) or local (single item) level of the ensemble. Initial results were consistent with reciprocal interference between global and local ensemble processing. However, further testing revealed that local interference effects were better explained by interference from another summary statistic, the range of the set. Furthermore, participants were unable to disambiguate single items from the ensemble display from other items that were within the ensemble range but, critically, were not actually present in the ensemble. Thus, it appears that local item values are likely inferred based on their relationship to higher-order summary statistics such as the range and the mean. These results conflict with claims that local information is captured alongside global information in summary representations. In such studies, successful identification of set members was not compared with misidentification of items within the range, but which were nevertheless not presented within the set.

Spatially intermixed objects of different categories are parsed automatically

Our visual system is able to separate spatially intermixed objects into different categorical groups (e.g., berries and leaves) using the shape of feature distribution: Determining whether all objects belong to one or several categories depends on whether the distribution has one or several peaks. Despite the apparent ease of rapid categorization, it is a very computationally demanding task, given severely limited "bottlenecks" of attention and working memory capable of processing only a few objects at a time. Here, we tested whether this rapid categorical parsing is automatic or requires attention. We used the visual mismatch negativity (vMMN) ERP component known as a marker of automatic sensory discrimination. 20 volunteers (16 female, mean age-22.7) participated in our study. Loading participants' attention with a central task, we observed a substantial vMMN response to unattended background changes of categories defined by certain length-orientation conjunctions. Importantly, this occurred in conditions where the distributions of these features had several peaks and, hence, supported categorical separation. These results suggest that spatially intermixed objects are parsed into distinct categories automatically and give new insight into how the visual system can bypass the severe processing restrictions and form rich perceptual experience.

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.

Feature-specificity in visual statistical summary processing

Visual statistical summary processing enables people to extract the average feature of a set of items rapidly and accurately. Previous studies have demonstrated independent mechanisms for summarizing low (e.g. color, orientation) and high-level (facial identity, emotion) visual information. However, no study to date has conclusively determined whether there are feature-specific summarization mechanisms for low-level features or whether there are low-level, feature agnostic summarization mechanisms. To address this issue, we asked participants to report either the average orientation or the average size from a set of lines where both features varied. Participants completed these tasks either in single-task or mixed-task conditions; in the latter, successful performance required extraction of both summaries concurrently. If there were feature-specific summarization mechanisms that could operate in parallel, then errors in mean size and mean orientation tasks should be independent, in both single and mixed task conditions. On the other hand, a central domain-general mechanism for low-level summarization would imply a correlation between errors for both features and greater error in the mixed than single task trials. In Experiment 1, we found that there was no correlation between the mean size and mean orientation errors and performance was similar across single and mixed-task conditions, suggesting that there may be independent summarization mechanisms for size and orientation features. To further test the feature-specificity account, in Experiment 2 and 3 (with mask), we manipulated the display duration to determine whether there were any differences in the summarization of earlier (orientation) vs. later (size) features. While these experiments replicated the pattern of results observed in Experiment 1, at shorter display durations, no differences emerged across features. We argue that our data is consistent with independent, multi-level feature-specific statistical summary mechanisms for low-level visual features.

Quality of average representation can be enhanced by refined individual items

Ensemble perception is efficient because it summarizes redundant and complex information. However, it loses the fine details of individual items during the averaging process. Such characteristics of ensemble perception are similar to those of coarse processing. Here, we tested whether extracting an average of a set was similar to coarse processing. To manipulate coarse processing, we used the fast flicker adaptation known as suppressing coarse information processed by the magnocellular pathway. We hypothesized that if computing the average of a set relied on coarse processing, the precision of an averaging task should decrease after adaptation compared to baseline (no-adaptation). Across experiments with various features (orientation in Experiment 1, size in Experiment 2, and facial expression in Experiment 3), we found that suppressing coarse information did not disrupt the performance of the averaging tasks. Rather, adaptation increased the precision of mean representation. The precision of mean representation might have increased because fine information was relatively enhanced after adaptation. Our results suggest that the quality of ensemble representation relies on that of individual items.

