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Research Article  |   August 2010
The effect of spacing regularity on visual crowding
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Journal of Vision August 2010, Vol.10, 17. doi:10.1167/10.10.17
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      T. P. Saarela, G. Westheimer, M. H. Herzog; The effect of spacing regularity on visual crowding. Journal of Vision 2010;10(10):17. doi: 10.1167/10.10.17.

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Abstract

Crowding limits peripheral visual discrimination and recognition: a target easily identified in isolation becomes impossible to recognize when surrounded by other stimuli, often called flankers. Most accounts of crowding predict less crowding when the target–flanker distance increases. On the other hand, the importance of perceptual organization and target–flanker coherence in crowding has recently received more attention. We investigated the effect of target–flanker spacing on crowding in multi-element stimulus arrays. We show that increasing the average distance between the target and the flankers does not always decrease the amount of crowding but can even sometimes increase it. We suggest that the regularity of inter-element spacing plays an important role in determining the strength of crowding: regular spacing leads to the perception of a single, coherent, texture-like stimulus, making judgments about the individual elements difficult.

Introduction
A stimulus presented in the retinal periphery becomes difficult, if not impossible, to recognize when it is surrounded by other stimuli, a phenomenon often called visual crowding. Suggested explanations for crowding include compulsory pooling (Parkes, Lund, Angelucci, Solomon, & Morgan, 2001; Wilkinson, Wilson, & Ellemberg, 1997) or excessive integration (e.g., Pelli, Palomares, & Majaj, 2004) of stimulus features and limited attentional resolution (He, Cavanagh, & Intriligator, 1996), recently reviewed by Levi (2008) and Pelli and Tillman (2008). The strength of crowding can be manipulated in a number of ways. First, it is affected by target–flanker similarity: crowding is reduced when target and flankers differ along basic, low-level stimulus dimensions such as color, contrast polarity, or direction of motion (Gheri, Morgan, & Solomon, 2007; Kooi, Toet, Tripathy, & Levi, 1994). Second, the effectiveness of flankers in producing crowding can be diminished by changing the stimulus configuration while keeping low-level features constant (Livne & Sagi, 2007; Saarela, Sayim, Westheimer, & Herzog, 2009), by merging several distinct flankers into one large flanker (Mareschal, Morgan, & Solomon, 2008), and by increasing the flanker size relative to the target (Saarela et al., 2009). Third, the strength of crowding depends on the target–flanker separation (e.g., Bouma, 1970; Levi, Hariharan, & Klein, 2002; Pelli et al., 2004; Pelli & Tillman, 2008; Strasburger, Harvey, & Rentschler, 1991). “Bouma's law” (Bouma, 1970) states that, in order to have an effect, the flankers have to be closer to the target than about 0.5 times the target eccentricity. This translates into a fixed cortical distance in the primary visual cortex (Pelli, 2008). Note, however, that two different measures of target–flanker distance have been used when defining the critical spacing: center-to-center and edge-to-edge (see Strasburger, 2005). Recently, Levi and Carney (2009) opted for using the former one and suggested a “centroid hypothesis”: the amount of crowding is determined by the distance between the target and the flanker centroids. 
As perceptual organization of the stimulus has a strong effect on crowding, especially when several flankers are present (Livne & Sagi, 2007; Saarela et al., 2009), this paper focuses on the relationship between stimulus spacing and crowding strength in multi-element stimulus arrays. In two experiments, we tested the effect of flanker spacing on crowding using Gabor and letter stimuli. We examined the centroid hypothesis in further detail and show that increasing the average distance between the target and flanker centroids can sometimes increase crowding. The effect of flanker manipulations is not a simple function of flanker distance or the number of flankers. The key factor is the perceptual coherence between the target and flankers. 
Methods
Observers
