Serial consolidation of orientation information into visual short-term memory

Selectively maintaining an object's feature in visual working memory: A comparison between highly discriminable and fine-grained features

Selectively maintaining information is an essential function of visual working memory (VWM). Recent VWM studies have mainly focused on selective maintenance of objects, leaving the mechanisms of selectively maintaining an object's feature in VWM unknown. Based on the interactive model of perception and VWM, we hypothesized that there are distinct selective maintenance mechanisms for objects containing fine-grained features versus objects containing highly discriminable features. To test this hypothesis, we first required participants to memorize a dual-feature object (colored simple shapes vs. colored polygons), and informed them about the target feature via a retro-cue. Then a visual search task was added to examine the fate of the irrelevant feature. The selective maintenance of an object's feature predicted that the irrelevant feature should be removed from the active state of VWM and should not capture attention when presented as a distractor in the visual search task. We found that irrelevant simple shapes impaired performance in the visual search task (Experiment 1). However, irrelevant polygons did not affect visual search performance (Experiment 2), and this could not be explained by decay of polygons (Experiment 3) or by polygons not capturing attention (Experiment 4). These findings suggest that VWM adopts dissociable mechanisms to selectively maintain an object's feature, depending on the feature's perceptual characteristics.

The differential impact of face distractors on visual working memory across encoding and delay stages

External distractions often occur when information must be retained in visual working memory (VWM)-a crucial element in cognitive processing and everyday activities. However, the distraction effects can differ if they occur during the encoding rather than the delay stages. Previous research on these effects used simple stimuli (e.g., color and orientation) rather than considering distractions caused by real-world stimuli on VWM. In the present study, participants performed a facial VWM task under different distraction conditions across the encoding and delay stages to elucidate the mechanisms of distraction resistance in the context of complex real-world stimuli. VWM performance was significantly impaired by delay-stage but not encoding-stage distractors (Experiment 1). In addition, the delay distraction effect arose primarily due to the absence of distractor process at the encoding stage rather than the presence of a distractor during the delay stage (Experiment 2). Finally, the impairment in the delay-distraction condition was not due to the abrupt appearance of distractors (Experiment 3). Taken together, these findings indicate that the processing mechanisms previously established for resisting distractions in VWM using simple stimuli can be extended to more complex real-world stimuli, such as faces.

Temporal integration of target features across and within trials in the attentional blink

Attentional blink research has typically investigated attentional limitations in multiple target processing. The current study investigated the temporal integration of target features in the attentional blink. Across two experiments, we demonstrated that the orientation estimations of individual target items in the attentional blink paradigm were systematically biased. Specifically, there was evidence for both within- and across-trial biases, revealing a general bias towards previously presented stimuli. Moreover, both biases were found to be more salient for targets suffering from the attentional blink. The current study is the first to demonstrate an across-trial bias in responses in the attentional blink paradigm. This set of findings is in line with the literature, suggesting that the human visual system can implicitly summarize information presented over time, which may lead to biases. By investigating temporal integration in the attentional blink, we have been able to address the modulatory role of attention on biases imposed by the implicit temporal effects in estimation tasks. Our findings may inform future research on attentional blink, serial dependence, and ensemble perception.

Sustained attention required for effective dimension-based retro-cue benefit in visual working memory

In visual working memory (VWM) tasks, participants' performances can be improved through the use of dimension-based retro-cues, which direct internal attention to prioritize a particular dimension (e.g., color or orientation) of VWM representations even after the stimuli disappear. This phenomenon is known as the dimension-based retro-cue benefit (RCB). The present study investigates whether sustained attention is required for the dimension-based RCB by inserting interference or interruption between the retro-cue and the test array to distract attention. We tested the effects of perceptual interference or cognitive interruption on dimension-based RCB when the interference (Experiments 1 and 2 with masks) or interruption (Experiments 3 and 4 with an odd-even task) occurred concurrently with the stages for the maintenance of prioritized information (long cue-and-interference/interruption interstimulus interval, e.g., Experiments 1 and 3) or the deployment of attention (short cue-and-interference/interruption interstimulus interval, e.g., Experiments 2 and 4). Our results demonstrate that perceptual interference or cognitive interruption attenuates the dimension-based RCB. These findings suggest that sustained attention is necessary for the effective prioritization of a specific dimension of VWM representations.

