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Article  |   April 2011
Locus of spatial attention determines inward–outward anisotropy in crowding
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Journal of Vision April 2011, Vol.11, 1. doi:10.1167/11.4.1
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      Yury Petrov, Olga Meleshkevich; Locus of spatial attention determines inward–outward anisotropy in crowding. Journal of Vision 2011;11(4):1. doi: 10.1167/11.4.1.

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Abstract

It has long been known that an outward mask is much more disruptive than an inward mask in crowding (H. Bouma, 1973). We show that the locus of attention strongly affects this inward–outward anisotropy, removing it in some conditions and reversing it in others. In a 2AFC paradigm, subjects identified whether a high-contrast Gabor target of a given orientation was presented left or right of fixation. When a fixed eccentricity (8°) was used, the outward plaid mask produced much stronger crowding than the inward mask. When 7°, 8°, and 9° eccentricities were interleaved within the same run, diffusing attention, the inward and outward masks produced the same amount of crowding for all three eccentricities. When target identification was contingent on a foveal cue, biasing attention inward, the inward mask produced stronger crowding. Finally, a new contrast-detection paradigm was used to demonstrate that attention is generally mislocalized outward of the target, which may explain the commonly observed anisotropy in crowding. Our results suggest that spatial attention is intimately involved in the mechanism of crowding.

