Summary Statistical Representation Research Articles

Summary statistical representation of temporal frequency

Observers effortlessly extract global patterns of spatiotemporal features from multiple objects in dynamic scenes (e.g., the movement of a crowd). Studies have revealed that a variety of spatial features are efficiently integrated into ensemble representations (e.g., mean), even when displayed in temporally complex contexts. However, it is not yet clear whether the ensemble coding also applies to purely temporal features such as frequency. Here, we investigated whether the visual system can extract the mean frequency from a group of flickering objects and how many objects are integrated into this representation of ensemble temporal frequency. In the Experiment 1, the display contained four disks flickering at independent frequencies in parallel for 4 seconds. Participants reported whether the mean of display frequency was higher or lower than a subsequent single test flicker. Temporal frequencies for the display disks were extracted randomly from one of three distributions (positively-skewed, symmetric, or negatively-skewed in a range of 0.5 to 12 Hz.) Points of subjective equality (PSEs) for the estimated means significantly shifted in accordance with the means of the three distributions. In Experiment 2, we displayed a full group of 8 disks or subsets of them (1, 2, or 4 disks) and participants compared the mean of the displayed disks with the subsequent test flicker frequency. We plotted the data as a function of relative distance between the mean of all the 8 frequencies and the test flicker, and observed a trend that participants' sensitivity improved as the number of displayed disks increased, at least up to four disks. However, this effect was not very large, suggesting that participants could integrate multiple temporal frequencies and extract the mean from them, but the efficiency of integration was not as high as other low-level visual features such as size and orientation. Meeting abstract presented at VSS 2017

The perceived stability of scenes: serial dependence in ensemble representations

We are continuously surrounded by a noisy and ever-changing environment. Instead of analyzing all the elements in a scene, our visual system has the ability to compress an enormous amount of visual information into ensemble representations, such as perceiving a forest instead of every single tree. Still, it is unclear why such complex scenes appear to be the same from moment to moment despite fluctuations, noise, and discontinuities in retinal images. The general effects of change blindness are usually thought to stabilize scene perception, making us unaware of minor inconsistencies between scenes. Here, we propose an alternative, that stable scene perception is actively achieved by the visual system through global serial dependencies: the appearance of scene gist is sequentially dependent on the gist perceived in previous moments. To test this hypothesis, we used summary statistical information as a proxy for “gist” level, global information in a scene. We found evidence for serial dependence in summary statistical representations. Furthermore, we show that this kind of serial dependence occurs at the ensemble level, where local elements are already merged into global representations. Taken together, our results provide a mechanism through which serial dependence can promote the apparent consistency of scenes over time.

Ensemble perception of emotions in autistic and typical children and adolescents

Ensemble perception, the ability to assess automatically the summary of large amounts of information presented in visual scenes, is available early in typical development. This ability might be compromised in autistic children, who are thought to present limitations in maintaining summary statistics representations for the recent history of sensory input. Here we examined ensemble perception of facial emotional expressions in 35 autistic children, 30 age- and ability-matched typical children and 25 typical adults. Participants received three tasks: a) an ‘ensemble’ emotion discrimination task; b) a baseline (single-face) emotion discrimination task; and c) a facial expression identification task. Children performed worse than adults on all three tasks. Unexpectedly, autistic and typical children were, on average, indistinguishable in their precision and accuracy on all three tasks. Computational modelling suggested that, on average, autistic and typical children used ensemble-encoding strategies to a similar extent; but ensemble perception was related to non-verbal reasoning abilities in autistic but not in typical children. Eye-movement data also showed no group differences in the way children attended to the stimuli. Our combined findings suggest that the abilities of autistic and typical children for ensemble perception of emotions are comparable on average.

Fast ensemble representations for abstract visual impressions.

Much of the richness of perception is conveyed by implicit, rather than image or feature-level, information. The perception of animacy or lifelikeness of objects, for example, cannot be predicted from image level properties alone. Instead, perceiving lifelikeness seems to be an inferential process and one might expect it to be cognitively demanding and serial rather than fast and automatic. If perceptual mechanisms exist to represent lifelikeness, then observers should be able to perceive this information quickly and reliably, and should be able to perceive the lifelikeness of crowds of objects. Here, we report that observers are highly sensitive to the lifelikeness of random objects and even groups of objects. Observers' percepts of crowd lifelikeness are well predicted by independent observers' lifelikeness judgements of the individual objects comprising that crowd. We demonstrate that visual impressions of abstract dimensions can be achieved with summary statistical representations, which underlie our rich perceptual experience.

