While human eyesight is clearest at the point where the gaze is focused, peripheral vision makes objects to the side visible. This ability to detect movement and objects in a wider field of vision helps people to have a greater awareness of their surroundings. However, it is more difficult to identify an object using peripheral vision when it is surrounded by other items. This phenomenon is known as crowding and can affect many aspects of daily life, such as driving or spotting a friend in a crowd.

In our three-dimensional world, peripheral objects are often at different distances. This variation in depth could influence the effect of crowding, yet little is known about its effect. While previous research has investigated the effect of small differences in depth on crowding, the studies did not replicate real-world conditions.

To replicate depths that are likely to be encountered in the real world, Smithers et al. created a display using multiple screens positioned 0.4, 1.26 and 4 meters from the viewer. Images were displayed on the screens and researchers measured how well study participants could identify a target image when it was surrounded by similar, nearby images displayed closer or further away than the target. The experiments showed that most viewers are less able to recognize a target object when there are surrounding items and this effect is worsened when the items are separated from the object by large differences in depth.

The findings show that instead of diminishing the effect of crowding – as suggested by previous studies with small depth differences – large depth differences that more closely recreate those encountered in the real world can amplify the effect of crowding. This greater understanding of how humans process objects in three-dimensional environments could help to better estimate the impact of crowding on people with eye and neurological disorders. In turn, the information could be used to design environments that are easier for such individuals to navigate.

Visual crowding is a phenomenon in which a peripherally viewed object, that is easily identifiable in isolation, becomes harder to recognize or identify when it is surrounded by other objects, despite still being clearly visible (Bouma, 1970; Herzog et al., 2015; Levi, 2008; Pelli, 2008; Whitney and Levi, 2011). The importance of crowding is reflected by the tremendous amount of research on the topic and it has been extensively reviewed over the years (e.g. Coates et al., 2021; Herzog et al., 2015; Manassi and Whitney, 2018; Pelli, 2008; Strasburger et al., 2011; Whitney and Levi, 2011). This high level of interest is not surprising given that the natural environment is usually cluttered and mostly viewed in the peripheral visual field. Consequently, it is assumed that crowding has a large impact on our daily lives with implications for many everyday visual tasks including driving (Xia et al., 2020), reading (Legge, 2007), and face recognition (Kalpadakis-Smith et al., 2018; Louie et al., 2007). Crowding also has important clinical implications for people with glaucoma (Ogata et al., 2019; Shamsi et al., 2022), as well as for other disorders including central vision impairment (e.g. macular degeneration), amblyopia and dyslexia (Whitney and Levi, 2011). Through this body of research, we have been able to build a good understanding of the factors that mediate and moderate crowding and develop unifying theories (e.g. Balas et al., 2009; Harrison and Bex, 2015; Keshvari and Rosenholtz, 2016; van den Berg et al., 2012; van den Berg et al., 2010). However, despite the large body of literature, one area that remains surprisingly understudied is how depth affects crowding. This is important because we live in a three-dimensional environment and so to understand the significance of crowding in the real world it is essential to understand the role of depth information.

Kooi et al., 1994 were the first to investigate how depth influences crowding. The authors found that compared to when a peripheral target and flankers were at the same depth, there was a release from crowding when the target and flankers were stereoscopically presented in crossed (front) and uncrossed (behind) disparities (Kooi et al., 1994). Sayim et al., 2008 found that when flankers were at fixation depth, there was less foveal crowding when the target was stereoscopically presented in front or behind the flankers. Felisberti et al., 2005 also found an effect of depth on crowding in the parafovea, but to a more limited extent. They reported a release from crowding in two out of three subjects when the target appeared behind the flankers, but only in one of the three subjects when the target was in front of the flankers (Felisberti et al., 2005). Astle et al., 2014 extended on previous research by testing the effect of depth on crowding over a range of stereoscopically produced target-flanker disparities (±800 arcsec). In line with previous studies, Astle et al., 2014 found that when the target was at fixation depth, increasing target-flanker disparity systematically reduced crowding. They also found that the release from crowding was asymmetric whereby crowding was greater when the flankers were in front of the target compared to behind it (Astle et al., 2014).