Introduction
Crowding is a common phenomenon in peripheral vision. Stimuli, clearly visible when presented alone, appear scrambled when presented next to each other. Our inability to read without employing central vision (try to read two or more lines above where your eyes are) is a striking example of crowding. 
Crowding has been studied since the early 1960s (Stuart & Burian, 1962), but its physiological basis is still not understood. In our recent study, we showed that crowding cannot be reduced to surround suppression (Petrov, Popple, & McKee, 2007). In particular, we demonstrated that unlike suppression, crowding is strongly asymmetric along the radial direction: a mask outward of the target crowds more strongly than the same mask positioned inward, above or below. Bouma (1973) was the first to study this peculiar property of crowding. He noticed that it is much easier to recognize the initial letter of a word when the word was presented to the left of fixation and the final letter when the word was presented to the right of fixation; in short, the outermost letter was most easily identified. Note that this is counterintuitive: one would expect to see the letter best when it is closest to fixation. This property of crowding has since been observed in numerous studies (e.g., Bex, Dakin, & Simmers, 2003; Chastain, 1982; Krumhansl, 1977; Legge, Mansfield, & Chung, 2001; Wolford & Hollingsworth, 1974). 
Besides outward asymmetry, crowding has other spatial asymmetries. Crowding is (on the average) stronger in the upper visual field (He, Cavanagh, & Intriligator, 1996), stronger along the radial direction (Toet & Levi, 1992), and, other factors taken into account, somewhat stronger for items arranged horizontally (Feng, Jiang, & He, 2007). The most pronounced of these other asymmetries is the radial–tangential asymmetry. Crowding is 2–2.5 times stronger for items arranged along the radial (meridional) direction than along the tangential (isoeccentric) direction (Toet & Levi, 1992). Still, this is a weak effect compared to the outward asymmetry of crowding. The outward mask is, on the average, 4 times more disruptive than the inward mask in crowding (Petrov et al., 2007). Besides, radial–tangential asymmetries are widespread in the peripheral vision and may merely reflect generic organization of early visual processing (e.g., V1 architecture). Examples of such generic asymmetry include grating resolution and visibility (Rovamo, Virsu, Laurinen, & Hyvarinen, 1982), curvature detection (Fahle, 1986), and motion detection (Scobey & van Kan, 1991). In our recent study, we demonstrated that, like crowding, surround suppression is significantly stronger in the radial direction (Petrov et al., 2007). Surround suppression is the inhibition of contrast sensitivity by a surround mask, and in many aspects, surround suppression is similar to crowding but not in the asymmetry that is specific to crowding. Thus, the radial–tangential anisotropy is rather unspecific, which makes it a poor choice for probing links between crowding and attention. On the contrary, the outward asymmetry appears to be a hallmark property of crowding. 
Because crowded features remain visible but ambiguous (Pelli, Palomares, & Majaj, 2004), the prevailing explanation for crowding is that it involves some form of spatial pooling, where the individual feature information is pooled over a local area of visual field (Levi, Klein, & Hariharan, 2002; Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Pelli et al., 2004). A conceptually similar “mislocalization” explanation was originally proposed by Krumhansl (1977) and Wolford (1975). It remains unknown what causes the spatial pooling itself. The existing proposals fall into three broad categories: 
  1.  
    “Neuronal,” due to larger size of V1 receptive fields in the periphery (Flom, Weymouth, & Kahneman, 1963), larger size of V1 hypercolumns in the periphery (Levi, Klein, & Aitsebaomo, 1985), long-range horizontal connections resulting in surround suppression in the periphery (Fitzpatrick, 2000; Gilbert, 1998), or imperfect co-registration of feature maps in the periphery (Neri & Levi, 2006). The common assumption is that once features fall within the same receptive field (including its “extra-classical” suppressive outskirts), the features interfere with each other and cannot be processed separately.
  2.  
    “Conceptual,” due to some high-order grouping process particularly active in the periphery, including texture formation (Orbach & Wilson, 1999; Parkes et al., 2001; Wilkinson, Wilson, & Ellemberg, 1997) or more general Gestalt-like grouping (Banks, Larson, & Prinzmetal, 1979; Estes, Allmeyer, & Reder, 1976).
  3.  
    “Attentional,” due to reduced spatial resolution of attention in the periphery (He et al., 1996; Intriligator & Cavanagh, 2001).