Integration of contours defined by second-order contrast-modulation of texture

Boundaries in the visual world can be defined by changes in luminance and texture in the input image. A "contour integration" process joins together local changes into percepts of lines or edges. A previous study tested the integration of contours defined by second-order contrast-modulation. Their contours were placed in a background of random wavelets. Participants performed near chance. We re-visited second-order contour integration with a different task. Participants distinguished contours with "good continuation" from distractors. We measured thresholds in different amounts of external orientation or position noise. This gave two noise-masking functions. We also measured thresholds for contours with a baseline curvature to assess performance with more curvy targets. Our participants were able to discriminate the good continuation of second-order contours. Thresholds were higher than for first-order contours. In our modelling, we found this was due to multiple factors. There was a doubling of equivalent internal noise between first- and second-order contour integration. There was also a reduction in efficiency. The efficiency difference was only significant in our orientation noise condition. For both first- and second-order stimuli, participants were also able to perform our task with more curved contours. We conclude that humans can integrate second-order contours, even when they are curved. There is however reduced performance compared to first-order contours. We find both an impaired input to the integrating mechanism, and reduced efficiency seem responsible. Second-order contour integration may be more affected by the noise background used in the previous study. Difficulty segregating that background may explain their result.

Perceptual learning of ensemble and outlier perception

Previous studies have demonstrated a complex relationship between ensemble perception and outlier detection. We presented two array of heterogeneously oriented stimulus bars and different mean orientations and/or a bar with an outlier orientation, asking participants to discriminate the mean orientations or detect the outlier. Perceptual learning was found in every case, with improved performance accuracy and speeded responses. Testing for improved accuracy through cross-task transfer, we found considerable transfer from training outlier detection to mean discrimination performance, and none in the opposite direction. Implicit learning in terms of increased accuracy was not found in either direction when participants performed one task, and the second task's stimulus features were present. Reaction time improvement was found to transfer in all cases. This study adds to the already broad knowledge concerning perceptual learning and cross-task transfer of training effects.

Roles of saliency and set size in ensemble averaging

Ensemble statistics are often thought of as a reliable impression of numerous items despite limited capacities to consciously represent each individual. However, whether all items equally contribute to ensemble summaries (e.g., mean) and whether they might be affected by known limited-capacity processes, such as focused attention, is still debated. We addressed these questions via a recently described "amplification effect," a systematic bias of perceived mean (e.g., average size) towards the more salient "tail" of a feature distribution (e.g., larger items). In our experiments, observers adjusted the mean orientation of sets of items varying in set size. We made some of the items more salient or less salient by changing their size. While the whole orientation distribution was fixed, the more salient subset could be shifted relative to the set mean or differ in range. We measured the bias away from the set mean and the standard deviation (SD) of errors, as it is known to reflect the physical range from which ensemble information is sampled. We found that bias and SD changes followed the shifts and range changes in salient subsets, providing evidence for amplification. However, these changes were weaker than those expected from sampling only salient items, suggesting that less salient items were also sampled. Importantly, the SD decreased as a function of set size, which is only possible if the number of sampled elements increased with set size. Overall, we conclude that orientation summary statistics are sampled from an entire ensemble and modulated by the amplification effect of attention.

Emotional judgments of scenes are influenced by unintentional averaging

Background

The visual system uses ensemble perception to summarize visual input across a variety of domains. This heuristic operates at multiple levels of vision, compressing information as basic as oriented lines or as complex as emotional faces. Given its pervasiveness, the ensemble unsurprisingly can influence how an individual item is perceived, and vice versa.

Methods

In the current experiments, we tested whether the perceived emotional valence of a single scene could be influenced by surrounding, simultaneously presented scenes. Observers first rated the emotional valence of a series of individual scenes. They then saw ensembles of the original images, presented in sets of four, and were cued to rate, for a second time, one of four.