Neural interactions in working memory explain decreased recall precision and similarity-based feature repulsion

Over the last several years, the study of working memory (WM) for simple visual features (e.g., colors, orientations) has been dominated by perspectives that assume items in WM are stored independently of one another. Evidence has revealed, however, systematic biases in WM recall which suggest that items in WM interact during active maintenance. In the present study, we report two experiments that replicate a repulsion bias between metrically similar colors during active storage in WM. We also observed that metrically similar colors were stored with lower resolution than a unique color held actively in mind at the same time. To account for these effects, we report quantitative simulations of two novel neurodynamical models of WM. In both models, the unique behavioral signatures reported here emerge directly from laterally-inhibitory neural interactions that serve to maintain multiple, distinct neural representations throughout the WM delay period. Simulation results show that the full pattern of empirical findings was only obtained with a model that included an elaborated spatial pathway with sequential encoding of memory display items. We discuss implications of our findings for theories of visual working memory more generally.

The role of processing efficiency and selection history in the limit of visual awareness in shape perception

A growing body of research indicates that the limit in instant conscious awareness, or the unit of access, for some object features such as color, orientation, and direction of motion is more than one. In four experiments we explored the roles of processing efficiency and selection history in shape perception. Two targets, which were geometric shapes (less efficient) or alphabet letters (more efficient), were shown simultaneously or sequentially. The task was to judge whether a test probe matched one of the targets. In different experiments, the two types of trials were presented in separate blocks, interleaved couplets, or randomly within the same block during testing but regrouped in data analyses such that the same type of trials was either repeated or not repeated. Accuracy was higher in the sequential than simultaneous trials for geometric shapes, but not for upright letters, when the same trial type was blocked or in the repeated condition. These results suggest that processing efficiency and selection history both play a role in the unit of access in shape perception. They also underscore the flexibility of the visual system, which uses different factors to maximize conscious visual perception at a given time.

Little Support for Discrete Item Limits in Visual Working Memory

Some theorists argue that working memory is limited to a discrete number of items and that additional items are not encoded at all. Adam et al. (2017) presented evidence supporting this hypothesis: Participants reproduced visual features of up to six items in a self-chosen order. After the third or fourth response, error distributions were indistinguishable from guessing. I present four experiments with young adults (each N = 24) reexamining this finding. Experiment 1 presented items slowly and sequentially. Experiment 2 presented them simultaneously but longer than in the experiments of Adam et al. Experiments 3 and 4 exactly replicated one original experiment of Adam et al. All four experiments failed to replicate the evidence for guessing-like error distributions. Modeling data from individuals revealed a mixture of some who do and others who do not produce guessing-like distributions. This heterogeneity increases the credibility of an alternative to the item-limit hypothesis: Some individuals decide to guess on hard trials even when they have weak information in memory.

A major role for retrieval and/or comparison in the set-size effects of change detection

Set-size effects in change detection have been attributed to capacity limits in a variety of processes, including perception, memory encoding, memory storage, memory retrieval, comparison, and decision. In this study, we investigated the locus of the effect of increasing set size from 1 to 2. The task was to detect a 90 degree change in the orientation of 1 or 2 briefly presented Gabor patterns in noise. To measure purely attentional effects and not another phenomena, such as crowding, a precue was used to manipulate relevant set size while keeping the display constant. The locus of the capacity limit was determined by varying when observers were cued to a single relevant stimulus. To begin, we measured the baseline set-size effect for change detection. Next, a dual-task procedure and a 100% valid postcue was added to test for an effect of decision: This modification did not reliably change the set-size effects. In the critical experiments, a 100% valid cue was provided during the retention interval between displays, or only one stimulus was presented in the second display (local recognition). For both of these conditions, there was only a relatively small set-size effect. These results are consistent with the bulk of capacity limits being in memory retrieval or comparison and not in perception, memory encoding, or memory storage.

