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Extensive research in the behavioral sciences has addressed people’s ability to learn stationary probabilities, which stay constant over time, but only recently have there been attempts to model the cognitive processes whereby people learn—and track—nonstationary probabilities. In this context, the old debate on whether learning occurs by the gradual formation of associations or by occasional shifts between hypotheses representing beliefs about distal states of the world has resurfaced. Gallistel et al. (2014) pitched the two theories against each other in a nonstationary probability learning task. They concluded that various qualitative patterns in their data were incompatible with trial-by-trial associative learning and could only be explained by a hypothesis-testing model. Here, we contest that claim and demonstrate that it was premature. First, we argue that their experimental paradigm consisted of two distinct tasks: probability tracking (an estimation task) and change detection (a decision-making task). Next, we present a model that uses the (associative) delta learning rule for the probability tracking task and bounded evidence accumulation for the change detection task. We find that this combination of two highly established theories accounts well for all qualitative phenomena and outperforms the alternative model proposed by Gallistel et al. (2014) in a quantitative model comparison. In the spirit of cumulative science, we conclude that current experimental data on human learning of nonstationary probabilities can be explained as a combination of associative learning and bounded evidence accumulation and does not require a new model.

Base rate neglect refers to people's apparent tendency to underweight or even ignore base rate information when estimating posterior probabilities for events, such as the probability that a person with a positive cancer-test outcome actually does have cancer. While often replicated, almost all evidence for the phenomenon comes from studies that used problems with extremely low base rates, high hit rates, and low false alarm rates. It is currently unclear whether the effect generalizes to reasoning problems outside this "corner" of the entire problem space. Another limitation of previous studies is that they have focused on describing empirical patterns of the effect at the group level and not so much on the underlying strategies and individual differences. Here, we address these two limitations by testing participants on a broader problem space and modeling their responses at a single-participant level. We find that the empirical patterns that have served as evidence for base-rate neglect generalize to a larger problem space, albeit with large individual differences in the extent with which participants "neglect" base rates. In particular, we find a bi-modal distribution consisting of one group of participants who almost entirely ignore the base rate and another group who almost entirely account for it. This heterogeneity is reflected in the cognitive modeling results: participants in the former group were best captured by a linear-additive model, while participants in the latter group were best captured by a Bayesian model. We find little evidence for heuristic models. Altogether, these results suggest that the effect known as "base-rate neglect" generalizes to a large set of reasoning problems, but varies largely across participants and may need a reinterpretation in terms of the underlying cognitive mechanisms.

Extensive research in the behavioural sciences has addressed people’s ability to learn stationary probabilities, which stay constant over time, but only recently have there been attempts to model the cognitive processes whereby people learn – and track – non-stationary probabilities. In this context, the old debate on whether learning occurs by gradual formation of associations or by occasional shifts between hypotheses representing beliefs about distal states of the world has resurfaced. Gallistel et al. (2014) pitched the two theories against each other in a non-stationary probability learning task. They concluded that various qualitative patterns in their data were incompatible with trial-by-trial associative learning and could only be explained by a hypothesis-testing model. Here, we contest that claim and demonstrate that it was premature. First, we argue that their experimental paradigm consisted of two distinct tasks: probability tracking (an estimation task) and change detection (a decision-making task). Next, we present a model that uses the (associative) delta learning rule for the probability tracking task and bounded evidence accumulation for the change-detection task. We find that this combination of two highly established theories accounts well for all qualitative phenomena and outperforms the alternative model proposed by Gallistel et al. in a quantitative model comparison. In the spirit of cumulative science, we conclude that current experimental data on human learning of non-stationary probabilities can be explained as a combination of associative learning and bounded evidence accumulation and does not require a new model.

Humans as well as some nonhuman animals can estimate object numerosities-such as the number of sheep in a flock-without explicit counting. Here, we report on a negative time-order effect (TOE) in this type of judgment: When nonsymbolic numerical stimuli are presented sequentially, the second stimulus is overestimated compared to the first. We examined this "recent is more" effect in two comparative judgment tasks: larger-smaller discrimination and same-different discrimination. Ideal-observer modeling revealed evidence for a TOE in 88.2% of the individual data sets. Despite large individual differences in effect size, there was strong consistency in effect direction: 87.3% of the identified TOEs were negative. The average effect size was largely independent of task but did strongly depend on both stimulus magnitude and interstimulus interval. Finally, we used an estimation task to obtain insight into the origin of the effect. We found that subjects tend to overestimate both stimuli but the second one more strongly than the first one. Overall, our findings are highly consistent with findings from studies on TOEs in nonnumerical judgments, which suggests a common underlying mechanism. (PsycINFO Database Record