Results

Results confirmed that the perceived emotional valence of the cued image was pulled toward the mean emotion of the surrounding ensemble on the majority of trials, even though the ensemble was task-irrelevant. Control experiments and analyses confirmed that the pull was driven by high-level, ensemble information.

Conclusion

We conclude that high-level ensemble information can influence how we perceive individual items in a crowd, even when working memory demands are low and the ensemble information is not directly task-relevant.

Negative afterimages facilitate the detection of real images

Negative, or complementary afterimages are experienced following brief adaptation to chromatic or achromatic stimuli, and are believed to be formed in the post-receptoral layers of the retinae. Afterimages can be cancelled by the addition of real images, suggesting that afterimages and real images are processed by similar mechanisms. However given their retinal origin, afterimage signals represented at the cortical level might have different spatio-temporal properties from their real images counterparts. To test this we determined whether afterimages reduce the contrast threshold of added real images, i.e. produce the classic "dipper" function characteristic of contrast discrimination, a behavior believed to be cortically mediated. Stimuli were chromatic and achromatic disks on a grey background. Observers adapted for 1.0 s to two side-by-side disks of a particular color. Following stimulus offset, a test disk added to one side was ramped downwards for 1.5 s to approximately match the temporal characteristic of the afterimage, and the observer was required to indicate the side containing the test disk. The test hue/brightness was either the same as that of the afterimage or a different hue/brightness. The independent variable was the contrast of the adaptor. A dipper followed by masking was observed in most conditions in which the afterimage and test colors had the same hue or brightness. We conclude that afterimages are represented similarly to their real image counterparts at the cortical level.

Nonlinear transduction of emotional facial expression

To create neural representations of external stimuli, the brain performs a number of processing steps that transform its inputs. For fundamental attributes, such as stimulus contrast, this involves one or more nonlinearities that are believed to optimise the neural code to represent features of the natural environment. Here we ask if the same is also true of more complex stimulus dimensions, such as emotional facial expression. We report the results of three experiments combining morphed facial stimuli with electrophysiological and psychophysical methods to measure the function mapping emotional expression intensity to internal response. The results converge on a nonlinearity that accelerates over weak expressions, and then becomes shallower for stronger expressions, similar to the situation for lower level stimulus properties. We further demonstrate that the nonlinearity is not attributable to the morphing procedure used in stimulus generation.

Independent and parallel visual processing of ensemble statistics: Evidence from dual tasks

The visual system can represent multiple objects in a compressed form of ensemble summary statistics (such as object numerosity, mean, and feature variance/range). Yet the relationships between the different types of visual statistics remain relatively unclear. Here, we tested whether two summaries (mean and numerosity, or mean and range) are calculated independently from each other and in parallel. Our participants performed dual tasks requiring a report about two summaries in each trial, and single tasks requiring a report about one of the summaries. We estimated trial-by-trial correlations between the precision of reports as well as correlations across observers. Both analyses showed the absence of correlations between different types of ensemble statistics, suggesting their independence. We also found no decrement (except that related to the order of report explained by memory retrieval) in performance in dual compared to single tasks, which suggests that two statistics of one ensemble can be processed in parallel.

Adaptation to mean and variance: Interrelationships between mean and variance representations in orientation perception

When there are many visual items, the visual system could represent their summary statistics (e.g., mean, variance) to process them efficiently. Although many previous studies have investigated the mean or variance representation itself, a relationship between these two ensemble representations has not been investigated much. In this study, we tested the potential interaction between mean and variance representations by using a visual adaptation method. We reasoned that if mean and variance representations interact with each other, an adaptation aftereffect to either mean or variance would influence the perception of the other. Participants watched a sequence of orientation arrays containing a specific statistical property during the adaptation period. To produce an adaptation aftereffect specific to variance or mean, one property of the adaptor arrays (variance or mean) had a fixed value while the other property was randomly varied. After the adaptation, participants were asked to discriminate the property of the test array that was randomly varied during the adaptation. We found that the adaptation aftereffect of orientation variance influenced the sensitivity of mean orientation discrimination (Experiment 1), and that the adaptation aftereffect of mean orientation influenced the bias of orientation variance discrimination (Experiment 2). These results suggest that mean and variance representations do closely interact with each other. Considering that mean and variance reflect the representative value and dispersion of multiple items respectively, the interactions between mean and variance representations may reflect their complementary roles to summarize complex visual information effectively.