A direct neural measure of variable precision representations in visual working memory

Visual working memory (VWM) is an active representation enabling the manipulation of item information even in the absence of visual input. A common way to investigate VWM is to analyze the performance at later recall. This approach, however, leaves uncertainties about whether the variation of recall performance is attributable to item encoding and maintenance or to the testing of memorized information. Here, we record the contralateral delay activity (CDA), an established electrophysiological measure of item storage and maintenance, in human subjects performing a delayed orientation precision estimation task. This allows us to link the fluctuation of recall precision directly to the process of item encoding and maintenance. We show that for two sequentially encoded orientation items, the CDA amplitude reflects the precision of orientation recall of both items, with higher precision being associated with a larger amplitude. Furthermore, we show that the CDA amplitudes for the items vary independently from each other, suggesting that the precision of memory representations fluctuates independently.NEW & NOTEWORTHY The present work demonstrates for the first time that the contralateral delay activity (CDA), an online electrophysiological measure of the number of representations maintained in memory, is also a reliable measure of the precision of memory representations. Furthermore, we show that the CDA fluctuates independently for individual items held in memory, thereby providing unambiguous direct neurophysiological support for independently fluctuating memory representations.

Temporally coherent perturbation of neural dynamics during retention alters human multi-item working memory

Temporarily storing a list of items in working memory (WM), a fundamental ability in cognition, has been posited to rely on the temporal dynamics of multi-item neural representations during retention. However, the causal evidence, particularly in human subjects, is still lacking, let alone WM manipulation. Here, we develop a novel "dynamic perturbation" approach to manipulate the relative memory strength of WM items held in human brain, by presenting temporally correlated luminance sequences during retention to interfere with the multi-item neural dynamics. Six experiments on more than 150 subjects confirm the effectiveness of this WM manipulation approach. A computational model combining continuous attractor neural network (CANN) and short-term synaptic plasticity (STP) principles further reproduces all the empirical findings. The model reveals that the "dynamic perturbation" modifies the synaptic efficacies of WM items through STP principles, eventually leading to changes in their relative memory strengths. Our results support the causal role of temporal dynamics of neural network in mediating multi-item WM, and offer a promising, purely bottom-up approach to manipulate WM.

The two-stage process in visual working memory consolidation

Two hypotheses have been proposed to explain the formation manner for visual working memory (VWM) representations during the consolidation process: an all-or-none process hypothesis and a coarse-to-fine process hypothesis. However, neither the all-or-none process hypothesis nor the coarse-to-fine process hypothesis can stipulate clearly how VWM representations are formed during the consolidation process. In the current study, we propose a two-stage process hypothesis to reconcile these hypotheses. The two-stage process hypothesis suggests that the consolidation of coarse information is an all-or-none process in the early consolidation stage, while the consolidation of detailed information is a coarse-to-fine process in the late consolidation stage. By systematically manipulating the encoding time of memory stimuli, we asked participants to memorize one (Experiment 1) or two (Experiment 2) orientations in different encoding time intervals. We found that the memory rate increased linearly as the encoding time increased. More importantly, VWM precision remained constant when the encoding time was short, while the precision increased linearly as the encoding time increased when the encoding time was sufficient. These results supported the two-stage process hypothesis, which reconciles previous conflicting findings in the literature.

Negative emotional state modulates visual working memory in the late consolidation phase

Although a considerable literature has grown up around the interactions between emotional state and visual working memory (VWM) performance, the mechanism underlying the impact of the negative emotional state on VWM remains unclear. The present study aimed to test whether the influence of emotional state is related to the early phase or late phase of VWM consolidation process. Across three experiments, we found that the negative emotional state did not affect VWM performance when the presentation time of stimuli was short. However, when the presentation time was long, the negative emotional state increased the VWM precision and reduced the VWM number. According to the two-phase model proposed by Ye et al. (2017. A two-phase model of resource allocation in visual working memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 43(10), 1557-1566. doi: 10.1037/xlm0000376), the results suggested that negative emotional state could affect the late phase of resource allocation in VWM consolidation process, but it has no impact on the early consolidation phase. The findings from this study make important contributions to the current literature regarding the emotional modulation of VWM.