Fleeting impressions of economic value via summary statistical representations

Fleeting impressions of economic value via summary statistical representations

Evidence for a Global Sampling Process in Extraction of Summary Statistics of Item Sizes in a Set.

Several studies have shown that our visual system may construct a “summary statistical representation” over groups of visual objects. Although there is a general understanding that human observers can accurately represent sets of a variety of features, many questions on how summary statistics, such as an average, are computed remain unanswered. This study investigated sampling properties of visual information used by human observers to extract two types of summary statistics of item sets, average and variance. We presented three models of ideal observers to extract the summary statistics: a global sampling model without sampling noise, global sampling model with sampling noise, and limited sampling model. We compared the performance of an ideal observer of each model with that of human observers using statistical efficiency analysis. Results suggest that summary statistics of items in a set may be computed without representing individual items, which makes it possible to discard the limited sampling account. Moreover, the extraction of summary statistics may not necessarily require the representation of individual objects with focused attention when the sets of items are larger than 4.

Incidental statistical summary representation over time.

Information taken in by the human visual system allows individuals to form statistical representations of sets of items. One's knowledge of natural categories includes statistical information, such as average size of category members and the upper and lower boundaries of the set. Previous research suggests that when subjects attend to a particular dimension of a set of items presented over an extended duration, they quickly learn about the central tendency of the set. However, it is unclear whether such learning can occur incidentally, when subjects are not attending to the relevant dimension of the set. The present study explored whether subjects could reproduce global statistical properties of a set presented over an extended duration when oriented to task-irrelevant properties of the set. Subjects were tested for their memory of its mean, its smallest and largest exemplars, the direction of its skew, and the relative distribution of the items. Subjects were able to accurately recall the average size circle, as well as the upper and lower boundaries of a set of 4,200 circles displayed over an extended period. This suggests that even without intending to do so, they were encoding and updating a statistical summary representation of a task-irrelevant attribute of the circles over time. Such incidental encoding of statistical properties of sets is thus a plausible mechanism for establishing a representation of typicality in category membership.

The centroid paradigm: Quantifying feature-based attention in terms of attention filters.

This paper elaborates a recent conceptualization of feature-based attention in terms of attention filters (Drew et al., Journal of Vision, 10(10:20), 1-16, 2010) into a general purpose centroid-estimation paradigm for studying feature-based attention. An attention filter is a brain process, initiated by a participant in the context of a task requiring feature-based attention, which operates broadly across space to modulate the relative effectiveness with which different features in the retinal input influence performance. This paper describes an empirical method for quantitatively measuring attention filters. The method uses a "statistical summary representation" (SSR) task in which the participant strives to mouse-click the centroid of a briefly flashed cloud composed of items of different types (e.g., dots of different luminances or sizes), weighting some types of items more strongly than others. In different attention conditions, the target weights for different item types in the centroid task are varied. The actual weights exerted on the participant's responses by different item types in any given attention condition are derived by simple linear regression. Because, on each trial, the centroid paradigm obtains information about the relative effectiveness of all the features in the display, both target and distractor features, and because the participant's response is a continuous variable in each of two dimensions (versus a simple binary choice as in most previous paradigms), it is remarkably powerful. The number of trials required to estimate an attention filter is an order of magnitude fewer than the number required to investigate much simpler concepts in typical psychophysical attention paradigms.