Distinguishing target biases and strategic guesses in visual working memory

Previous studies have shown that when there are statistical regularities in the items stored in visual working memory, the responses are biased toward the ensemble average. This statistical-regularity-induced bias could happen in two ways: (1) a target bias, where the individual memory representations are pulled toward the ensemble average; or (2) a strategic guess, for items that are not memorized, other information in the ensemble (e.g., another item) is reported as a substitute. Here, these two mechanisms are distinguished on the basis of a three-part model (target responses + swap responses + random guesses; e.g., Bays, Catalao, & Husain, 2009, Journal of Vision, 9, 7). The strategic guess is operationalized as swap responses, whereas the target bias is reflected by a bias parameter in the target responses. This model was applied on 8 data sets (22 observers each). In this model, contributions of target biases and strategic guesses can be clearly distinguished from each other because they lead to distinctive patterns in the distribution of responses. In the present results, strategic guesses always contributed substantially to the statistical-regularity-induced biases, whereas target biases were limited to specific conditions. All in all, the Bayesian inference in visual working memory is much more limited than what is previously advocated.

Relating categorization to set summary statistics perception

Two cognitive processes have been explored that compensate for the limited information that can be perceived and remembered at any given moment. The first parsimonious cognitive process is object categorization. We naturally relate objects to their category, assume they share relevant category properties, often disregarding irrelevant characteristics. Another scene organizing mechanism is representing aspects of the visual world in terms of summary statistics. Spreading attention over a group of objects with some similarity, one perceives an ensemble representation of the group. Without encoding detailed information of individuals, observers process summary data concerning the group, including set mean for various features (from circle size to face expression). Just as categorization may include/depend on prototype and intercategory boundaries, so set perception includes property mean and range. We now explore common features of these processes. We previously investigated summary perception of low-level features with a rapid serial visual presentation (RSVP) paradigm and found that participants perceive both the mean and range extremes of stimulus sets, automatically, implicitly, and on-the-fly, for each RSVP sequence, independently. We now use the same experimental paradigm to test category representation of high-level objects. We find participants perceive categorical characteristics better than they code individual elements. We relate category prototype to set mean and same/different category to in/out-of-range elements, defining a direct parallel between low-level set perception and high-level categorization. The implicit effects of mean or prototype and set or category boundaries are very similar. We suggest that object categorization may share perceptual-computational mechanisms with set summary statistics perception.

Perceiving set mean and range: Automaticity and precision

To compensate for the limited visual information that can be perceived and remembered at any given moment, many aspects of the visual world are represented as summary statistics. We acquire ensemble representations of element groups as a whole, spreading attention over objects, for which we encode no detailed information. Previous studies found that different features of items (from size/orientation to facial expression/biological motion) are summarized to their mean, over space or time. Summarizing is economical, saving time and energy when the environment is too rich and complex to encode each stimulus separately. We investigated set perception using rapid serial visual presentation sequences. Following each sequence, participants viewed two stimuli, member and nonmember, indicating the member. Sometimes, unbeknownst to participants, one stimulus was the set mean, and or the nonmember was outside the set range. Participants preferentially chose stimuli at/near the mean, a "mean effect," and more easily rejected out-of-range stimuli, a "range effect." Performance improved with member proximity to the mean and nonmember distance from set mean and edge, though they were instructed only to remember presented stimuli. We conclude that participants automatically encode both mean and range boundaries of stimulus sets, avoiding capacity limits and speeding perceptual decisions.