Previous work has shown that humans distribute their visual working memory (VWM) resources flexibly across items: the higher the importance of an item, the better it is remembered. A related, but much less studied question is whether people also have control over the total amount of VWM resource allocated to a task. Here, we approach this question by testing whether increasing monetary incentives results in better overall VWM performance. In three experiments, subjects performed a delayed-estimation task on the Amazon Turk platform. In the first two experiments, four groups of subjects received a bonus payment based on their performance, with the maximum bonus ranging from $0 to $10 between groups. We found no effect of the amount of bonus on intrinsic motivation or on VWM performance in either experiment. In the third experiment, reward was manipulated on a trial-by-trial basis using a within-subjects design. Again, no evidence was found that VWM performance depended on the magnitude of potential reward. These results suggest that encoding quality in visual working memory is insensitive to monetary reward, which has implications for resource-rational theories of VWM.

Humans can estimate numerosities–such as the number sheep in a flock–without deliberate counting. A number of biases have been identified in these estimates, which seem primarily rooted in the spatial organization of objects (grouping, symmetry, etc). Most previous studies on the number sense used static stimuli with extremely brief exposure times. However, outside the laboratory, visual scenes are often dynamic and freely viewed for prolonged durations (e.g., a flock of moving sheep). The purpose of the present study is to examine grouping-induced numerosity biases in stimuli that more closely mimic these conditions. To this end, we designed two experiments with limited-dot-lifetime displays (LDDs), in which each dot is visible for a brief period of time and replaced by a new dot elsewhere after its disappearance. The dynamic nature of LDDs prevents subjects from counting even when they are free-viewing a stimulus under prolonged presentation. Subjects estimated the number of dots in arrays that were presented either as a single group or were segregated into two groups by spatial clustering, dot size, dot color, or dot motion. Grouping by color and motion reduced perceived numerosity compared to viewing them as a single group. Moreover, the grouping effect sizes between these two features were correlated, which suggests that the effects may share a common, feature-invariant mechanism. Finally, we find that dot size and total stimulus area directly affect perceived numerosity, which makes it difficult to draw reliable conclusions about grouping effects induced by spatial clustering and dot size. Our results provide new insights into biases in numerosity estimation and they demonstrate that the use of LDDs is an effective method to study the human number sense under prolonged viewing. Leo Poom and Ronald van der Berg contributed equally to this work.

Economically important food tree species in sub-Saharan Africa should be domesticated to enhance their production within agro forestry systems. The African bush mango trees (Irvingia species) are highly preserved and integrated in agro forestry systems in tropical Africa. However, the taxonomic debate related to the species or varietal status of the bitter and sweet fruited African bush mango trees hinders their domestication process and rational use. Amplified fragment length polymorphisms (AFLPs) and chloroplast simple sequence repeats (cpSSRs) were used in this study to assess the genetic diversity of African bush mango trees and to test the distinction between bitter and sweet fruited trees, sampled across Togo, Benin, Nigeria and Cameroon. Both the AFLPs and cpSSRs showed low genetic diversity for the Dahomey Gap bitter trees population. This is due to the higher fragmentation and the continuous reduction of this small sized population occurring in a limited forest ecosystem. The higher polymorphism and genetic diversity of the sweet mango tree populations in Benin and Togo showed the effects of domestication of materials of different geographical origin coupled with the frequent long distance transfer of genetic materials. When used separately, the AFLPs and cpSSRs failed to consistently discriminate the populations and type of trees. From the combined dataset, both markers differentiated geographically recognizable groups; bitter from sweet mango trees. However, Nigerian sweet mango trees clustered with the bitter ones. The suitability of AFLPs and cpSSRs to test our hypotheses within Irvingia needs to be thoroughly reassessed. Key words: AFLP, Benin, cpSSR, Togo, Dahomey Gap, Irvingia, taxonomy, domestication.