Taken together these studies appear to paint the picture that a difference in depth between a target and flankers reduces crowding. This could challenge the concept that crowding is ubiquitous in three-dimensional natural environments (Whitney and Levi, 2011) because it implies that depth differences between natural objects could prevent crowding from being a problem (Figure 1). However, all the above studies tested only small depth differences between target and flankers that do not reflect the often-large differences in depth between objects in the real world. Furthermore, the generalizability of these studies to real world depth is also limited by the fact that depth cues were generated stereoscopically. One potential problem with stereo displays is that disparity information often does not match with accommodation or defocus blur which can detrimentally affect depth perception (Hoffman et al., 2008; Watt et al., 2005).

Figure 1

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To our knowledge, four studies have investigated the effect of depth on crowding using a real depth display. All four studies used two orthogonally positioned screens viewed through a half-transparent mirror allowing stimuli to be displayed on two different depth planes simultaneously (Eberhardt et al., 2021; Eberhardt and Huckauf, 2019; Eberhardt and Huckauf, 2017; Eberhardt and Huckauf, 2020). Eberhardt and Huckauf, 2017 kept a target and flankers at the same depth and presented them 0.06 diopters (i.e. 1/focal length in meters), in front, behind or at the same depth as fixation. The authors found that this small difference in depth between the stimuli and fixation planes had no effect on the amount of crowding compared to when everything was presented at the fixation plane (Eberhardt and Huckauf, 2017). Eberhardt and Huckauf, 2019 repeated and expanded on this work with the addition of a ±0.1 diopter depth difference between fixation and the stimuli in addition to the ±0.06 diopter condition. The results showed that crowding was greater when the stimuli were furthest from fixation compared to when they were closer to fixation, regardless of whether the stimuli were in front or behind the fixation plane (Eberhardt and Huckauf, 2019). More recently, Eberhardt and Huckauf, 2020 used the same approach to investigate the effect of depth on crowding when the target and flankers were separated in depth. When flanker depth was varied while the target was at fixation depth, crowding increased with increasing target-flanker depth difference (Eberhardt and Huckauf, 2020). This result is the opposite to the findings of other studies in which small differences in depth between the target and flankers were introduced with stereoscopic disparity (Astle et al., 2014; Felisberti et al., 2005; Kooi et al., 1994; Sayim et al., 2008). Furthermore, the authors also found that when flanker depth was varied while the target was at fixation depth, crowding was greater when the flankers were behind the target and fixation compared to in front of it (Eberhardt and Huckauf, 2020). When target depth was varied while the flankers were at fixation, there was more crowding when the target was in front of the flankers and fixation compared to when it was behind them (Eberhardt and Huckauf, 2020).

In light of the above discrepancies, and the prevalence of depth information in real world scenes, there is a pressing need for a better understanding of how visual crowding is affected by depth differences representative of those experienced between objects in the real world. Therefore, using a novel multi-depth plane display consisting of screens at 0.4 m (near screen), 1.26 m (mid screen), and 4 m (far screen) viewing distances (Figure 2), we investigate how crowding is affected by large, real differences in target-flanker depth. These viewing distances were chosen because 4 m is close to optical infinity while 0.4 m is the clinical standard for near distance, with 1.26 m being in the middle of these two extremes in log units. Given in diopters, the near, mid, and far screens were at 2.5 diopters, 0.79 diopters and 0.25 diopters receptively.

Figure 2

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For the main study, naive observers were tasked with reporting the orientation of a peripherally viewed target (Figure 3) in a series of five experiments (see Methods for details and Figure 4 for example trial). The target was surrounded by a flanker ring with a target-flanker spacing of 5°, 2.5°, 1.25°, 0.625°, or infinity, i.e., no flanker ring (Figure 3). In Experiments 1 and 2, the target was always presented at fixation depth while the depth of the flanker ring was varied. Conversely, in Experiments 3 and 4 the flanker ring was presented at fixation depth while target depth was varied. Finally, for Experiment 5, the target, flanker ring and fixation were presented together on the same screen at three different depths. To quantify crowding for each stimulus condition we used the reported target orientation across repeated trials to calculate perceptual error (see Methods), which is reported in degrees.