Coding of low-level position and orientation information in human naturalistic vision

Orientation and position of small image segments are considered to be two fundamental low-level attributes in early visual processing, yet their encoding in complex natural stimuli is underexplored. By measuring the just-noticeable differences in noise perturbation, we investigated how orientation and position information of a large number of local elements (Gabors) were encoded separately or jointly. Importantly, the Gabors composed various classes of naturalistic stimuli that were equated by all low-level attributes and differed only in their higher-order configural complexity and familiarity. Although unable to consciously tell apart the type of perturbation, observers detected orientation and position noise significantly differently. Furthermore, when the Gabors were perturbed by both types of noise simultaneously, performance adhered to a reliability-based optimal probabilistic combination of individual attribute noises. Our results suggest that orientation and position are independently coded and probabilistically combined for naturalistic stimuli at the earliest stage of visual processing.

Effects of the Simultaneous Presentation of Corresponding Auditory and Visual Stimuli on Size Variance Perception

To overcome limitations in perceptual bandwidth, humans condense various features of the environment into summary statistics. Variance constitutes indices that represent diversity within categories and also the reliability of the information regarding that diversity. Studies have shown that humans can efficiently perceive variance for visual stimuli; however, to enhance perception of environments, information about the external world can be obtained from multisensory modalities and integrated. Consequently, this study investigates, through two experiments, whether the precision of variance perception improves when visual information (size) and corresponding auditory information (pitch) are integrated. In Experiment 1, we measured the correspondence between visual size and auditory pitch for each participant by using adjustment measurements. The results showed a linear relationship between size and pitch-that is, the higher the pitch, the smaller the corresponding circle. In Experiment 2, sequences of visual stimuli were presented both with and without linked auditory tones, and the precision of perceived variance in size was measured. We consequently found that synchronized presentation of audio and visual stimuli that have the same variance improves the precision of perceived variance in size when compared with visual-only presentation. This suggests that audiovisual information may be automatically integrated in variance perception.

Ensemble statistics accessed through proxies: Range heuristic and dependence on low-level properties in variability discrimination

People can quickly and accurately compute not only the mean size of a set of items but also the size variability of the items. However, it remains unknown how these statistics are estimated. Here we show that neither parallel access to all items nor random subsampling of just a few items is sufficient to explain participants' estimations of size variability. In three experiments, we had participants compare two arrays of circles with different variability in their sizes. In the first two experiments, we manipulated the congruency of the range and variance of the arrays. The arrays with congruent range and variability information were judged more accurately, indicating the use of range as a proxy for variability. Experiments 2B and 3 showed that people also are not invariant to low- or mid-level visual information in the arrays, as comparing arrays with different low-level characteristics (filled vs. outlined circles) led to systematic biases. Together, these experiments indicate that range and low- or mid-level properties are both utilized as proxies for variability discrimination, and people are flexible in adopting these strategies. These strategies are at odds with the claim of parallel extraction of ensemble statistics per se and random subsampling strategies previously proposed in the literature.

Serial dependence in the perception of visual variance

The recent history of perceptual experience has been shown to influence subsequent perception. Classically, this dependence on perceptual history has been examined in sensory-adaptation paradigms, wherein prolonged exposure to a particular stimulus (e.g., a vertically oriented grating) produces changes in perception of subsequently presented stimuli (e.g., the tilt aftereffect). More recently, several studies have investigated the influence of shorter perceptual exposure with effects, referred to as serial dependence, being described for a variety of low- and high-level perceptual dimensions. In this study, we examined serial dependence in the processing of dispersion statistics, namely variance-a key descriptor of the environment and indicative of the precision and reliability of ensemble representations. We found two opposite serial dependences operating at different timescales, and likely originating at different processing levels: A positive, Bayesian-like bias was driven by the most recent exposures, dependent on feature-specific decision making and appearing only when high confidence was placed in that decision; and a longer lasting negative bias-akin to an adaptation aftereffect-becoming manifest as the positive bias declined. Both effects were independent of spatial presentation location and the similarity of other close traits, such as mean direction of the visual variance stimulus. These findings suggest that visual variance processing occurs in high-level areas but is also subject to a combination of multilevel mechanisms balancing perceptual stability and sensitivity, as with many different perceptual dimensions.