In tasks such as visual search and change detection, a key question is how observers integrate noisy measurements from multiple locations to make a decision. Decision rules proposed to model this process have fallen into two categories: Bayes-optimal (ideal observer) rules and ad-hoc rules. Among the latter, the maximum-of-outputs (max) rule has been the most prominent. Reviewing recent work and performing new model comparisons across a range of paradigms, we find that in all cases except for one, the optimal rule describes human data as well as or better than every max rule either previously proposed or newly introduced here. This casts doubt on the utility of the max rule for understanding perceptual decision-making.

The precision with which items are encoded in working memory and attention decreases with the number of encoded items. Current theories typically account for this “set size effect” by postulating a hard constraint on the allocated amount of encoding resource, commonly formalized as samples, spikes, slots, or bits. While these theories have produced models that are quantitatively successful, they offer no principled explanation for the very existence of set size effects: given their detrimental consequences for behavioral performance, why have these effects not been weeded out by evolutionary pressure, for example by scaling the amount of allocated encoding resource with set size? Here, we propose a theory that is based on an ecological notion of rationality: set size effects establish an optimal trade-off between behavioral performance and the neural costs associated with stimulus encoding. We derive models from this theory for four visual working memory and attention tasks and find that it accounts well for data in eleven different experiments. Our results suggest that set size effects have a rational basis and that ecological costs should be considered in models of human behavior.

Although visual working memory (VWM) has been studied extensively, it is unknown how people form confidence judgments about their memories. Peirce (1878) speculated that Fechner's law-which states that sensation is proportional to the logarithm of stimulus intensity-might apply to confidence reports. Based on this idea, we hypothesize that humans map the precision of their VWM contents to a confidence rating through Fechner's law. We incorporate this hypothesis into the best available model of VWM encoding and fit it to data from a delayed-estimation experiment. The model provides an excellent account of human confidence rating distributions as well as the relation between performance and confidence. Moreover, the best-fitting mapping in a model with a highly flexible mapping closely resembles the logarithmic mapping, suggesting that no alternative mapping exists that accounts better for the data than Fechner's law. We propose a neural implementation of the model and find that this model also fits the behavioral data well. Furthermore, we find that jointly fitting memory errors and confidence ratings boosts the power to distinguish previously proposed VWM encoding models by a factor of 5.99 compared to fitting only memory errors. Finally, we show that Fechner's law also accounts for metacognitive judgments in a word recognition memory task, which is a first indication that it may be a general law in metacognition. Our work presents the first model to jointly account for errors and confidence ratings in VWM and could lay the groundwork for understanding the computational mechanisms of metacognition. (PsycINFO Database Record

Three questions have been prominent in the study of visual working memory limitations: (a) What is the nature of mnemonic precision (e.g., quantized or continuous)? (b) How many items are remembered? (c) To what extent do spatial binding errors account for working memory failures? Modeling studies have typically focused on comparing possible answers to a single one of these questions, even though the result of such a comparison might depend on the assumed answers to both others. Here, we consider every possible combination of previously proposed answers to the individual questions. Each model is then a point in a 3-factor model space containing a total of 32 models, of which only 6 have been tested previously. We compare all models on data from 10 delayed-estimation experiments from 6 laboratories (for a total of 164 subjects and 131,452 trials). Consistently across experiments, we find that (a) mnemonic precision is not quantized but continuous and not equal but variable across items and trials; (b) the number of remembered items is likely to be variable across trials, with a mean of 6.4 in the best model (median across subjects); (c) spatial binding errors occur but explain only a small fraction of responses (16.5% at set size 8 in the best model). We find strong evidence against all 6 documented models. Our results demonstrate the value of factorial model comparison in working memory.

Summary Demanding tasks often require a series of decisions to reach a goal. Recent progress in perceptual decision-making has served to unite decision accuracy, speed, and confidence in a common framework of bounded evidence accumulation, furnishing a platform for the study of such multi-stage decisions. In many instances, the strategy applied to each decision, such as the speed-accuracy trade-off, ought to depend on the accuracy of the previous decisions. However, as the accuracy of each decision is often unknown to the decision maker, we hypothesized that subjects may carry forward a level of confidence in previous decisions to affect subsequent decisions. Subjects made two perceptual decisions sequentially and were rewarded only if they made both correctly. The speed and accuracy of individual decisions were explained by noisy evidence accumulation to a terminating bound. We found that subjects adjusted their speed-accuracy setting by elevating the termination bound on the second decision in proportion to their confidence in the first. The findings reveal a novel role for confidence and a degree of flexibility, hitherto unknown, in the brain’s ability to rapidly and precisely modify the mechanisms that control the termination of a decision., Graphical Abstract, Highlights • Many tasks require a series of correct decisions to reach a goal • Confidence in a decision affects the termination criterion for the next decision • Use of confidence to change the speed-accuracy trade-off can increase reward, van den Berg et al. show that when making a sequence of decisions to achieve a goal, the subjective confidence in the accuracy of the first decision precisely and rapidly alters the decision-making process of the second decision.