Ensemble perception of emotions in children with autism

Ensemble perception, the ability to rapidly and automatically assess the summary or ‘gist’ of large amounts of information presented in visual scenes, is available early in typical development (Sweeny et al., in press). Ensemble perception might be compromised in children with autism, who have been proposed to present limitations in their abilities to maintain and/or use summary statistics representations for the recent history of sensory input, which might be responsible for their unique perceptual experience (Pellicano & Burr, 2012). Here we examined ensemble perception of emotions in 29 children with autism, aged between 6 and 14 years, 30 age- and ability-matched typical children, and 12 typical adults. Participants received three child-friendly tasks: a) an average (ensemble perception) emotion discrimination task, assessing their ability to judge the average happiness of a set of ‘morphs’; b) a non-average happiness discrimination task, evaluating baseline emotion discrimination; and c) a face identification task, estimating children’s ability to identify morphs that had been previously presented to them. We also monitored participants' eye movements while they performed the three tasks using a Tobii X2-30 eye tracker (30 Hz). All three groups presented better precision in the non-average than in the average emotion discrimination task, while children’s precision and accuracy in the three tasks were worse than those of adults- suggestive of a gradual and parallel maturation of emotion discrimination, ensemble perception, and face-processing abilities. Unexpectedly, children with autism were indistinguishable from typical children in their precision and accuracy across the three tasks. On eye-movement variables, the three groups did not differ in terms of the average number of fixations and the number of morphs sampled per trial. Contrary Pellicano and Burr (2012), these findings suggest that autistic children’s abilities for ensemble perception of emotions are largely similar to those of typical children.

Perceiving the lifelikeness of crowds: summary statistical representations of abstract visual dimensions

Perceiving the lifelikeness of crowds: summary statistical representations of abstract visual dimensions

The antisaccade task: Vector inversion contributes to a statistical summary representation of target eccentricities.

Antisaccades require the top-down suppression of a stimulus-driven prosaccade (i.e., response suppression) and the inversion of a target's spatial location to mirror-symmetrical space (i.e., vector inversion). Moreover, recent work has shown that antisaccade amplitudes are characterized by a statistical summary representation (SSR) of the target eccentricities included in a stimulus-set--a result suggesting that antisaccades are supported via the same relative visual information as perceptions. The present investigation sought to determine whether response suppression and the disruption of real-time control or vector inversion contribute to a SSR in oculomotor control. Participants completed pro- and antisaccades (target eccentricities of 10.5°, 15.5°, and 20.5°) in blocks of trials that differed with regard to the frequency that individual target eccentricities were presented. The manipulation of target eccentricity frequency was used to determine whether the most frequently presented target within a stimulus-set (i.e., the SSR) influences saccade amplitudes. Moreover, we disrupted the real-time control of prosaccades by requiring participants to suppress their response for a brief visual delay (i.e., 2000 ms: so-called delay prosaccade). As expected, antisaccades and delay prosaccades produced equivalent reaction times. In turn, amplitudes for delay prosaccades were refractory to the manipulation of target eccentricity frequency, whereas antisaccades were biased in the direction of the most frequently presented target within a stimulus-set. Accordingly, we propose that vector inversion contributes to the mediation of target eccentricities via a SSR and that such a phenomenon provides convergent evidence that a relative visual percept mediates antisaccades.

Statistical Summary Representation: Contents and Mechanisms

Humans are capable of extracting statistical information from multiple stimuli and forming statistical summary representation(SSR), in which central tendency and variability of the stimuli are represented. According to the use of attentional resource, the mechanisms of SSR could be categorized into ensemble processing under distributed attention and individual processing under focused attention. Both mechanisms interact in the working memory, constructing the representation of multiple stimuli. SSR occurs across different stimulus types in both low-level and high-level processing, suggesting that it may be a common encoding method in perception. Future work on SSR may focus on its neural substrates and its impact on decision making.

Feedback-driven tuning of statistical summary representations

The amount of sensory data encountered by the visual system often exceeds its processing capacity. One solution is to exploit statistical structure in the natural environment to generate a more efficient representation of the information (Simoncelli & Olshausen, 2001). For example, the visual system may construct a “statistical summary representation” over groups of visual objects, reflecting their general properties (Alvarez, 2011). Indeed, it has been shown that observers are able to quickly and accurately extract average values over a range of visual feature dimensions, including size (Chong & Treisman, 2003), orientation (Parkes et al. 2001), and emotional expression (Haberman & Whitney, 2007). However, it remains an open question as to how observers learn to produce such accurate estimates of these summary statistics. Although good performance on these tasks suggests that summary features are readily accessible, it is not clear to what extent these statistical operations are performed automatically—integrating over sensory information in an unsupervised fashion, or are penetrable to task demands—flexibly incorporating observer goals and error-related feedback to maximize performance (Bauer, 2009; Myczek & Simons, 2008). In the present study, we sought to understand the role of learning in statistical summary representations. Specifically, we examined the contribution of task practice and performance feedback to perceptual discrimination of the centroid (i.e., mean location) of a set of objects (Alvarez & Oliva, 2008). We hypothesized that providing vector error feedback (i.e., containing both distance and direction information) while observers practiced making pointing movements toward the centroid would improve the fidelity of their centroid representations. This improvement might be reflected in reduced error during training and lower discrimination thresholds in an independent perceptual test.