Sequential Presentation Protects Working Memory From Catastrophic Interference

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map-like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism.

A Simple, Biologically Plausible Feature Detector for Language Acquisition

Language has a complex grammatical system we still have to understand computationally and biologically. However, some evolutionarily ancient mechanisms have been repurposed for grammar so that we can use insight from other taxa into possible circuit-level mechanisms of grammar. Drawing upon recent evidence for the importance of disinhibitory circuits across taxa and brain regions, I suggest a simple circuit that explains the acquisition of core grammatical rules used in 85% of the world's languages: grammatical rules based on sameness/difference relations. This circuit acts as a sameness detector. “Different” items are suppressed through inhibition, but presenting two “identical” items leads to inhibition of inhibition. The items are thus propagated for further processing. This sameness detector thus acts as a feature detector for a grammatical rule. I suggest that having a set of feature detectors for elementary grammatical rules might make language acquisition feasible based on relatively simple computational mechanisms.

Working memory capacity affects trade-off between quality and quantity only when stimulus exposure duration is sufficient: Evidence for the two-phase model

The relation between visual working memory (VWM) capacity and attention has attracted much interest. In this study, we investigated the correlation between the participants’ VWM capacity and their ability to voluntarily trade off the precision and number of items remembered. The two-phase resource allocation model proposed by Ye et al. (2017) suggests that for a given set size, it takes a certain amount of consolidation time for an individual to control attention to adjust the VWM resources to trade off the precision and number. To verify whether trade-off ability varies across VWM capacity, we measured each individual’s VWM capacity and then conducted a colour recall task to examine their trade-off ability. By manipulating the task requirement, participants were instructed to memorise either more colours in a low-precision way or fewer colours in a high-precision way. We conducted two experiments by adjusting stimulus duration to be longer than predicted critical value (Experiment 1) and duration shorter than predicted critical value (Experiment 2). While the results of Experiment 1 showed a positive correlation between the VWM capacity and trade-off ability, the results of Experiment 2 showed a lack of such correlation. These results are consistent with the prediction from the two-phase model.

Parallel consolidation into visual working memory results in reduced precision representations

Information can be consolidated into visual working memory in parallel, i.e. two items can be consolidated in the same time required to consolidate one. However, while motion direction items consolidated in parallel are encoded at a reduced precision, no such reduction has been reported for colour. Here we examine two possible explanations for the inconsistency between the phenomena associated with consolidating these features in parallel: i) that reduced precision can only be detected when more than two colour items are consolidated in parallel, or ii) that the exposure duration used in previous studies was too long, allowing observers serially consolidate items. Our results show that (like motion direction) colour items consolidated in parallel are encoded at a reduced precision and the critical feature for detecting this phenomenon is the exposure duration. Furthermore, we demonstrate that this process is limited to two items. These findings indicate a general principle of consolidation into visual working memory, that is, a trade-off between the number of items consolidated in parallel and the precision at which they are encoded.

The bilateral field advantage effect in memory precision

Previous research has demonstrated that visual working memory performance is better when visual items are allocated in both left and right visual fields than within only one hemifield. This phenomenon is called the bilateral field advantage (BFA). The BFA is thought to be driven by an enhanced probability of storage, rather than by greater precision. In the present experiments, we sought to test whether the BFA can also extend to precision when the parameters of the task are modified. Using a moderate number of to-be-remembered items and 400 ms presentation time, we found better precision in the bilateral condition than in the unilateral condition. The classic BFA was still found in the form of an enhanced probability of storage, when presentation time was 200 ms. Thus, the BFA appears to convey both enhanced precision and greater probability of storage. The BFA is most likely due to the allocation of more attentional resources, when items are presented in both left and right visual fields.