Serial dependence in the perception of visual variance

The recent history of perceptual experience has been shown to influence subsequent perception. Classically, this dependence on perceptual history has been examined in sensory-adaptation paradigms, wherein prolonged exposure to a particular stimulus (e.g., a vertically oriented grating) produces changes in perception of subsequently presented stimuli (e.g., the tilt aftereffect). More recently, several studies have investigated the influence of shorter perceptual exposure with effects, referred to as serial dependence, being described for a variety of low- and high-level perceptual dimensions. In this study, we examined serial dependence in the processing of dispersion statistics, namely variance-a key descriptor of the environment and indicative of the precision and reliability of ensemble representations. We found two opposite serial dependences operating at different timescales, and likely originating at different processing levels: A positive, Bayesian-like bias was driven by the most recent exposures, dependent on feature-specific decision making and appearing only when high confidence was placed in that decision; and a longer lasting negative bias-akin to an adaptation aftereffect-becoming manifest as the positive bias declined. Both effects were independent of spatial presentation location and the similarity of other close traits, such as mean direction of the visual variance stimulus. These findings suggest that visual variance processing occurs in high-level areas but is also subject to a combination of multilevel mechanisms balancing perceptual stability and sensitivity, as with many different perceptual dimensions.

The development of perceptual averaging: learning what to do, not just how to do it

The mature visual system condenses complex scenes into simple summary statistics (e.g., average size, location, orientation, etc.). However, children, often perform poorly on perceptual averaging tasks. Children's difficulties are typically thought to represent the suboptimal implementation of an adult-like strategy. This paper examines another possibility: that children actually make decisions in a qualitatively different way to adults (optimal implementation of a non-ideal strategy). Ninety children (6-7, 8-9, 10-11 years) and 30 adults were asked to locate the middle of randomly generated dot-clouds. Nine plausible decision strategies were formulated, and each was fitted to observers' trial-by-trial response data (Reverse Correlation). When the number of visual elements was low (N < 6), children used a qualitatively different decision strategy from adults: appearing to "join up the dots" and locate the gravitational center of the enclosing shape. Given denser displays, both children and adults used an ideal strategy of arithmetically averaging individual points. Accounting for this difference in decision strategy explained 29% of children's lower precision. These findings suggest that children are not simply suboptimal at performing adult-like computations, but may at times use sensible, but qualitatively different strategies to make perceptual judgments. Learning which strategy is best in which circumstance might be an important driving factor of perceptual development.

Cognitive Bias for the Distribution of Ball Landing Positions in Amateur Tennis Players (Cognitive Bias for the Motor Variance in Tennis)

This study aimed to investigate whether the isotropy bias (estimating one's own motor variance as an approximately circular distribution rather than a vertically elongated distribution) arises in tennis players for the estimation of the two-dimensional variance for forehand strokes in tennis (Experiment 1), as well as the process underlying the isotropy bias (Experiment 2). In Experiment 1, 31 tennis players were asked to estimate prospectively their distribution of ball landing positions. They were then instructed to hit 50 forehand strokes. We compared the eccentricity of the ellipse calculated from estimated and observed landing positions. Eccentricity was significantly smaller in the estimated ellipse than in the observed ellipse. We assumed that the isotropy bias for the estimated ellipse comes from the process of variance estimation. In Experiment 2, nine participants estimated the 95% confidence interval of 300 dots. Eccentricity was significantly smaller in their estimated ellipses than it was in the ellipses for the dots, though the magnitude of bias decreased for the estimation of dots. These results suggest that the isotropy bias in tennis ball landing position includes the bias of recognizing landing position and the bias of estimating the ellipse confidence interval from the recognized landing position.