Five observers participated in the experiments. Three had normal vision; two were myopic and wore appropriate correction. One of the authors (TS) was an observer. Observers trained on the tasks before the actual experiments. 
Equipment
Stimuli were presented on a Mitsubishi Diamond Pro 900u CRT monitor that was driven by a NVIDIA GeForce 7300 GT graphics card. The screen was refreshed at 60 Hz and it had a spatial resolution of 1024 × 768 pixels. The screen covered 33.8 × 25.6 degrees of visual angle from the viewing distance of 57 cm that was used during the experiment. The gray background used in the experiments had a luminance of 36 cd/m2
Stimuli
Gabor orientation discrimination
The stimuli were grayscale luminance modulations around the screen background luminance. The stimuli were Gabor patches, with a luminance profile described by 
G ( x , y ) = L [ 1 + c exp ( ( x x 0 ) 2 / σ x 2 ( y y 0 ) 2 / σ y 2 ) sin ( 2 π f ( x x 0 ) ) ] ,
(1)
where L is the background luminance, c is the carrier contrast, and σ x and σ y are the space constants of the Gaussian envelope that is centered on x 0, y 0. The spatial frequency f of the carrier was 4 cycles per degree. The Gabors were vertically elongated, with σ x = 0.125 deg and σ y = 0.5 deg. 
As the Gabor carriers were in sine phase with respect to the center of the Gaussian envelope, the mean luminance remained constant across the stimulus. The Michelson contrast c of the carrier was always 0.8. The flanking Gabors were always vertical, as given by the equation above. The orientation of the target Gabor was varied from vertical to measure the discrimination threshold (see Procedure section). 
Letter orientation identification
The stimulus was the uppercase letter T, presented as a luminance decrement against the background luminance. The size (width and height) of the T was 0.5 deg, and stroke width was 1/5 of the size. The possible orientations of the T were the four cardinal orientations (upright or rotated 90, 180, or 270 degrees). 
The (absolute) Weber contrast (ΔL/L, where L is the background luminance and ΔL is the size of the decrement) of the flankers was always 0.2. The contrast of the target was varied to measure the contrast threshold for identification (see Procedure section). 
Procedure
Gabor orientation discrimination
Orientation discrimination for a Gabor target was measured with the method of constant stimuli and a single-interval design. There were two possible locations for the target: 7.5 deg to the left and 7.5 deg to the right of the fixation mark, which was presented in the middle of the screen. 
The observer started a trial with a key press. The two possible target locations were then indicated by short line segments 1 deg above and below the horizontal meridian and 7.5 deg to the left and to the right of fixation. After 750 ms, the stimulus was presented for 250 ms at one of the two possible locations (randomized across trials). The markers for target location were visible during the stimulus presentation and disappeared simultaneously with the stimulus. The observer indicated with a key press whether the target was tilted clockwise or counterclockwise from vertical. Auditory feedback was given after incorrect responses. The response initiated the next trial. 
The target tilts from vertical were selected based on pilot experiments. In each condition, the presentation of each tilt level was balanced across sign (clockwise or counterclockwise) and target location (left or right of fixation). The presentation order of target tilts was randomized. 
There were five experimental conditions. In the baseline condition, the target was presented without flanking Gabors. In the “tight,” “shifted,” and “wide” conditions, the target was flanked on either side by 4 vertical Gabors. In the “added” condition, there were 7 flankers on either side. The horizontal center-to-center displacements, in degrees, between the flankers and the target were given as follows: “tight”: (−4, −3, −2, −1, 1, 2, 3, 4); “shifted”: (−4, −3, −2, −1.5, 1.5, 2, 3, 4); “wide”: (−6, −4.5, −3, −1.5, 1.5, 3, 4.5, 6); “added”: (−6, −5.25, −4.5, −3.75, −3, −2.25, −1.5, 1.5, 2.25, 3, 3.75, 4.5, 5.25, 6). Note that the flanker spacings were multiples of the carrier period, so all the Gabors in a given stimulus effectively had the same carrier. See insets in Figure 1 for examples of the stimuli. 
Figure 1
 