The bandwidth of VWM consolidation varies with the stimulus feature: Evidence from event-related potentials

Our previous work suggests that 2 colors can be consolidated into visual short-term memory (VSTM) in parallel without a loss of memory precision, whereas consolidation of 2 orientations is performed in a strictly serial manner. Those experiments compared VSTM performance for simultaneously and sequentially presented stimuli. However, there is still controversy about whether the bandwidth for consolidation is determined by the type of information. To further investigate this issue, here we measured electroencephalography while participants attempted to consolidate 1, 2 or 4 simultaneously presented colors (Experiment 1) or orientations (Experiment 2) under limited presentation times. We used the contralateral delay activity (CDA) as an electrophysiological marker of the number of items that were consolidated. For colored stimuli, the CDA amplitude increased between set-size 1 and 2 but did not further increase for set size 4. By contrast, for orientation, the CDA amplitude remained at the set size 1 amplitude as set size increased to 2 or 4 items. Furthermore, in a long exposure duration (300 ms) condition that did not limit the consolidation process, the CDA amplitude pattern indicated that VSTM capacity is limited to about 3 colored items and about 2 orientation items in our paradigm. Thus, the CDA effects observed in the short presentation time was not limited by VSTM storage, but rather by consolidation. These results are consistent with our previous behavioral research and suggest that the bandwidth of VSTM consolidation is determined by the stimulus feature. (PsycINFO Database Record

Central attention is serial, but midlevel and peripheral attention are parallel-A hypothesis

In this brief review, we argue that attention operates along a hierarchy from peripheral through central mechanisms. We further argue that these mechanisms are distinguished not just by their functional roles in cognition, but also by a distinction between serial mechanisms (associated with central attention) and parallel mechanisms (associated with midlevel and peripheral attention). In particular, we suggest that peripheral attentional deployments in distinct representational systems may be maintained simultaneously with little or no interference, but that the serial nature of central attention means that even tasks that largely rely on distinct representational systems will come into conflict when central attention is demanded. We go on to review both the behavioral and neural evidence for this prediction. We conclude that even though the existing evidence mostly favors our account of serial central and parallel noncentral attention, we know of no experiment that has conclusively borne out these claims. As such, this article offers a framework of attentional mechanisms that will aid in guiding future research on this topic.

A two-phase model of resource allocation in visual working memory

Two broad theories of visual working memory (VWM) storage have emerged from current research, a discrete slot-based theory and a continuous resource theory. However, neither the discrete slot-based theory or continuous resource theory clearly stipulates how the mental commodity for VWM (discrete slot or continuous resource) is allocated. Allocation may be based on the number of items via stimulus-driven factors, or it may be based on task demands via voluntary control. Previous studies have obtained conflicting results regarding the automaticity versus controllability of such allocation. In the current study, we propose a two-phase allocation model, in which the mental commodity could be allocated only by stimulus-driven factors in the early consolidation phase. However, when there is sufficient time to complete the early phase, allocation can enter the late consolidation phase, where it can be flexibly and voluntarily controlled according to task demands. In an orientation recall task, we instructed participants to store either fewer items at high-precision or more items at low-precision. In 3 experiments, we systematically manipulated memory set size and exposure duration. We did not find an effect of task demands when the set size was high and exposure duration was short. However, when we either decreased the set size or increased the exposure duration, we found a trade-off between the number and precision of VWM representations. These results can be explained by a two-phase model, which can also account for previous conflicting findings in the literature. (PsycINFO Database Record

Orientation Probability and Spatial Exogenous Cuing Improve Perceptual Precision and Response Speed by Different Mechanisms

We are faster and more accurate at detecting frequently occurring objects than infrequent ones, just as we are faster and more accurate at detecting objects that have been spatially cued. Does this behavioral similarity reflect similar processes? To evaluate this question we manipulated orientation probability and exogenous spatial cuing within a single perceptual estimation task. Both increased target probability and spatial cuing led to shorter response initiation times and more precise perceptual reports, but these effects were additive. Further, target probability changed the shape of the distribution of errors while spatial cuing did not. Different routes and independent mechanisms could lead to changes in behavioral measures that look similar to each other and to ‘attentional’ effects.