Is There a Common Summary Statistical Process for Representing the Mean and Variance? A Study Using Illustrations of Familiar Items

A number of studies revealed that our visual system can extract different types of summary statistics, such as the mean and variance, from sets of items. Although the extraction of such summary statistics has been studied well in isolation, the relationship between these statistics remains unclear. In this study, we explored this issue using an individual differences approach. Observers viewed illustrations of strawberries and lollypops varying in size or orientation and performed four tasks in a within-subject design, namely mean and variance discrimination tasks with size and orientation domains. We found that the performances in the mean and variance discrimination tasks were not correlated with each other and demonstrated that extractions of the mean and variance are mediated by different representation mechanisms. In addition, we tested the relationship between performances in size and orientation domains for each summary statistic (i.e. mean and variance) and examined whether each summary statistic has distinct processes across perceptual domains. The results illustrated that statistical summary representations of size and orientation may share a common mechanism for representing the mean and possibly for representing variance. Introspections for each observer performing the tasks were also examined and discussed.

The equivalent internal orientation and position noise for contour integration

Contour integration is the joining-up of local responses to parts of a contour into a continuous percept. In typical studies observers detect contours formed of discrete wavelets, presented against a background of random wavelets. This measures performance for detecting contours in the limiting external noise that background provides. Our novel task measures contour integration without requiring any background noise. This allowed us to perform noise-masking experiments using orientation and position noise. From these we measure the equivalent internal noise for contour integration. We found an orientation noise of 6° and position noise of 3 arcmin. Orientation noise was 2.6x higher in contour integration compared to an orientation discrimination control task. Comparing against a position discrimination task found position noise in contours to be 2.4x lower. This suggests contour integration involves intermediate processing that enhances the quality of element position representation at the expense of element orientation. Efficiency relative to the ideal observer was lower for the contour tasks (36% in orientation noise, 21% in position noise) compared to the controls (54% and 57%).

The numerosity and mean size of multiple objects are perceived independently and in parallel

It is well documented that people are good at the rapid representation of multiple objects in the form of ensemble summary statistics of different types (numerosity, the average feature, the variance of features, etc.). However, there is not enough clarity regarding the links between statistical domains. The relations between different-type summaries (numerosity and the mean) are of particular interest, since they can shed light on (1) a very general functional organization of ensemble processing and (2) mechanisms of statistical computations (whether averaging takes into account numerical information, as in regular statistics). Here, we show no correlation between the precision of estimated numerosity and that of the estimated mean. We also found that people are very good at dividing attention between numerosity and the mean size of a single set (Experiment 1); however, they show some cost of dividing attention between two same-type (two numerosities or two mean sizes, Experiment 2) and two different-type (one numerosity and one mean size, Experiment 3) summaries when each summary is ascribed to a different set. These results support the idea of domain specificity of numerosity and mean size perception, which also implies that, unlike regular statistics, computing the mean does not require numerosity information. We also conclude that computational capacity of ensemble statistics is more limited by encoding several ensembles than computing several summaries.

Ensemble Perception

To understand visual consciousness, we must understand how the brain represents ensembles of objects at many levels of perceptual analysis. Ensemble perception refers to the visual system's ability to extract summary statistical information from groups of similar objects-often in a brief glance. It defines foundational limits on cognition, memory, and behavior. In this review, we provide an operational definition of ensemble perception and demonstrate that ensemble perception spans across multiple levels of visual analysis, incorporating both low-level visual features and high-level social information. Further, we investigate the functional usefulness of ensemble perception and its efficiency, and we consider possible physiological and cognitive mechanisms that underlie an individual's ability to make accurate and rapid assessments of crowds of objects.