Figure 3

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Figure 4

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Due to the nature of the experimental set up, and the large distances being tested, it is possible that head movements, diplopia, or local suppression (see Discussion) could have resulted in differences in the perceived position of the target relative to the flanker ring. Therefore, in all experiments except Experiment 5, observers were also asked to report the perceived location of the target relative to the position of the flanker ring (Figure 4). This enabled us to examine how perceptual error was affected by factors such as target misalignment and possible diplopia (see Discussion).

Perceptual error

Target always at fixation depth with variable flanker depth

Experiment 1: Target and fixation at 1.26 m with flanker ring presented at each depth (Figure 5A and Figure 5—figure supplement 1A)

Perceptual error was higher when the flanker ring was displayed in front of, or behind, the target and fixation plane (mixed effects multiple linear regression models compared via LRT for effect of flanker depth: χ²₍₂₎=20.67, p<0.001). As expected, perceptual error decreased as target-flanker spacing increased (effect of target-flanker spacing: χ²₍₁₎=31.71, p<0.001). There was no significant interaction between flanker depth and target-flanker spacing (χ²₍₂₎=5.56, p=0.062).

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Experiment 2: Target and fixation at 0.4 m or 4 m with flanker ring presented at each depth (Figure 5B and Figure 5—figure supplement 1B)

Perceptual error tended to increase with increasing flanker depth when the flanker ring was behind the target and fixation plane, however, the effect of flanker depth was much weaker when the flanker ring was in front of the target and fixation (interaction between target-fixation depth and flanker depth: χ²₍₂₎=17.18, p<0.001). Perceptual error decreased with increasing target-flanker spacing, in a manner corresponding to target-fixation depth (interaction between target-flanker spacing and target-fixation depth: χ²₍₁₎=9.2, p=0.002). There was no significant interaction between target-flanker spacing and flanker screen and (χ²₍₂₎=4.52, p=0.104).

Flanker ring always at fixation depth with variable target depth

Experiment 3: Flanker ring and fixation at 1.26 m with target presented at each depth (Figure 6A and Figure 6—figure supplement 1A)

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Overall, perceptual error was higher when the target was displayed in front of, or behind, the flanker ring and fixation (effect of target depth: χ²₍₂₎=36.93, p<0.001), with the greatest perceptual error occurring when the target was behind the flanker ring and fixation. Perceptual error decreased as target-flanker spacing increased (effect of target-flanker spacing: χ²₍₁₎=45.99, p<0.001). There was no significant interaction between target depth and target-flanker spacing (χ²₍₂₎=3.55, p=0.17).

Experiment 4: Flanker ring and fixation at 0.4 m or 4 m with target presented at each depth (Figure 6B and Figure 6—figure supplement 1B)

Perceptual error was greatest when the target was displayed behind the flanker ring and fixation, while the effect of depth was less prominent when the target was displayed in front of the flanker ring and fixation (interaction between flanker-fixation depth and target depth: χ²₍₂₎=61.87, p<0.001). Perceptual error decreased as target-flanker spacing increased (effect of target-flanker spacing: χ²₍₁₎=29.92, p<0.001). There was no significant interaction between flanker-fixation depth and target-flanker spacing (χ²₍₁₎=0.14, p=0.71) nor between target depth and target-flanker spacing (χ²₍₂₎=1.43, p=0.488).

Target and flanker ring at fixation depth

Experiment 5: Target and flanker ring always at fixation depth (Figure 7)

Perceptual error decreased as target-flanker spacing increased (effect of target-flanker spacing: χ²₍₁₎=64.8, p<0.001). There was also a significant effect of target-flanker-fixation depth (χ²₍₂₎=8.75, p=0.013) resulting from a higher perceptual error for stimuli displayed at 4 m. There was no significant interaction between target-flanker-fixation depth and target-flanker spacing (χ²₍₂₎=1.72, p=0.424).