Effect of stimulus spacing on crowding in orientation discrimination. Crowding strength is shown from four experimental conditions in which the flanker distances from the target were varied. Crowding is quantified as the threshold elevation (the experimental threshold divided by the control threshold, which was measured without flanking stimuli), with values larger than 1 (the dashed line) indicating crowding. The conditions, from top to bottom, are (1) “tight”: tight, regular spacing; (2) “shifted”: innermost flankers shifted away from the target; (3) “wide”: all flankers shifted to produce a wider, regular spacing; (4) “added”: more flankers added in between those in (3). The target location was indicated with two white markers as shown in the stimulus icons. The data shown are averages across all observers. Error bars show ±SEM.
Figure 1
 
Effect of stimulus spacing on crowding in orientation discrimination. Crowding strength is shown from four experimental conditions in which the flanker distances from the target were varied. Crowding is quantified as the threshold elevation (the experimental threshold divided by the control threshold, which was measured without flanking stimuli), with values larger than 1 (the dashed line) indicating crowding. The conditions, from top to bottom, are (1) “tight”: tight, regular spacing; (2) “shifted”: innermost flankers shifted away from the target; (3) “wide”: all flankers shifted to produce a wider, regular spacing; (4) “added”: more flankers added in between those in (3). The target location was indicated with two white markers as shown in the stimulus icons. The data shown are averages across all observers. Error bars show ±SEM.
There were 200 trials in a block, and all five conditions were mixed within a block. The blocks were repeated enough times (usually 8) to get a good fit of the psychometric function to the data (see Data analysis section). 
Letter orientation identification
The basic procedure was the same as in the Gabor orientation discrimination experiment, with the following exceptions. The markers for the target location were presented 0.5 deg above and below the horizontal meridian. The observer indicated by a key press in which of the four possible cardinal orientations the target was. The target was presented an equal number of times at each orientation and each possible target location, in random order. The orientation of each flanker was randomized across trials. The target contrasts were selected based on pilot experiments. In each condition, the presentation of each contrast level was balanced across target location and contrast. The order of presentation of target contrasts was randomized. The horizontal center-to-center displacements, in degrees, between the flankers and the target were given as follows: “tight”: (−4, −3, −2, −1, 1, 2, 3, 4); “shifted”: (−4.00, −3.00, −2.00, −1.25, 1.25, 2.00, 3.00, 4.00); “wide”: (−5.00, −3.75, −2.50, −1.25, 1.25, 2.50, 3.75, 5.00); “added”: (−5.00, −4.375, −3.75, −3.125, −2.50, −1.875, −1.25, 1.25, 1.875, 2.50, 3.125, 3.75, 4.375, 5.00). See insets in Figure 3 for examples of the stimuli. 
Data analysis
The data were pooled across blocks and across the two target locations. Gabor data: The proportion of “tilted clockwise” responses was calculated at each target tilt level. Psychometric functions (cumulative normal) were fit to the data, and the standard deviation was used as the discrimination threshold. Letter data: Psychometric functions (Weibull) were fit to the proportion-correct data from each condition to extract the identification threshold (the stimulus value at which the underlying psychometric function reached a value of 0.5). Maximum likelihood fits and bootstrapped error estimates were obtained using the psignifit toolbox for Matlab (Wichmann & Hill, 2001a, 2001b). For each observer, we calculated the threshold elevation in each flanker condition as the threshold in that condition divided by the threshold in the control condition measured with no flankers. Thus, a value of 1 indicates no crowding and a value greater than 1 indicates crowding. The average data shown are average threshold elevations across observers. 
Results
In the first experiment, we measured orientation discrimination thresholds for a near-vertical Gabor presented at 7.5 degrees eccentricity along the horizontal meridian in five experimental conditions (Figure 1). In the baseline condition, the target was presented alone. In the “tight” condition, the target was flanked on either side by 4 tightly spaced vertical Gabors. The spacing was regular (1 deg) throughout the whole array. As expected, crowding in this condition was strong: the discrimination thresholds were highly elevated relative to the baseline. In the “shifted” condition, the innermost flankers were moved away from the target (distance 1.5 deg), resulting, as expected, in a decrease in crowding relative to the “tight” condition. Next, in the “wide” condition, all the other flankers were moved away from the target as well, resulting in a wider, regular spacing (1.5 deg) throughout the whole array. Although the average flanker–target distance was now greater than in the “shifted” condition, crowding, on average, was not reduced but increased (see below for individual differences). Finally, the “added” condition had all the flankers as the “wide” condition plus additional flankers inserted in between them. Here, although the closest flanker distance from the target and the average target–flanker distance were the same as in the “wide” condition, and more flankers were added, crowding was reduced. 
Thresholds from individual observers are shown in Figure 2. One observer, S2, differed from the other observers in the “added” condition. While crowding was very weak for the other observers, for S2, crowding was strong. However, it was not stronger compared to the “wide” condition despite the additional flanking elements in “added.” Two observers, S3 (one of the authors) and S5, did not show an increase in thresholds between the “shifted” and “wide” conditions. Finally, there is a peculiarity in the thresholds of S4. While the pattern of thresholds in the four conditions with flankers is comparable to other observers, S4's threshold in the “shifted” condition is lower than the baseline threshold. 
Figure 2
 