The pooling proposals are usually non-specific about what happens to the signal, which makes it harder to test them. One common assumption is that the location of individual features is lost (Krumhansl, 1977; Wolford, 1975): when experiencing crowding, we retain the “what” part of the signal but not the “where” part. There have been few direct attempts to test the validity of this prediction, but the results are not conclusive (Nandy & Tjan, 2007; Popple, Petrov, & Levi, 2006). The aim of our recent study (Petrov & Popple, 2007) was to determine what kind of information is lost in crowding. We used Gabor stimuli, which are more tractable than letters. This allowed us to analyze confusion patterns arising in crowding and demonstrate that crowding cannot be explained by a loss of individual feature information, such as individual location (a “where” loss). We argued, instead, that local feature contrast is the only information available in crowding. For example, in our study where subjects simultaneously identified individual slants (left or right) of three juxtaposed Gabor patches, only the presence or absence of the slant contrast sites (left–right or right–left) could be identified. Because it is well known that strong feature contrast becomes salient before attention is employed (e.g., Treisman & Gelade, 1980; Wolfe, Cave, & Franzel, 1989), these results support models that explain crowding by some constraints or limitations of attentional resolution. We hypothesize that only feature contrast is preserved in crowding because feature contrast is processed and retained before attention is engaged; visual information is pooled and lost due to the insufficient spatial resolution of attention. Poder (2006) provided more supporting evidence for this hypothesis. He demonstrated that crowding is dramatically reduced when the number of distractors around a (distinctly colored) target is increased. This decrease of crowding with increasing density of masks cannot be easily accounted by any “neuronal” proposal. Poder explains this effect on crowding by the increased saliency of the target. This phenomenon is well known in visual search (e.g., Bacon & Egeth, 1991; Meinecke & Donk, 2002; Sagi & Julesz, 1987). The saliency of the target increases either because of the increased color contrast with the dense background of distractors or because the background items group together to form a texture. 
Chakravarthi and Cavanagh (2007), He et al. (1996), and Intriligator and Cavanagh (2001) studied spatial resolution of visual attention and found multiple similarities between crowding and attention. Based on these similarities, He et al. proposed that crowding occurs when the spatial mechanism of attention is unable to resolve the target from its neighbors in the periphery. The goal of our present study was to thoroughly test this hypothesis. The three steps below define our approach: 
  1.  
    Identify a characteristic property of crowding that can be used to probe the connection between crowding and attention. Based on our prior studies, we propose outward asymmetry of crowding as such a characteristic property.
  2.  
    Explore how manipulations of attention affect crowding, using the outward asymmetry as the principal indicator.
  3.  
    Determine if some intrinsic property of attention (e.g., its outward bias) can explain the characteristic asymmetry of crowding.
Several recent studies have shown that attracting spatial attention by precuing the target location diminishes crowding by improving accuracy of target identification, or reducing the critical distance, or both (Felisberti, Solomon, & Morgan, 2005; Huckauf & Heller, 2002; Scolari, Kohnen, Barton, & Awh, 2007; Strasburger, 2005; Yeshurun & Rashal, 2010). In this study, we explored how spatial cuing affects the outward asymmetry of crowding. Within our experimental paradigm, attention is considered to be a spatial phenomenon. This does not imply that other modes of attention allocation, i.e., object-based (Duncan, 1984; Kahneman, 1973), feature-based (Maljkovic & Nakayama, 1994, 1996; McAdams & Maunsell, 2000), or a combination thereof (Logan, 1996) are irrelevant, but here we focus on the spatial aspect of attention. Although the spotlight and zoom-lens models of attention (Posner, Snyder, & Davidson, 1980; Eriksen & St James, 1986; Eriksen & Yeh, 1985) appear to be useful when discussing our results, our paradigm is not contingent on the validity of these models. We merely assume that various kinds of cuing and stimulus configurations may change the spatial distribution of attention. 
Methods
This section describes methods for Experiments 1 and 2. Methods for Experiment 3 differed significantly and are described separately in the Results and discussion section. 
Stimuli
The stimulus configuration used for the first two experiments is shown in Figure 1. The target was a standard cosine phase Gabor (a sinusoidal grating of period λ in cosine phase windowed by a two-dimensional Gaussian with spatial standard deviation σ = λ/√2) in which ∼1.5 periods of the sinusoidal pattern were visible. The Gabor was slanted ±45° from the vertical; its contrast fixed at 45%. The plaid mask was made of two transparently overlaid Gabor patches. The patches were exact replicas of the target, except that one Gabor patch was rotated by 90°. Contrast of both patches was 45%; the resulting plaid contrast was close to 90%. The separation between the mask and the target was fixed at 4λ. The stimuli were displayed on a gray background and viewed on a linearized 21″ ViewSonic G225f monitor. The display resolution was set to 1600 × 1200 pixels, and for the typical viewing distance of 65 cm, a pixel subtended ∼1 min of arc. 
Figure 1
 