Figure 7

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Perceived target position relative to the flanker ring

Target always at fixation depth with variable flanker depth

Experiment 1: Target and fixation at 1.26 m with flanker ring presented at each depth (Figure 8A and Figure 8—figure supplement 1)

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In Experiment 1, most observers consistently reported seeing the target inside the flanker ring. However, when the flanker ring was away from target-fixation depth there was a reduction in the proportion of observers who consistently reported seeing the target within the flanker ring when the target-flanker spacing was small (mixed effects binary logistic regression models compared via LRT; interaction between target-flanker spacing and flanker depth: χ²₍₂₎=36.12, p<0.001). This effect was greatest when the flanker ring was displayed behind the target and fixation.

Note that in all four experiments, the response to the control (i.e. no flanker condition) indicates the probability of an observer making an inaccurate report (e.g. they selected the wrong option by mistake or missed the stimulus and reported a guess rather than selecting the ‘Unsure’ option).

Experiment 2: Target and fixation at 0.4 m or 4 m with flanker ring presented at each depth (Figure 8B and Figure 8—figure supplement 2)

As with the previous experiment, when the flanker ring was away from target-fixation depth, there was a reduction in the overall proportion of trials in which observers reported seeing the target within the flanker ring (interaction between target-fixation depth and flanker depth: χ²₍₂₎=374.26, p<0.001). The greatest reduction occurred when target-flanker spacing was smaller (effect of target-flanker spacing: χ²₍₁₎=178.65, p<0.001). There was no significant interaction between flanker depth and target-flanker spacing (χ²₍₂₎=0.24, p=0.886) nor between target-fixation depth and target-flanker spacing (χ²₍₁₎=1.64, p=0.2).

Flanker ring always at fixation depth with variable target depth

Experiment 3: Flanker ring and fixation at 1.26 m with target presented at each depth (Figure 9A and Figure 9—figure supplement 1)

When the target was away from flanker-fixation depth, observers were less likely to report seeing the target within the flanker ring. This effect was greatest when target-flanker spacing was smaller and when the target was displayed in front of the flanker ring and fixation (interaction between target-flanker spacing and target depth: χ²₍₂₎=100.38, p<0.001).

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Experiment 4: Flanker ring and fixation at 0.4 m or 4 m with target presented at each depth (Figure 9 and Figure 9—figure supplement 2)

As with the previous experiment, the greater the difference between target depth and flanker-fixation depth, the less likely observers were to report seeing the target within the flanker ring (interaction between flanker-fixation depth and target depth: χ²₍₂₎=779.49, p<0.001), particularly when target-flanker spacing was small (interaction between target-flanker spacing and target depth: χ²₍₂₎=23.27, p<0.001). However, target-flanker spacing had a weaker effect on the proportion of trials in which observers reported seeing the target within the flanker ring when the flanker ring and fixation were near compared to far (interaction between target-flanker spacing and flanker-fixation depth: χ²₍₁₎=56.23, p<0.001).

Individual differences in perceptual error and perceived target position in experienced observers

While we were able to detect overall statistically significant trends in the results, it is apparent from Figures 5—9 that there is a large amount of variation within the data. This raises questions about whether the variation is because the effects of depth are highly variable between some observers, or because the naive observers were not very stable at indicating their perception. The latter could be due to the naive observers being relatively inexperienced at the task, despite receiving training, since each observer only participated in a single experiment. Therefore, to investigate the effects of depth at the individual level we repeated the study with a small number of highly trained, experienced observers who performed all five experiments (see Methods for details).

Target always at fixation depth with variable flanker depth

Experiments 1 and 2 with experienced observers (Figure 10 and Figure 10—figure suppliments 1 and 2)

The small sample size means direct comparisons between these results and the results reported above for the main study should be avoided. Nevertheless, the overall effects reported above are also apparent in most of the experienced observers (Figure 10). However, Figure 10 shows that even among highly trained, experienced observers there is a large amount of variation both between and within subjects. For instance, when the target and fixation are on the near screen (0.4 m) and target-flanker spacing is 0.625°, ES3 and ES4 both exhibit a similar increase in perceptual error with increasing flanker depth, which is consistent with the overall effect shown in Figure 5B. In contrast, ES2 shows the opposite trend for the same stimulus condition, a reduction in perceptual error with increased flanker depth. However, when the target and fixation were on the mid screen (1.26 m) and target-flanker spacing is 0.625°, ES2 does exhibit an increase in perceptual error when the flanker ring is behind the target and fixation (as do ES1 and ES3), thus providing an example of between and within subject variation. The variation in perceptual error between subjects cannot solely be explained by differences in the perceived position of the target relative to the flanker ring (Figure 10—figure supplements 1 and 2). For example, when the target and fixation were on the near screen and target-flanker spacing was 0.625°, the perceived target positions reported by ES2 and ES4 were remarkably similar (Figure 10—figure supplement 2) despite exhibiting the previously mentioned opposite effects of depth on perceptual error (Figure 10).