Orientation discrimination thresholds for individual observers used in calculating the average results in Figure 1. Error bars show the bootstrapped standard errors.
Figure 2
 
Orientation discrimination thresholds for individual observers used in calculating the average results in Figure 1. Error bars show the bootstrapped standard errors.
In the second experiment, we used another stimulus class often utilized in crowding research, letters. The stimulus was the letter T presented in one of the four cardinal orientations, and observers identified its orientation. The flankers were composed of letter Ts as well, each in random orientation (see stimulus icons in Figure 3). Contrast thresholds were measured for the identification of target orientation. The pattern of results was similar to the first experiment (Figure 3). Tight, regular spacing (1 deg) resulted in strong crowding that was relieved when the innermost flankers were moved outward (to 1.25 deg from the target, “shifted” condition). There was a tendency for crowding to increase when all other flankers were moved away from the target to form again a regular stimulus array (“wide”). When more flankers were added while keeping the closest flanker distance and average flanker distance, i.e., the distance between centroids, constant, crowding was reduced. 
Figure 3
 
Effect of stimulus spacing on crowding in letter orientation identification. Experimental conditions are similar to those in Figure 1. The task was to identify the orientation of the target T. Crowding strength is quantified as threshold elevation (threshold divided by the control threshold measured without flanking stimuli). The data shown are averages across all observers. Error bars show ±SEM.
Figure 3
 
Effect of stimulus spacing on crowding in letter orientation identification. Experimental conditions are similar to those in Figure 1. The task was to identify the orientation of the target T. Crowding strength is quantified as threshold elevation (threshold divided by the control threshold measured without flanking stimuli). The data shown are averages across all observers. Error bars show ±SEM.
The data from individual observers are consistent (Figure 4), although the magnitudes of the effects vary. None of the observers showed a decrease in crowding between “shifted” and “wide” conditions although the average flanker distance was increased, nor did they show an increase between “wide” and “added” even though more flankers were introduced. 
Figure 4
 
Letter orientation identification thresholds for individual observers used in calculating the average results in Figure 3. Error bars show the bootstrapped standard errors.
Figure 4
 