Decisions are accompanied by a degree of confidence that a selected option is correct. A sequential sampling framework explains the speed and accuracy of decisions and extends naturally to the confidence that the decision rendered is likely to be correct. However, discrepancies between confidence and accuracy suggest that confidence might be supported by mechanisms dissociated from the decision process. Here we show that this discrepancy can arise naturally because of simple processing delays. When participants were asked to report choice and confidence simultaneously, their confidence, reaction time and a perceptual decision about motion were explained by bounded evidence accumulation. However, we also observed revisions of the initial choice and/or confidence. These changes of mind were explained by a continuation of the mechanism that led to the initial choice. Our findings extend the sequential sampling framework to vacillation about confidence and invites caution in interpreting dissociations between confidence and accuracy. DOI: http://dx.doi.org/10.7554/eLife.12192.001, eLife digest To understand how the brain makes decisions is to understand how we think – how we deal with information, interpret it and agree with a particular interpretation of the information. Neuroscience has begun to uncover the mechanisms that underlie these processes by linking the activity of nerve cells in the brain to different aspects of making decisions. These include how long it takes to reach a decision, why we make errors and how confident we feel about a decision. Sometimes when we make a decision and have committed to an answer, we then change our minds. Now, van den Berg et al. have asked whether the brain mechanisms that support a change of mind also support a change in confidence. To investigate this problem, human volunteers were asked to perform a difficult task where they had to decide whether a field of randomly moving dots had a tendency to drift to the left or to the right. During the experiment, van den Berg et al. recorded how long the volunteers took to make their decision, how confident the volunteers felt about their choice, and whether they were correct. Analyzing this data revealed that all of these measures could be explained by a mechanism where the brain accumulates evidence only until there appears to be enough evidence to favor one choice over the other. This process specifies how confident an individual should be based on the quality of the sensory evidence and how long it takes to make a decision. In addition, van den Berg et al. found that occasionally a volunteer changed their mind about how confident they were about a decision after they’d made it, as if they had continued to think about it. This was despite the volunteers receiving no more information about the task or how well they had done once they had made their decision. Therefore, it appears that the brain processed additional information that had already been detected but did not have time to affect the initial choice. The activity of the nerve cells in the brain was not recorded as the volunteers made their decisions. Future experiments that incorporate these measurements could help reveal how the brain performs the necessary computations and account for the time delay seen in processing some of the data. Where is this delayed information processed in the brain, and how does it lead to a change of mind? DOI: http://dx.doi.org/10.7554/eLife.12192.002

In laboratory visual search experiments, distractors are often statistically independent of each other. However, stimuli in more naturalistic settings are often correlated and rarely independent. Here, we examine whether human observers take stimulus correlations into account in orientation target detection. We find that they do, although probably not optimally. In particular, it seems that low distractor correlations are overestimated. Our results might contribute to bridging the gap between artificial and natural visual search tasks.

Cueing attention after the disappearance of visual stimuli biases which items will be remembered best. This observation has historically been attributed to the influence of attention on memory as opposed to subjective visual experience. We recently challenged this view by showing that cueing attention after the stimulus can improve the perception of a single Gabor patch at threshold levels of contrast. Here, we test whether this retro-perception actually increases the frequency of consciously perceiving the stimulus, or simply allows for a more precise recall of its features. We used retro-cues in an orientation-matching task and performed mixture-model analysis to independently estimate the proportion of guesses and the precision of non-guess responses. We find that the improvements in performance conferred by retrospective attention are overwhelmingly determined by a reduction in the proportion of guesses, providing strong evidence that attracting attention to the target’s location after its disappearance increases the likelihood of perceiving it consciously.