Experimental stimuli were comprised of the Gabor targets and plaid masks. The masks were positioned either (top) inward or (bottom) outward with respect to the Gabor targets.
Figure 1
 
Experimental stimuli were comprised of the Gabor targets and plaid masks. The masks were positioned either (top) inward or (bottom) outward with respect to the Gabor targets.
Subjects
Five observers with normal or corrected visual acuity were tested. Three of the observers were naive to the purpose of the study; all five were experienced psychophysical observers. Observers were trained for a short time (2–5 min) to get acquainted with the stimuli and the task. 
Psychometric procedure
We used a two-alternative forced-choice procedure (2AFC), the stimuli were simultaneously presented at two symmetric locations 8° left and right of a fixation point, and the task was to identify the location where the target Gabor was slanted to the left. Stimulus duration was 100 ms. A fixation cross was displayed at the center of the screen through the whole trial duration. The inward and outward masks were used in separate blocks. The mask was presented at both target locations in a mirror-symmetrical fashion with respect to the fixation cross. 
To measure crowding, the Gabor period λ and, correspondingly, the target size, the mask size, and the target–mask separation all varied according to the adaptive algorithm of Kontsevich and Tyler (1999), until observers were unable to perform the task, which determined a threshold stimulus size (Neri & Levi, 2006). This approach is similar to the “critical spacing” method, the only difference is that here the target and mask sizes vary proportionally to the target–mask separation. This procedure has the advantage of precluding the mask overlapping the target. Instead of using the “critical spacing,” we measured crowding in terms of a crowding factor defined as the ratio of the masked to unmasked size thresholds (λs). Factor 1 corresponded to no crowding. This is a measure of crowding strength instead of crowding extent, but these two measures are, clearly, positively correlated. Both thresholds were measured within the same experimental session to minimize variation of results due to performance fluctuations. Average spatial frequency threshold for the masked condition was approximately 5 cpd. Observers carried out three blocks of 150 trials per block for each condition. Uncertainties of the psychometric thresholds were taken as the maximum of the two: (i) threshold variation calculated from the results of the adaptive algorithm and (ii) threshold variation in between the three experimental blocks. The threshold uncertainties were propagated to the crowding factor, and the resulting uncertainties (1 SEM) are represented by error bars in the figures. 
Results and discussion
The first two experiments described in this section directly tested the hypothesized connection between crowding and attention. We manipulated attention and observed the effects of this manipulation on crowding. The experimental data are shown in Figures 2 and 3. The third experiment showed that attention per se has the same characteristic outward asymmetry as crowding, and the results are presented in Figure 5
Figure 2
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) Focused attention (target at 8° eccentricity). (Right) Diffused attention (targets at 7°, 8°, and 9° eccentricities interleaved, data pooled over the three locations). Error bars represent 1 standard error of the mean (SEM) for the crowding factors.
Figure 2
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) Focused attention (target at 8° eccentricity). (Right) Diffused attention (targets at 7°, 8°, and 9° eccentricities interleaved, data pooled over the three locations). Error bars represent 1 standard error of the mean (SEM) for the crowding factors.
Figure 3
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) No foveal cue (replotted from Figure 2). (Right) Task contingent on a foveal cue. Note the change of scale between the two panels.
Figure 3
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) No foveal cue (replotted from Figure 2). (Right) Task contingent on a foveal cue. Note the change of scale between the two panels.
Experiment 1: Crowding with attention diffused
The goal of this experiment was to study the effect of diffusing attention over a large area around the target. If the inward–outward asymmetry of crowding results from some property of attention allocation, then diffusing attention over a much larger area should make the asymmetry weaker. To this end, we compared crowding for two conditions studied in separate experimental blocks. In the focused attention block, the target always appeared at 8° eccentricity. In the diffused attention block, 7°, 8°, and 9° eccentricities were interleaved within the same run, which forced observers to spread their attention over a large area covering all three eccentric loci. Because the nature of the task allowed subjects to attend to targets in either the left visual field, or the right visual field, or both, different observers could be using different strategies. Consequently, we use the terms “focused” and “diffused” as applied to attention distribution in each visual hemifield. There is accumulating behavioral (Belger & Banich, 1998; Liederman, 1998; Luck, Hillyard, Mangun, & Gazzaniga, 1989) and electrophysiological (Müller & Hübner, 2002; Müller, Malinowski, Gruber, & Hillyard, 2003) evidence that attention can be applied independently to left and right hemifields; therefore, what strategy was chosen by each subject is, possibly, of little importance. 
Figure 2 presents data for five observers. Left and right panels display the crowding factor for focused and diffused attention conditions, respectively. Crowding factors for inward and outward masks are plotted along x- and y-axes, respectively. The diagonal line indicates equally strong crowding for outward and inward masks. For the diffused attention condition, crowding strength did not differ significantly among the three eccentric loci, and the corresponding data were pooled. Each datum represents an individual subject's data. As expected, the outward mask produced significantly stronger crowding for the focused attention condition. This is manifested in all data points except S3 being more than 2 SEM away from the diagonal line. The ratio of outward to inward mask crowding strengths (note that crowding factor 1 corresponds to no crowding) showed significant individual variation, averaging to about 4 among the observers. For the diffused attention condition, crowding by the outward mask decreased while crowding by the inward mask increased for all observers to the effect that the outward mask and the inward mask produced the same amount of crowding (within the experimental error) for all but one observer (S4); even for this observer, the inward–outward anisotropy was much reduced. The results indicate that attention allocation and crowding are closely related: diffusing attention causes crowding for outward and inward masks to level off. 