Letter orientation identification thresholds for individual observers used in calculating the average results in Figure 3. Error bars show the bootstrapped standard errors.
The observers informally reported that, perceptually, in the conditions where the spacing was regular (whether “tight” or “wide”), the target appeared less distinct and less separate from the flankers. The target was more distinct and judging the target attributes tended to be easier in the “shifted” and “added” conditions. 
Discussion
Crowding is a key limiting factor in peripheral vision. Although its properties and underlying mechanisms are not fully understood, there is reasonable agreement on some properties. First, crowding strength is thought to decrease as the flanker distance increases (but see also Levi, Klein, & Aitsebaomo, 1985). This has been shown experimentally, and it is also expressed in what is often called “Bouma's law” (Bouma, 1970) and more recently in the “centroid hypothesis” (Levi & Carney, 2009), which conjectures that crowding strength is determined by the distance between target and flanker centroids. Second, the views of crowding as inappropriate integration of features and as insufficient attentional resolution both predict that increasing the number of distracting features should produce more crowding. However, the results presented in this paper show that, when multiple flankers are present, the strength of crowding cannot be explained solely in terms of (1) the distance of the flanker closest to the target, (2) the average distance between target and flanker centroids, or (3) the number of flankers in the array. 
First, the “shifted,” “wide,” and “added” conditions had the closest flanker in exactly the same position, yet there were large differences in the amount of crowding that they induced. Second, the average distance between target and flanker centroids was greater in the “wide” than it was in the “shifted” condition, but crowding was stronger in the “wide” condition. These results argue against a simple relationship between flanker distance and crowding. Third, the stimulus in the “added” condition had the same average flanker distance as that in the “wide” condition, plus additional flankers, yet it produced weaker crowding, showing that the sheer number of flankers that could be pooled or that could otherwise interfere with the target does not explain crowding. 
Note also that the target locations were clearly indicated to the observer in each condition, so the effect of flanker manipulation on crowding cannot be attributed to changes in uncertainty with respect to the target location. 
Our results do not conflict with Bouma's law, which has been demonstrated several times with relatively simple stimulus arrangements. They do show, however, that, with more complex stimuli, factors other than average target–flanker separation play an important role in determining crowding strength. The conditions in which crowding was strongest were those with a regular inter-element spacing throughout the whole stimulus array, and the observers also reported the target to be less salient in these conditions. We argue that it is the spacing regularity that matters: with regular spacings, all the elements are grouped together and the stimulus array is perceived as a coherent texture that includes both targets and flankers. While being part of the whole, the attributes of a single element (the target) can be assessed with less accuracy. Consequently, crowding is strong. When that coherence breaks down, so that the target stands out as an individual element, as was the case in the “shifted” and “added” conditions, crowding is reduced. 
This effect is not unique to a specific stimulus or task. Crowding has been studied using a variety of stimuli and tasks, and it is not always clear whether the different studies tap into the same neural mechanisms. Here, we demonstrated similar effects of stimulus spacing using very different stimuli (Gabors and letters) and tasks, suggesting either a common site for the interactions or a similar processing principle at different stages of visual processing. Our results are also consistent with a growing body of literature showing how perceptual organization and the strength of crowding are tightly coupled (e.g., Banks & White, 1984; Gheri et al., 2007; Livne & Sagi, 2007; Mareschal et al., 2008; Põder, 2006; Saarela et al., 2009). Crowding strength and perceptual segmentation go hand in hand: targets that are rated as conspicuous suffer from substantially less crowding than targets that are rated as belonging to the same perceptual whole with the flankers (Saarela et al., 2009). In foveal vision, similar results have been observed with vernier targets and flanking lines (Malania, Herzog, & Westheimer, 2007; Sayim, Westheimer, & Herzog, 2008). Flanker size contributes to the perceptual segmentation and thus to crowding (Saarela et al., 2009), and similar patterns of results have been found also in backward and metacontrast masking: larger pattern masks can improve performance compared to smaller ones (Duangudom, Francis, & Herzog, 2007; Herzog & Fahle, 2002; Herzog & Koch, 2001; Kolers, 1962; Macknik & Haglund, 1999; Schiller & Greenfield, 1969; Sturr, Frumkes, & Veneruso, 1965; Wehrhahn, Li, & Westheimer, 1996). 
Mareschal et al. (2008) demonstrated that several surrounding flankers can cause more crowding than a single annulus that comprises the flankers. Levi and Carney (2009) confirmed this and suggested that the annulus produces less crowding than several distinct flankers because it provides fewer “independent samples” that can contribute to crowding. However, merging flankers together can also substantially increase crowding. For example, crowding is increased when small flankers are merged together to form larger ones if this merging makes the flankers more similar to the target and reduces the segmentation between the target and the flankers (Saarela et al., 2009). Thus, it is not the sheer number of flankers, or the number of independent samples, it is how well the target blends in with the flankers (e.g., Mareschal et al., 2008; Saarela et al., 2009). In the “added” condition of the present study, although the flankers were not physically merged together, the added flankers gave the appearance of a single target flanked by two separate groups of elements instead of a target that is a part of a homogeneous group of similar elements. Consequently, the added flankers did not strengthen crowding. 
Conclusion
We suggest that, in multi-element stimulus arrays, crowding is strongest with a regular inter-element spacing. Regular spacing leads to the perception of a homogeneous texture, making judgments about the target more difficult. When the spacing between elements helps make the target more distinct and easier to assess, crowding is weaker. 
Acknowledgments
We would like to thank Michael Landy for use of office space and computers when preparing this manuscript and Denis Pelli for helpful comments. TS was supported by the Swiss National Science Foundation PBELP1-125415. 
Commercial relationships: none. 
Corresponding author: T. P. Saarela. 
Email: saarela@cns.nyu.edu. 
Address: Department of Psychology and Center for Neural Science, New York University, 6 Washington Place, New York, NY 10003, USA. 
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Figure 1
 