The ability to search efficiently for a target in a cluttered environment is one of the most remarkable functions of the nervous system. This task is difficult under natural circumstances, as the reliability of sensory information can vary greatly across space and time and is typically a priori unknown to the observer. In contrast, visual-search experiments commonly use stimuli of equal and known reliability. In a target detection task, we randomly assigned high or low reliability to each item on a trial-by-trial basis. An optimal observer would weight the observations by their trial-to-trial reliability and combine them using a specific nonlinear integration rule. We found that humans were near-optimal, regardless of whether distractors were homogeneous or heterogeneous and whether reliability was manipulated through contrast or shape. We present a neural-network implementation of near-optimal visual search based on probabilistic population coding. The network matched human performance.

Performance on visual working memory tasks decreases as more items need to be remembered. Over the past decade, a debate has unfolded between proponents of slot models and slotless models of this phenomenon (Ma, Husain, Bays (Nature Neuroscience 17, 347-356, 2014). Zhang and Luck (Nature 453, (7192), 233-235, 2008) and Anderson, Vogel, and Awh (Attention, Perception, Psychophys 74, (5), 891-910, 2011) noticed that as more items need to be remembered, “memory noise” seems to first increase and then reach a “stable plateau.” They argued that three summary statistics characterizing this plateau are consistent with slot models, but not with slotless models. Here, we assess the validity of their methods. We generated synthetic data both from a leading slot model and from a recent slotless model and quantified model evidence using log Bayes factors. We found that the summary statistics provided at most 0.15 % of the expected model evidence in the raw data. In a model recovery analysis, a total of more than a million trials were required to achieve 99 % correct recovery when models were compared on the basis of summary statistics, whereas fewer than 1,000 trials were sufficient when raw data were used. Therefore, at realistic numbers of trials, plateau-related summary statistics are highly unreliable for model comparison. Applying the same analyses to subject data from Anderson et al. (Attention, Perception, Psychophys 74, (5), 891-910, 2011), we found that the evidence in the summary statistics was at most 0.12 % of the evidence in the raw data and far too weak to warrant any conclusions. The evidence in the raw data, in fact, strongly favored the slotless model. These findings call into question claims about working memory that are based on summary statistics.

Change detection is a classic paradigm that has been used for decades to argue that working memory can hold no more than a fixed number of items (“item-limit models”). Recent findings force us to consider the alternative view that working memory is limited by the precision in stimulus encoding, with mean precision decreasing with increasing set size (“continuous-resource models”). Most previous studies that used the change detection paradigm have ignored effects of limited encoding precision by using highly discriminable stimuli and only large changes. We conducted two change detection experiments (orientation and color) in which change magnitudes were drawn from a wide range, including small changes. In a rigorous comparison of five models, we found no evidence of an item limit. Instead, human change detection performance was best explained by a continuous-resource model in which encoding precision is variable across items and trials even at a given set size. This model accounts for comparison errors in a principled, probabilistic manner. Our findings sharply challenge the theoretical basis for most neural studies of working memory capacity., Author Summary Working memory is a fundamental aspect of human cognition. It allows us to remember bits of information over short periods of time and make split-second decisions about what to do next. Working memory is often tested using a change detection task: subjects report whether a change occurred between two subsequent visual images that both contain multiple objects (items). The more items are present in the images, the worse they do. The precise origin of this phenomenon is not agreed on. The classic theory asserts that working memory consists of a small number of slots, each of which can store one item; when there are more items than slots, the extra items are discarded. A modern model postulates that working memory is fundamentally limited in the quality rather than the quantity of memories. In a metaphor: instead of watering only a few plants in our garden, we water all of them, but the more plants we have, the less water each will receive on average. We show that this new model does much better in accounting for human change detection responses. This has consequences for the entire field of working memory research.

It is commonly believed that visual short-term memory (VSTM) consists of a fixed number of “slots” in which items can be stored. An alternative theory in which memory resource is a continuous quantity distributed over all items seems to be refuted by the appearance of guessing in human responses. Here, we introduce a model in which resource is not only continuous but also variable across items and trials, causing random fluctuations in encoding precision. We tested this model against previous models using two VSTM paradigms and two feature dimensions. Our model accurately accounts for all aspects of the data, including apparent guessing, and outperforms slot models in formal model comparison. At the neural level, variability in precision might correspond to variability in neural population gain and doubly stochastic stimulus representation. Our results suggest that VSTM resource is continuous and variable rather than discrete and fixed and might explain why subjective experience of VSTM is not all or none.