Experiment 2: Crowding with attention biased to the fovea
In the second experiment, we explored the effect of biasing attention inward with respect to the target. The stimuli and the task were the same as in the previous experiment (focused attention condition), except that the task was made contingent on a foveal cue. The new task was: (i) to observe a 1° bright line slanted 45° left or right off the vertical, which appeared superimposed over the fixation mark for 40 ms, 100 ms prior to the main stimulus appearance, and (ii) indicate on which side of fixation the target Gabor had the same slant (left or right). Note that in Experiment 1 the target was always a left-slanted Gabor. The goal of this manipulation was to bias attention inward (or even retain it within the fovea region) during the stimulus presentation. We chose the 100-ms interval between cue and stimulus onset based on the following considerations: 
  1.  
    300-ms interval is known to maximize the effect of the foveal cue (Cheal & Lyon, 1991); therefore, it is reasonable to assume that 100 ms (or less) after cue onset attention is still engaged in processing the foveal cue and is bound to the foveal region, at least to some extent.
  2.  
    We found that at shorter intervals the experimental task became too hard.
  3.  
    Pilot experiment showed that interval durations from 100 ms to 300 ms produced similar results; we chose the bottom of the range to ensure that observers had the least time to shift their attention to the target area.
Here, we implied that observers had to shift or bias their attention toward the foveal location in order to do the task. It is also conceivable that observers could split attention between the foveal location and the peripheral location(s). Although we cannot completely exclude such scenario, it appears unlikely. Malinowski, Fuchs, and Müller (2007) provide evidence that humans are much less able to split attention within the same hemifield compared to splitting it across two hemifields. 
The target Gabor was shown for 100 ms, the same as in Experiment 1. Crowding factors measured in this experiment for four observers are plotted in the right panel of Figure 3. For comparison, data for the same observers from the previous experiment (the focused attention condition) were replotted in the left panel. The most obvious effect of biasing attention inward was to invert the inward–outward asymmetry of crowding for 3 subjects. The asymmetry was significantly shifted in the same direction for the remaining subject, S3. This change in inward–outward asymmetry resulted primarily from increased crowding by the inward mask. Otherwise, the effects of biasing attention inward were rather idiosyncratic: the crowding produced by the outward mask decreased significantly for observers S1 and S2 but increased for observers S3 and S4. 
Note that because the task in this experiment was contingent on the foveal cue, there could be an additional attentional load as compared to the previous experiment due to the necessity to process both the cue and the target, if these two tasks were not carried out sequentially. This additional factor could influence the results, but because we did not directly compare Experiments 1 and 2, this was not a concern. 
Experiment 3: Outward bias of spatial attention
The results so far suggest that attention allocation plays a major role in crowding. It would be interesting to see whether attention allocation can explain the characteristic inward–outward asymmetry of crowding. 
This experiment focused on the properties of attention allocation per se. The logic of the new paradigm that we used was given as follows. Because focused attention enhances contrast sensitivity in peripheral vision (Pestilli & Carrasco, 2005), the profile of contrast sensitivity around the attended location should mirror the distribution of spatial attention. By measuring the pattern of contrast sensitivity around the attended spot, we will learn about the distribution of attention in its vicinity. The challenge of this approach is that the focus of attention moves, sometimes uncontrollably, when the stimulus changes, or even when the observer expects that a certain change is about to happen. To solve this attention instability problem, we used a novel paradigm—contrast-detection task with covert spatial probing. The idea is simple: we wanted to draw the observer's attention to a certain location and probe contrast sensitivity around this location in a discreet manner, i.e., without alerting the observer to the fact that the target actually appears at slightly different locations. 
To this end, we used two concurrent contrast-detection tasks: one known (open) to the subject and used merely as an attention grabber and one secret and used to probe the resulting attention distribution. No feedback was given for either task. The method of constant stimuli proved to be very advantageous for the open task. A horizontal 5-cpd Gabor target appeared at 8° eccentricity, left or right of a fixation point for 100 ms (see Figure 4). The 5-cpd spatial frequency was chosen to match the average target threshold frequency for Experiments 1 and 2 (focused attention). High-contrast locator lines identified the two target locations at all times. No mask was used in this experiment, because attention rather than crowding was investigated here. The task was to indicate in which of the two locations the target appeared. We intentionally used a wide range of contrasts in the method of constant stimuli, from sub-threshold to significantly above threshold. The obvious supra-threshold targets along with the locator lines enabled us to convince observers to focus their attention at the two designated areas. At the same time, the presence of sub-threshold and near-threshold targets ensured that observers paid close attention to the task. 
Figure 4
 