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Flanker ring always at fixation depth with variable target depth

Experiments 3 and 4 with experienced observers (Figure 11 and Figure 11—figure suppliments 1 and 2)

Like the results from the repeat of Experiments 1 and 2 with the experienced subjects, Figure 11 shows there was also a relatively large amount of between and within subject variation in Experiments 3 and 4 when repeated with the experienced subjects. For instance, if we look at the analogous stimulus condition to the one used in the previous example, that is, flanker ring and fixation on the near screen (0.4 m) with a target-flanker spacing of 0.625°, ES1, ES3, and ES4 all exhibit an increase in perceptual error with increasing target depth, which is consistent with the overall effect shown in Figure 6B. In contrast, ES2 again shows the opposite effect for the same stimulus condition, a reduction in perceptual error with increasing target depth. Again, the variation in perceptual error between subjects cannot solely be explained by differences in the perceived position of the target relative to the flanker ring (Figure 11—figure supplements 1 and 2). For instance, the perceived target positions reported by ES2 and ES3 were very similar (Figure 11—figure supplement 2) when the flanker ring and fixation were on the near screen and target-flanker spacing was 0.625°, yet the two observers exhibited the opposite effect of increasing target depth on perceptual error (Figure 11).

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Target and flanker ring at fixation depth

Experiment 5 with experienced observers (Figure 12)

Figure 12 shows there was also some variation between the experienced subjects in Experiment 5 with ES2 and ES3 both exhibiting the highest perceptual error when the target, flanker ring and fixation were furthest away (though this is less pronounced at greater eccentricities for ES3). ES1 and ES4 on the other hand both show a less consistent effect of depth.

Figure 12

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In all experiments, perceptual error generally decreased as the target-flanker spacing increased, which is in line with previous crowding research (Bouma, 1970; Pelli, 2008). Overall, perceptual error was higher when the target or flanker ring were presented at a different depth from the other and from fixation. The greatest differences in perceptual error among the different depth conditions occurred when the target or flanker ring were presented behind fixation depth. In contrast, when the target or flanker ring were presented in front of fixation depth, the differences in perceptual error among depth conditions were notably smaller. The results also show that when the target, flanker ring and fixation were all at the same depth plane, crowding tended to increase with the absolute distance of the stimuli from the observer. However, in all the main experiments with naive observers there was a large amount of variation within the data. Follow up experiments with a small sample of highly trained, experienced observers were largely consistent with the main effects observed in the main study. Moreover, the experienced observers also exhibited a high degree of between subject variation, which supports the suggestion that the variability in the main data from the large sample of naive observers is representative of the natural variation between different individuals. Therefore, although significant effects were found at the population level, the effects of large differences in target-flanker depth can be highly variable at the individual level. This demonstrates the importance of using a large sample size to investigate effects that are not necessarily detectable at the individual level. The discussion of the findings will focus on the overall results from the main study on naive participants, with the findings from the small sample of experienced observers used to provide additional context and insight.

The main finding that a depth difference between the flankers and the target led to an increase, rather than a decrease, in perceptual error is different from the findings of several previous studies that investigated the effect of depth on crowding using a stereoscopic presentation (Astle et al., 2014; Felisberti et al., 2005; Kooi et al., 1994; Sayim et al., 2008). For example, Astle et al., 2014 found that when the target was presented at fixation depth (comparable to Experiments 1 and 2 in our study), increasing the disparity between the target and flankers resulted in less crowding, and ultimately a complete release from crowding. The authors also reported that crowding was greater when flankers were presented in crossed disparity (in front of the target and fixation), compared to uncrossed disparity (behind the target and fixation) (Astle et al., 2014). Similarly, when the flankers were presented at fixation depth (comparable to Experiments 3 and 4 in our study), Sayim et al., 2008 found that foveal crowding was lower when the target was presented in front of or behind the flankers and fixation.

