**There are different opinions about the roles of local interactions and central processing capacity in visual search. This study attempts to clarify the problem using a new version of relevant set cueing. A central precue indicates two symmetrical segments (that may contain a target object) within a circular array of objects presented briefly around the fixation point. The number of objects in the relevant segments, and density of objects in the array were varied independently. Three types of search experiments were run: (a) search for a simple visual feature (color, size, and orientation); (b) conjunctions of simple features; and (c) spatial configuration of simple features (rotated Ts). For spatial configuration stimuli, the results were consistent with a fixed global processing capacity and standard crowding zones. For simple features and their conjunctions, the results were different, dependent on the features involved. While color search exhibits virtually no capacity limits or crowding, search for an orientation target was limited by both. Results for conjunctions of features can be partly explained by the results from the respective features. This study shows that visual search is limited by both local interference and global capacity, and the limitations are different for different visual features.**

^{1}

*d′*(Põder, 2004). The crowding effect is described as a Gaussian function of target–flanker distance (Levi, Klein, & Hariharan, 2002), and set-size affects

*d′*according a power function: where

*d′*

_{1}is

*d′*for set size 1 and no crowding,

*n*is set size,

*b*is a measure of set-size effect,

*a*is maximum crowding effect (when interobject distance drops to 0),

*d*is interobject distance, and

*s*is spatial extent (standard deviation) of Gaussian crowding zone.

*d*′

_{n}) as as a function of local SNR (

*d′*) and set size:

*x*= −0.5, and

_{D}*x*= 0.5, log likelihood ratio (target present /target absent) for a single trial is where

_{T}*x*is noisy internal variable for object

_{i}*i*, and

*σ*is standard deviation of noise. The ideal model selects “target present” when

*L*> 0, and “target absent” otherwise.

*d′*was calculated for the yes–no search. The results follow slightly curved lines in log-log coordinates. The simulation results can be very precisely (

_{n}*R*

^{2}> 0.999) approximated by a relatively simple polynomial formula: In the model fitting procedure, this approximation was used rather than running simulations at each iteration.

*d′*) should be larger for conditions with larger noise (lower performance). Therefore, assuming that crowding increases noise, the set-size effects should increase with crowding. The present data indicate that there is rather an opposite trend, which may indicate that usual SDT assumptions do not hold in crowding conditions (Palmer, 1994; Palmer et al., 2000). A simple modification may, at least partly, correct the problem. Crowding has been frequently described as an obligatory pooling of signals within a built-in integration field (Parkes et al., 2001). Thus, it is possible that, aside from adding a noise, crowding extends the effective set size, including all the relevant and irrelevant objects within a crowding zone. For example, when two relevant objects are densely surrounded by irrelevant ones, the effective set size might be 4 or 6, and it does not change much when changing the relevant set size only.

*n*was replaced with an effective set-size

*n*. It was supposed that instead of an “ideal” window of spatial attention (with weight of one in the positions of relevant objects, and zero elsewhere), the observer had to use a blurred window—the ideal one convolved with a Gaussian filter with a standard deviation

_{e}*s*. Effective set size was increased in proportion to irrelevant objects that were sampled by that window. where

*n*is the number of relevant objects,

*N*is the number of displayed objects, and

*w*and

_{i}*w*are the weights of the attentional window at the positions of objects

_{j}*i*and

*j*. This pooling mechanism does not need additional free parameters as its effect is determined by the spatial parameter

*s*already present in the original crowding mechanism.

*s*= 0.2E, which corresponds to usual crowding zone 0.5E, and minimum interobject distance

*d*= 0.13E, this calculation yields effective set sizes 7.7, 8.5, and 11.6, for relevant set sizes 2, 4, and 8, respectively. When

*d*> 2.5

*s*, the pooling effect virtually disappears (

*n*≈

_{e}*n*).

*b*) for capacity limitation, two (

*a*and

*s*) for crowding effect, and one (

*d′*

_{1}) for overall level of performance. The model predicts

*d′*s for yes–no visual search task. The predicted

*d′*s can be converted into the predictions of unbiased proportion correct where Φ is standard normal distribution function (Macmillan & Creelman, 1991).