Stimuli used for Experiment 3. The square (not shown in the actual experiment) indicates the attention attractor Gabor; this target appeared in 2/3 of the trials, and its contrast varied according to the method of constant stimuli protocol. A sub-threshold Gabor appeared in the remaining 1/3 of the trials instead of the attractor Gabor. The test Gabor target was displaced left or right of the 8° location as shown (only one location was used on a given trial).
Figure 4
 
Stimuli used for Experiment 3. The square (not shown in the actual experiment) indicates the attention attractor Gabor; this target appeared in 2/3 of the trials, and its contrast varied according to the method of constant stimuli protocol. A sub-threshold Gabor appeared in the remaining 1/3 of the trials instead of the attractor Gabor. The test Gabor target was displaced left or right of the 8° location as shown (only one location was used on a given trial).
The secret task was the same as the open task, except that the Gabor target contrast was fixed at the same sub-threshold or near-threshold value at all times. The value was chosen individually for each subject in a pilot experiment. The target contrast was considered sub/near threshold if the target detection was between 65 and 70% correct at 8° eccentricity. The target appeared either left or right of the 8° location in increments of 0.3°, i.e., ±0.3°, ±0.6°, ±0.9°, and ±1.2° along the horizontal meridian. The four pairs of offsets were tested in separate blocks. In each block, 2/3 of the trials were randomly allocated for the open 8° task and 1/3 for the secret task with a spatial offset. By interleaving the high-saliency open task with low-saliency secret task, we obscured the occurrence of the offset targets. Even for the informed observer S1, both tasks appeared as a single 8° task, and it was nearly impossible to notice the occurrence of the offset peripheral targets. Uninformed observers S2 and S3 confirmed after the experiment that they did not notice that targets occasionally appeared at unexpected locations. Possibly, the high attentional load required to do the task precluded subjects from consciously registering that occasionally the target locations were offset. Note that if observers had noticed occasional target offsets they would have noticed them more frequently for inward offsets than for outward offsets, because this is where their performance was better (Figure 5). Thus, if anything, this could bias their attention inward, which is opposite to what was observed. 
Figure 5
 
Results of Experiment 3. The Gabor target was presented at different eccentricities, either at the attended location (blue symbols) or inward–outward off the attended 8° location (red symbols). The data were fitted with cubic functions. The difference between the two curves (shown in magenta) was shifted by +0.5 along the y-axis for illustration purposes.
Figure 5
 