Limited capacity for memory tasks with multiple features within a single object

Memory for multiple features might be limited by the number of features, the number of objects, or both. To focus on the role of features, we tested memory for a variable number of features within a single object. Subjects studied a single ellipse that varied in four features: size, orientation, contrast, and position. We conducted two experiments that differed in how memory was tested. If performance is limited only by the number of objects to be remembered, there should be no effect of the number of relevant features within a single object. Instead, for both experiments, the proportion correct was lower when four features had to be remembered rather than one. The magnitude of these effects varied with the details of the two experiments. Although similar results have been reported for experiments using multiple objects, the present experiments are some of the first to have demonstrated such an effect for a single object. This result is inconsistent with theories in which visual memory has a discrete limit on the number of stored objects, and no limit on the stored features within an object. Instead, it seems likely that objects and features both play roles in limiting performance in memory tasks.

The privileged role of location in visual working memory

Reports have conflicted about the possible special role of location in visual working memory (WM). One important question is: Do we maintain the locations of objects in WM even when they are irrelevant to the task at hand? Here we used a continuous response scale to study the types of reporting errors that participants make when objects are presented at the same or at different locations in space. When several objects successively shared the same location, participants exhibited a higher tendency to report features of the wrong object in memory; that is, they responded with features that belonged to objects retained in memory but not probed at retrieval. On the other hand, a similar effect was not observed when objects shared a nonspatial feature, such as color. Furthermore, the effect of location on reporting errors was present even when its manipulation was orthogonal to the task at hand. These findings are consistent with the view that binding together different nonspatial features of an object in memory might be mediated through an object’s location. Hence, spatial location may have a privileged role in WM. The relevance of these findings to conceptual models, as well as to neural accounts of visual WM, is discussed.

The bandwidth of consolidation into visual short-term memory (VSTM) depends on the visual feature

We investigated the nature of the bandwidth limit in the consolidation of visual information into visual short-term memory. In the first two experiments, we examined whether previous results showing differential consolidation bandwidth for color and orientation resulted from methodological differences by testing the consolidation of color information with methods used in prior orientation experiments. We briefly presented two color patches with masks, either sequentially or simultaneously, followed by a location cue indicating the target. Participants identified the target color via button-press (Experiment 1) or by clicking a location on a color wheel (Experiment 2). Although these methods have previously demonstrated that two orientations are consolidated in a strictly serial fashion, here we found equivalent performance in the sequential and simultaneous conditions, suggesting that two colors can be consolidated in parallel. To investigate whether this difference resulted from different consolidation mechanisms or a common mechanism with different features consuming different amounts of bandwidth, Experiment 3 presented a color patch and an oriented grating either sequentially or simultaneously. We found a lower performance in the simultaneous than the sequential condition, with orientation showing a larger impairment than color. These results suggest that consolidation of both features share common mechanisms. However, it seems that color requires less information to be encoded than orientation. As a result two colors can be consolidated in parallel without exceeding the bandwidth limit, whereas two orientations or an orientation and a color exceed the bandwidth and appear to be consolidated serially.

Visual working memory capacity for color is independent of representation resolution

Background

The relationship between visual working memory (VWM) capacity and resolution of representation have been extensively investigated. Several recent ERP studies using orientation (or arrow) stimuli suggest that there is an inverse relationship between VWM capacity and representation resolution. However, different results have been obtained in studies using color stimuli. This could be due to important differences in the experimental paradigms used in previous studies.

Methodology/Principal Findings

We examined whether the same relationship between capacity and resolution holds for color information. Participants performed a color change detection task while their electroencephalography was recorded. We manipulated representation resolution by asking participants to detect either a salient change (low-resolution) or a subtle change (high-resolution) in color. We used an ERP component known as contralateral delay activity (CDA) to index the amount of information maintained in VWM. The result demonstrated the same pattern for both low- and high-resolution conditions, with no difference between conditions.

Conclusions/Significance

This result suggests that VWM always represents a fixed number of approximately 3–4 colors regardless of the resolution of representation.