Effect of stimulus spacing on crowding in orientation discrimination. Crowding strength is shown from four experimental conditions in which the flanker distances from the target were varied. Crowding is quantified as the threshold elevation (the experimental threshold divided by the control threshold, which was measured without flanking stimuli), with values larger than 1 (the dashed line) indicating crowding. The conditions, from top to bottom, are (1) “tight”: tight, regular spacing; (2) “shifted”: innermost flankers shifted away from the target; (3) “wide”: all flankers shifted to produce a wider, regular spacing; (4) “added”: more flankers added in between those in (3). The target location was indicated with two white markers as shown in the stimulus icons. The data shown are averages across all observers. Error bars show ±SEM.
Figure 1
 
Effect of stimulus spacing on crowding in orientation discrimination. Crowding strength is shown from four experimental conditions in which the flanker distances from the target were varied. Crowding is quantified as the threshold elevation (the experimental threshold divided by the control threshold, which was measured without flanking stimuli), with values larger than 1 (the dashed line) indicating crowding. The conditions, from top to bottom, are (1) “tight”: tight, regular spacing; (2) “shifted”: innermost flankers shifted away from the target; (3) “wide”: all flankers shifted to produce a wider, regular spacing; (4) “added”: more flankers added in between those in (3). The target location was indicated with two white markers as shown in the stimulus icons. The data shown are averages across all observers. Error bars show ±SEM.
Figure 2
 
Orientation discrimination thresholds for individual observers used in calculating the average results in Figure 1. Error bars show the bootstrapped standard errors.
Figure 2
 
Orientation discrimination thresholds for individual observers used in calculating the average results in Figure 1. Error bars show the bootstrapped standard errors.
Figure 3
 
Effect of stimulus spacing on crowding in letter orientation identification. Experimental conditions are similar to those in Figure 1. The task was to identify the orientation of the target T. Crowding strength is quantified as threshold elevation (threshold divided by the control threshold measured without flanking stimuli). The data shown are averages across all observers. Error bars show ±SEM.
Figure 3
 
Effect of stimulus spacing on crowding in letter orientation identification. Experimental conditions are similar to those in Figure 1. The task was to identify the orientation of the target T. Crowding strength is quantified as threshold elevation (threshold divided by the control threshold measured without flanking stimuli). The data shown are averages across all observers. Error bars show ±SEM.
Figure 4
 
Letter orientation identification thresholds for individual observers used in calculating the average results in Figure 3. Error bars show the bootstrapped standard errors.
Figure 4
 
Letter orientation identification thresholds for individual observers used in calculating the average results in Figure 3. Error bars show the bootstrapped standard errors.
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