Results of Experiment 3. The Gabor target was presented at different eccentricities, either at the attended location (blue symbols) or inward–outward off the attended 8° location (red symbols). The data were fitted with cubic functions. The difference between the two curves (shown in magenta) was shifted by +0.5 along the y-axis for illustration purposes.
Because the tested locations covered 6.8°–9.2° eccentricity range, contrast sensitivity varied from location to location not only due to the sampled distribution of attention but also due to the conventional decrease of sensitivity with eccentricity. In order to account for the eccentricity effect, we carried out a control experiment in which we sampled contrast sensitivity over different eccentricities in an overt fashion. This was a conventional contrast-detection experiment, i.e., trials did not include the high-salience attractor task. The sub- or near-threshold Gabor target, previously used in the secret task, in this experiment appeared always at a given spatial location clearly indicated by the localizer lines. Different locations were tested in separate blocks, to ensure that attention was focused on one location only in each block. 
Figure 5 shows the results of the main and the control experiments for three observers. S1 and S2 carried out about 1,200 trials per datum, while S3 carried out about 450 trials, which explains larger error bars for this subject. The proportion of correct answers is plotted as a function of target eccentricity. The red symbols represent results for the secret detection task in the main experiment, and the blue symbols represent results for the control experiment. Each data set was fitted with a cubic polynomial. Error bars were determined as the larger of the two: (i) SEM based on the binomial distribution assumption for the number of correct answers and (ii) SEM based on repeated runs of the same experiment (each subject completed 3 or more runs). Inverse of these variations was used as weights for the cubic fitting routine. By subtracting the control experiment data, we removed the eccentricity effect, which made the modulation around the attended location more apparent. The resulting curve is plotted in magenta in Figure 5. As expected, in the control experiment, sensitivity declines in a monotonic fashion as the target eccentricity grows. Strikingly, the secret task detection sensitivity displays a peculiar trend: it dips inward and pitches outward of the attended 8° location, forming an inflection point centered approximately at the attended location (8.1°, 8.1°, 7.7° for subjects S1, S2, and S3, respectively). The position of the inflection point has been measured as the inflection of the difference of the two fitted cubic polynomials (the magenta curve). The dip–pitch trend (cubic behavior) can be measured as the cubic term coefficient for the polynomial fitted to the secret task data (red curve). The coefficient was significant for all 3 observers: −0.09 ± 0.02 for S1, −0.07 ± 0.02 for S2, and −0.11 ± 0.06 for S3. 
The simplest explanation of this surprising result is that the distribution of spatial attention is biased outward by approximately 10% (0.8° at the tested 8° location). There are two possible reasons for this bias: 
  1.  
    The “spotlight” of attention is asymmetric, with its nucleus at the attended location and its body bulging away from fixation like a comet tail pointing away from the sun.
  2.  
    The “spotlight” of attention is symmetric but shifted (mislocalized) outward as a whole.
Given the prominent shift of the maximum of the magenta curve outward of the attended location, the latter case appears more likely. For now, more data are needed to settle this question. 
Either hypothesis explains the outward asymmetry of crowding in the context of the “attentional” mechanism of crowding, i.e., due to reduced spatial resolution of attention in the periphery (He et al., 1996; Intriligator & Cavanagh, 2001). The “spotlight” of attention is deployed to discern a small peripheral item. All items within the “spotlight” are merged perceptually, thus making the target identification impossible. Items more eccentric than the target are more disruptive, because the attention spotlight is biased outward of the target focusing on the outward distractor instead. Because the “spotlight” of attention is biased to more eccentric locations, the target signal is pooled with the outward distractor's signal, while remaining fairly unaffected by the inward distractor's signal. 
Various studies (e.g., Eriksen, Pan, & Botella, 1993; Müller & Kleinschmidt, 2004; Müller, Mollenhauer, Rösler, & Kleinschmidt, 2005) indicated the Mexican hat distribution of the attentional field, where inhibitory field surrounds the attended location. The dip in performance inward of the attended 8° location agrees well with this model. 
Discussion: Inward–outward asymmetry of crowding
Motter and Simoni (2007) argued that due to the logarithmic compression of V1 cortical space with eccentricity (cortical magnification factor) the outward mask is closer to the target than the inward mask on the cortex, which may explain the inward–outward anisotropy of crowding (also see Pelli, 2008). The assumption was that the critical distance in crowding is defined by the target–mask cortical separation rather than by their visual space separation. As noted in our previous studies (Petrov & McKee, 2006; Petrov et al., 2007), there are reasons why the cortical magnification explanation is questionable. In particular, the inward–outward asymmetry appears to be too strong to be accounted by the cortical magnification in V1 or other retinotopic areas. The outward mask, at threshold, was on the average 1° more peripheral than the inward mask in Experiment 1 (focused attention condition). Given that the whole stimulus was at 8° eccentricity, the 1° difference in the mask eccentricity translates into a mere 6% difference in the target–mask cortical separation (see Pelli, 2008, for the relevant formulas). It is unlikely that such small difference in cortical spacing could result in the observed 300% (fourfold) increase in crowding, although one cannot exclude the possibility of such steep increase. The results of Experiments 1 and 2 clearly indicate that the inward–outward asymmetry of crowding cannot be explained by such low-level factors as cortical magnification, because attention manipulations in these experiments could not modify the magnification factor. 
In addition, the radial–tangential asymmetry of crowding cannot be explained by cortical magnification as data from primate and human retinotopy (Adams & Horton, 2003; Schira, Kontsevich, & Tuler, 2005; Tootell, Switkes, Silverman, & Hamilton, 1988; Van Essen, Newsome, & Maunsell, 1984) suggest that a radial–tangential asymmetry determined by equal cortical distance would, if anything, be in the opposite direction. This is because, at least along the vertical meridian, in order to travel an equal visual distance radially and tangentially, one must travel farther on cortex in the radial direction due to overlap when crossing ocular dominance columns. Along the horizontal meridian, the arrangement of columns is more haphazard and there is no particular cortical anisotropy other than magnification. In summary, these crowding asymmetries are not easily explained by retinotopy or cortical magnification, at least in the primary visual cortex. 
Recently, Dayan and Solomon (2010) suggested a quantitative model, where several paradoxical properties of crowding were successfully explained by optimal (Bayesian) inference operating over spatially extended receptive fields. In particular, their model explained the inward–outward asymmetry of crowding based on the fact that the receptive field sizes increase with eccentricity. Therefore, they argued, there are more receptive fields responding to both target and mask for the outward mask than for the inward mask, which explains the larger interference from the outward mask. Although the increase in the receptive field size with eccentricity in V1 is too slow to explain the observed asymmetry, in V4 the trend was strong enough to produce a factor of 2 increase in signal-to-noise ratio for the inward mask crowding compared to the outward mask crowding. Unlike Motter and Simoni's (2007) explanation, these results apply even for the small target–mask separations used in Experiments 1 and 2 here. However, Dayan and Solomon implicitly assumed that the density of cells/receptive fields remains constant with eccentricity in visual space. In fact, the density remains constant in cortical space, which means that, due to the magnification factor, the density in visual space decreases. The density decrease will reduce the predicted inward–outward asymmetry, because the decreasing receptive field density offsets the increasing receptive field size (decreasing the number of receptive fields responding to both the outward mask and the target). In any case, our present findings demonstrate that the inward–outward asymmetry of crowding is strongly modified by spatial attention and cannot be explained by cortical mapping alone. 
Conclusion
Crowding has the hallmark asymmetry: a mask presented outward of the target (with respect to fixation) obscures the target identity stronger than a mask at other locations. If crowding and attention are closely related, then the asymmetries in crowding and in attention allocation should be similar. Our results, rather strikingly, suggest that attention is commonly mislocalized outward of the target, which explains why the outward mask crowds more than the inward mask: observers miss the target and attend to the outward mask instead. The characteristic outward asymmetry of crowding disappears when attention is diffused by randomly interleaving trials with targets at different eccentricities, and the asymmetry reverses when attention is biased inward by a foveal cue. 
Acknowledgments
We would like to thank Dr. Suzanne McKee for helpful discussions. 
Commercial relationships: none. 
Corresponding author: Yury Petrov. 
Email: y.petrov@neu.edu. 
Address: 125 NI, 360 Huntington Ave., Boston, MA 02115, USA. 
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Figure 1
 