de Gardelle and Summerfield (1) claimed that, when judging the mean of a set of stimuli, it is optimal to downweight outliers, and that human subjects follow this robust averaging strategy. Here, we show that, in their task, the optimal observer would equally weight all observations. In ref. 1, subjects were presented with a set of eight colors that are denoted by a vector x = (x1, …, x8) and drawn independently from a Gaussian distribution on a red–blue color axis with variance σ2 and mean of either μ (blue) or −μ (red). On a given trial, μ was set randomly to one of two values, and σ2 was set randomly to one of three values. The subject indicated whether the mean was blue (C = 1) or red (C = −1). When the prior probabilities are equal, the optimal decision is based on the likelihoods of both options [i.e., p(x|C = 1) and p(x|C=−1)]. Because μ and σ2 are unknown to the observer, the optimal observer computes these likelihoods by averaging (marginalizing) over all six possibilities (Eq. 1)

Deciding whether a set of objects are the same or different is a cornerstone of perception and cognition. Surprisingly, no principled quantitative model of sameness judgment exists. We tested whether human sameness judgment under sensory noise can be modeled as a form of probabilistically optimal inference. An optimal observer would compare the reliability-weighted variance of the sensory measurements with a set size-dependent criterion. We conducted two experiments, in which we varied set size and individual stimulus reliabilities. We found that the optimal-observer model accurately describes human behavior, outperforms plausible alternatives in a rigorous model comparison, and accounts for three key findings in the animal cognition literature. Our results provide a normative footing for the study of sameness judgment and indicate that the notion of perception as near-optimal inference extends to abstract relations.

The brain encodes visual information with limited precision. Contradictory evidence exists as to whether the precision with which an item is encoded depends on the number of stimuli in a display (set size). Some studies have found evidence that precision decreases with set size, but others have reported constant precision. These groups of studies differed in two ways. The studies that reported a decrease used displays with heterogeneous stimuli and tasks with a short-term memory component, while the ones that reported constancy used homogeneous stimuli and tasks that did not require short-term memory. To disentangle the effects of heterogeneity and short-memory involvement, we conducted two main experiments. In Experiment 1, stimuli were heterogeneous, and we compared a condition in which target identity was revealed before the stimulus display with one in which it was revealed afterward. In Experiment 2, target identity was fixed, and we compared heterogeneous and homogeneous distractor conditions. In both experiments, we compared an optimal-observer model in which precision is constant with set size with one in which it depends on set size. We found that precision decreases with set size when the distractors are heterogeneous, regardless of whether short-term memory is involved, but not when it is homogeneous. This suggests that heterogeneity, not short-term memory, is the critical factor. In addition, we found that precision exhibits variability across items and trials, which may partly be caused by attentional fluctuations.

A key function of the brain is to interpret noisy sensory information. To do so optimally, observers must, in many tasks, take into account knowledge of the precision with which stimuli are encoded. In an orientation change detection task, we find that encoding precision does not only depend on an experimentally controlled reliability parameter (shape), but also exhibits additional variability. In spite of variability in precision, human subjects seem to take into account precision near-optimally on a trial-to-trial and item-to-item basis. Our results offer a new conceptualization of the encoding of sensory information and highlight the brain's remarkable ability to incorporate knowledge of uncertainty during complex perceptual decision-making.

An object in the peripheral visual field is more difficult to recognize when surrounded by other objects. This phenomenon is called “crowding”. Crowding places a fundamental constraint on human vision that limits performance on numerous tasks. It has been suggested that crowding results from spatial feature integration necessary for object recognition. However, in the absence of convincing models, this theory has remained controversial. Here, we present a quantitative and physiologically plausible model for spatial integration of orientation signals, based on the principles of population coding. Using simulations, we demonstrate that this model coherently accounts for fundamental properties of crowding, including critical spacing, “compulsory averaging”, and a foveal-peripheral anisotropy. Moreover, we show that the model predicts increased responses to correlated visual stimuli. Altogether, these results suggest that crowding has little immediate bearing on object recognition but is a by-product of a general, elementary integration mechanism in early vision aimed at improving signal quality., Author Summary Visual crowding refers to the phenomenon that objects become more difficult to recognize when other objects surround them. Recently there has been an explosion of studies on crowding, driven, in part, by the belief that understanding crowding will help to understand a range of visual behaviours, including object recognition, visual search, reading, and texture recognition. Given the long-standing interest in the topic and its relevance for a wide range of research fields, it is quite surprising that after nearly a century of research the mechanisms underlying crowding are still as poorly understood as they are today. A nearly complete lack of quantitative models seems to be one of the main reasons for this. Here, we present a mathematical, biologically motivated model of feature integration at the level of neuron populations. Using simulations, we demonstrate that several fundamental properties of the crowding effect can be explained as the by-product of an integration mechanism that may have a function in contour integration. Altogether, these results help differentiate between earlier theories about both the neural and functional origin of crowding.