*H*and

*F*are proportions of hits and false alarms, Φ is standard normal distribution function, and

*z*is the inverse of the normal distribution function. An individual data set consisted usually of 18 proportions correct. MS Excel Solver was used to find maximum likelihood parameters of the model by minimizing the likelihood ratio statistic

*G*.

^{2}This model assumes that an observer can attend a fixed number of objects (

*k*) in each trial. In order to account for the imperfect performance for small set sizes, this capacity limitation was combined with noisy percepts and ideal decision making. When relevant set size does not exceed the capacity limit (

*n*≤

*k*), the model behaves like unlimited capacity SDT model (

*b*= 0). With

*n*>

*k*, proportion correct (corrected for guessing) drops in proportion to

*k/n*. Thus, the proportion correct is This model also has four free parameters. It also included both crowding mechanisms.

*p*< 0.05 (seven had

*p*-values less than 0.01).

*p*< 10

^{−6}for unlimited capacity,

*p*< 10

^{−12}for no crowding, and

*p*< 0.05 for no noise crowding model). The limited capacity SDT model, the model without spatial pooling, and the serial model have equal numbers of parameters. For these models, differences in

*G*-statistic are equivalent to the differences in Akaike information criterion (AIC). Although the limited capacity SDT model has the minimum

*G*-statistic, the observed differences (1.7 and 2.4) are too small to exclude the other two models.

*b*is a measure of processing capacity limitations. It shows how much the relevant set size affects precision of individual object representations:

*b*= 0 for independent processing (unlimited capacity),

*b*= 1 for the fixed capacity (sample size) model, where variance of noise of the internal representations is proportional to set size, and

*b*≈ 2.0 for the serial search model. Crowding is traditionally characterized by critical distance—the maximum extent of crowding zone, in eccentricity units. Parameter

*s*is standard deviation of the assumed crowding zone with Gaussian profile. In order to simplify comparison with crowding studies, it is scaled by factor 2.5 that results in a critical distance measure, where crowding effect drops below 0.05 of its maximum value.

*p*< 0.01) and size (

*p*< 0.01); rotated Ts differed also from orientation (

*p*< 0.05) and color–size conjunction (

*p*< 0.01). For crowding distance, the only significant difference was between orientation and color searches (

*p*< 0.01). There appears to be a positive correlation between capacity limitations and crowding at the level of search conditions (Figure 4B), which is, however, statistically not significant.

*b*was larger than the expected range of 0 to 1. For the simple feature search, it was mostly larger than 0, and for an example of complex search, rotated Ts, it was about 1.5. One possible explanation might be a different efficiency of the relevant set selection for different set sizes. If spatial selection was very efficient with two relevant objects and not so efficient with eight objects, the data should exhibit some extra set-size effect. A slightly better performance in the condition without irrelevant objects, when spatial selection is not needed (set size 8, maximum interobject distance), seems to support this hypothesis. These data also suggest that selection explains relatively small part of the total set-size effect.

*a*in the model with two crowding mechanisms would be problematic because it represents only a part of crowding effect associated with increase of noise. It is also affected by a trade-off between the two mechanisms that is not well understood. Therefore, the parameters of crowding from the simpler model, with only the noise mechanism, are shown in Figure 4C. The crowding amplitude

*a*varies from 0.15 to 19.0, with a median of 4.3. This median effect corresponds to about fivefold drop of

*d′*as compared to the uncrowded conditions. There were no significant differences in this parameter across the search tasks.

*d′*

_{1}is fairly uninteresting. It is primarily determined by target–distractor differences that were selected in the pilot experiments. Its variance may reflect the accuracy of these adjustments. More specifically, as we tried to equalize performance for the simplest condition of set-size 2, the respective

*d′*,

*d′*

_{2}= 3.4, standard deviation 0.5, and there were no significant differences across the search tasks.

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^{1}Sample-size model, a classic of SDT-based fixed capacity, predicts a drop of

*d′*according to the inverse square root of the set size. Thus, the predicted set-size effect in terms of log-log slope is roughly two times stronger for a serial model as compared to asample-size model, at least within some linear range of

*d′*.