Mean vs. range in statistical summary representation

Mean vs. range in statistical summary representation

Efficient summary statistical representation when change localization fails

People are sensitive to the summary statistics of the visual world (e.g., average orientation/speed/facial expression). We readily derive this information from complex scenes, often without explicit awareness. Given the fundamental and ubiquitous nature of summary statistical representation, we tested whether this kind of information is subject to the attentional constraints imposed by change blindness. We show that information regarding the summary statistics of a scene is available despite limited conscious access. In a novel experiment, we found that while observers can suffer from change blindness (i.e., not localize where change occurred between two views of the same scene), observers could nevertheless accurately report changes in the summary statistics (or "gist") about the very same scene. In the experiment, observers saw two successively presented sets of 16 faces that varied in expression. Four of the faces in the first set changed from one emotional extreme (e.g., happy) to another (e.g., sad) in the second set. Observers performed poorly when asked to locate any of the faces that changed (change blindness). However, when asked about the ensemble (which set was happier, on average), observer performance remained high. Observers were sensitive to the average expression even when they failed to localize any specific object change. That is, even when observers could not locate the very faces driving the change in average expression between the two sets, they nonetheless derived a precise ensemble representation. Thus, the visual system may be optimized to process summary statistics in an efficient manner, allowing it to operate despite minimal conscious access to the information presented.

Mean representation beyond a shadow of a doubt: Summary statistical representation of shadows and lighting direction

Mean representation beyond a shadow of a doubt: Summary statistical representation of shadows and lighting direction

Temporal integration of high-level summary statistical representation

Temporal integration of high-level summary statistical representation

Averaging facial expression over time

The visual system groups similar features, objects, and motion (e.g., Gestalt grouping). Recent work suggests that the computation underlying perceptual grouping may be one of summary statistical representation. Summary representation occurs for low-level features, such as size, motion, and position, and even for high level stimuli, including faces; for example, observers accurately perceive the average expression in a group of faces (J. Haberman & D. Whitney, 2007, 2009). The purpose of the present experiments was to characterize the time-course of this facial integration mechanism. In a series of three experiments, we measured observers' abilities to recognize the average expression of a temporal sequence of distinct faces. Faces were presented in sets of 4, 12, or 20, at temporal frequencies ranging from 1.6 to 21.3 Hz. The results revealed that observers perceived the average expression in a temporal sequence of different faces as precisely as they perceived a single face presented repeatedly. The facial averaging was independent of temporal frequency or set size, but depended on the total duration of exposed faces, with a time constant of approximately 800 ms. These experiments provide evidence that the visual system is sensitive to the ensemble characteristics of complex objects presented over time.

Seeing the mean: Ensemble coding for sets of faces.

We frequently encounter groups of similar objects in our visual environment: a bed of flowers, a basket of oranges, a crowd of people. How does the visual system process such redundancy? Research shows that rather than code every element in a texture, the visual system favors a summary statistical representation of all the elements. The authors demonstrate that although it may facilitate texture perception, ensemble coding also occurs for faces-a level of processing well beyond that of textures. Observers viewed sets of faces varying in emotionality (e.g., happy to sad) and assessed the mean emotion of each set. Although observers retained little information about the individual set members, they had a remarkably precise representation of the mean emotion. Observers continued to discriminate the mean emotion accurately even when they viewed sets of 16 faces for 500 ms or less. Modeling revealed that perceiving the average facial expression in groups of faces was not due to noisy representation or noisy discrimination. These findings support the hypothesis that ensemble coding occurs extremely fast at multiple levels of visual analysis.