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Visual information is difficult to search and interpret when the density of the displayed information is high or the layout is chaotic. Visual information that exhibits such properties is generally referred to as being "cluttered." Clutter should be avoided in information visualizations and interface design in general because it can severely degrade task performance. Although previous studies have identified computable correlates of clutter (such as local feature variance and edge density), understanding of why humans perceive some scenes as being more cluttered than others remains limited. Here, we explore an account of clutter that is inspired by findings from visual perception studies. Specifically, we test the hypothesis that the so-called "crowding" phenomenon is an important constituent of clutter. We constructed an algorithm to predict visual clutter in arbitrary images by estimating the perceptual impairment due to crowding. After verifying that this model can reproduce crowding data we tested whether it can also predict clutter. We found that its predictions correlate well with both subjective clutter assessments and search performance in cluttered scenes. These results suggest that crowding and clutter may indeed be closely related concepts and suggest avenues for further research.

Perception of peripherally viewed shapes is impaired when surrounded by similar shapes. This phenomenon is commonly referred to as "crowding". Although studied extensively for perception of characters ( mainly letters) and, to a lesser extent, for orientation, little is known about whether and how crowding affects perception of other features. Nevertheless, current crowding models suggest that the effect should be rather general and thus not restricted to letters and orientation. Here, we report on a series of experiments investigating crowding in the following elementary feature dimensions: size, hue, and saturation. Crowding effects in these dimensions were benchmarked against those in the orientation domain. Our primary finding is that all features studied show clear signs of crowding. First, identification thresholds increase with decreasing mask spacing. Second, for all tested features, critical spacing appears to be roughly half the viewing eccentricity and independent of stimulus size, a property previously proposed as the hallmark of crowding. Interestingly, although critical spacings are highly comparable, crowding magnitude differs across features: Size crowding is almost as strong as orientation crowding, whereas the effect is much weaker for saturation and hue. We suggest that future theories and models of crowding should be able to accommodate these differences in crowding effects.

Contains fulltext : 54553.pdf (Publisher’s version ) (Open Access) While searching for objects, we combine information from multiple visual modalities. Classical theories of visual search assume that features are processed independently prior to an integration stage. Based on this, one would predict that features that are equally discriminable in single feature search should remain so in conjunction search. We test this hypothesis by examining whether search accuracy in feature search predicts accuracy in conjunction search. Subjects searched for objects combining color and orientation or size; eye movements were recorded. Prior to the main experiment, we matched feature discriminability, making sure that in feature search, 70% of saccades were likely to go to the correct target stimulus. In contrast to this symmetric single feature discrimination performance, the conjunction search task showed an asymmetry in feature discrimination performance: In conjunction search, a similar percentage of saccades went to the correct color as in feature search but much less often to correct orientation or size. Therefore, accuracy in feature search is a good predictor of accuracy in conjunction search for color but not for size and orientation. We propose two explanations for the presence of such asymmetries in conjunction search: the use of conjunctively tuned channels and differential crowding effects for different features.

Looking for a target in a visual scene becomes more difficult as the number of stimuli increases. In a signal detection theory view, this is due to the cumulative effect of noise in the encoding of the distractors, and potentially on top of that, to an increase of the noise (i.e., a decrease of precision) per stimulus with set size, reflecting divided attention. It has long been argued that human visual search behavior can be accounted for by the first factor alone. While such an account seems to be adequate for search tasks in which all distractors have the same, known feature value (i.e., are maximally predictable), we recently found a clear effect of set size on encoding precision when distractors are drawn from a uniform distribution (i.e., when they are maximally unpredictable). Here we interpolate between these two extreme cases to examine which of both conclusions holds more generally as distractor statistics are varied. In one experiment, we vary the level of distractor heterogeneity; in another we dissociate distractor homogeneity from predictability. In all conditions in both experiments, we found a strong decrease of precision with increasing set size, suggesting that precision being independent of set size is the exception rather than the rule.