Experimental stimuli were comprised of the Gabor targets and plaid masks. The masks were positioned either (top) inward or (bottom) outward with respect to the Gabor targets.
Figure 1
 
Experimental stimuli were comprised of the Gabor targets and plaid masks. The masks were positioned either (top) inward or (bottom) outward with respect to the Gabor targets.
Figure 2
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) Focused attention (target at 8° eccentricity). (Right) Diffused attention (targets at 7°, 8°, and 9° eccentricities interleaved, data pooled over the three locations). Error bars represent 1 standard error of the mean (SEM) for the crowding factors.
Figure 2
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) Focused attention (target at 8° eccentricity). (Right) Diffused attention (targets at 7°, 8°, and 9° eccentricities interleaved, data pooled over the three locations). Error bars represent 1 standard error of the mean (SEM) for the crowding factors.
Figure 3
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) No foveal cue (replotted from Figure 2). (Right) Task contingent on a foveal cue. Note the change of scale between the two panels.
Figure 3
 
Crowding factor as a function of the mask location (outward vs. inward). Each datum represents an individual subject's data. (Left) No foveal cue (replotted from Figure 2). (Right) Task contingent on a foveal cue. Note the change of scale between the two panels.
Figure 4
 
Stimuli used for Experiment 3. The square (not shown in the actual experiment) indicates the attention attractor Gabor; this target appeared in 2/3 of the trials, and its contrast varied according to the method of constant stimuli protocol. A sub-threshold Gabor appeared in the remaining 1/3 of the trials instead of the attractor Gabor. The test Gabor target was displaced left or right of the 8° location as shown (only one location was used on a given trial).
Figure 4
 
Stimuli used for Experiment 3. The square (not shown in the actual experiment) indicates the attention attractor Gabor; this target appeared in 2/3 of the trials, and its contrast varied according to the method of constant stimuli protocol. A sub-threshold Gabor appeared in the remaining 1/3 of the trials instead of the attractor Gabor. The test Gabor target was displaced left or right of the 8° location as shown (only one location was used on a given trial).
Figure 5
 
Results of Experiment 3. The Gabor target was presented at different eccentricities, either at the attended location (blue symbols) or inward–outward off the attended 8° location (red symbols). The data were fitted with cubic functions. The difference between the two curves (shown in magenta) was shifted by +0.5 along the y-axis for illustration purposes.
Figure 5
 
Results of Experiment 3. The Gabor target was presented at different eccentricities, either at the attended location (blue symbols) or inward–outward off the attended 8° location (red symbols). The data were fitted with cubic functions. The difference between the two curves (shown in magenta) was shifted by +0.5 along the y-axis for illustration purposes.
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