Several explanations for crowding have been proposed in which crowding occurs because target and flanking features are inappropriately grouped (Banks et al., 1979; Herzog and Manassi, 2015; Pachai et al., 2016). Consistent with this explanation, crowding can be alleviated when the flankers are grouped together and segmented from the target (Herzog and Manassi, 2015). One piece of evidence in support of this account is the reduction of crowding that can occur when flankers are presented at a different depth from the target (Astle et al., 2014; Felisberti et al., 2005; Kooi et al., 1994; Sayim et al., 2008). Our results challenge this view of crowding because it would predict that increasing the depth difference between target and flankers would decrease the probability of them being inappropriately grouped and increase the probability of the flankers being segmented from the target, thereby decreasing perceptual error, the opposite of our finding. Other models of crowding, such as texture processing and feature integration (Balas et al., 2009; Freeman and Simoncelli, 2011; Parkes et al., 2001; van den Berg et al., 2012; Wallis and Bex, 2012), sampling errors (Ester et al., 2015; Ester et al., 2014; Harrison and Bex, 2017; Harrison and Bex, 2016; Harrison and Bex, 2015), attentional resolution limits (He et al., 1996) or saccade properties (Nandy and Tjan, 2012) are agnostic concerning the influence of depth differences among targets and flankers. Therefore, each of these models would require modification to explain the increase in crowding that we observe with large real depth differences between a target and its flankers.

In contrast with studies that controlled depth with small stereoscopic disparities, our results do agree with the findings of Eberhardt and Huckauf, 2020 who also used a real-depth display and tested larger differences in depth between the target and flankers than previous studies had examined, though depth differences were still much smaller than those tested in our current study. When the target was at fixation depth (comparable to Experiments 1 and 2 in our study), Eberhardt and Huckauf, 2020 found that crowding increased with increasing target-flanker depth difference. The authors also found that crowding was greater when the flankers were behind the target and fixation compared to in front of it (Eberhardt and Huckauf, 2020). Our findings from Experiments 1 and 2 are consistent with these results. However, when the flankers were at fixation depth (comparable to Experiments 3 and 4 in our study), Eberhardt and Huckauf, 2020 found that crowding was higher when the target was in front of the flankers and fixation compared to when it was behind them. In contrast, in Experiments 3 and 4 we found that perceptual error was greatest when the target was presented behind the flanker ring and fixation rather than in front of it. This difference is likely due to a combination of high defocus blur when the target was behind fixation combined with the finding from Experiment 5 which found that in our study a larger absolute distance from the observer resulted in higher perceptual error.

Why the inconsistencies across studies? It is important to consider that most of the previous studies used very small depth differences, the largest being 0.1 diopters in Eberhardt and Huckauf, 2019; Eberhardt and Huckauf, 2020. In comparison, the depth difference in our study ranged from 0.54 diopters (between the mid and far screens) to 2.25 diopters (between the near and far screens). Our results, together with those from previous studies, suggest that small differences in depth between the target and flankers reduce crowding (Astle et al., 2014; Felisberti et al., 2005; Kooi et al., 1994; Sayim et al., 2008), while larger differences in depth can increase it (Eberhardt and Huckauf, 2020 and results from our study). Although this pattern is quite surprising, there is precedent for non-linear effects of depth on perceptual processing outside the crowding literature. In a multiple object tracking task, when the targets and distractors were distributed equally on two depth planes, tracking accuracy was better than the accuracy during trials in which targets and distractors appeared on a single depth plane when the depth difference between planes was small (~6 cm) (Ur Rehman et al., 2015; Viswanathan and Mingolla, 2002), but worse when the depth difference between planes was large (50 cm) (Ur Rehman et al., 2015).

How could depth affect perception in this nonlinear way? The geometry of the eyes and the 3D environment create interocular disparity differences between the images in each eye. When corresponding features in the images in each eye can be identified, the images can be fused to generate a binocular perceptual experience of depth (for review see Nityananda and Read, 2017). There is a horizontal and vertical spatial limit to the interocular disparity difference over which the visual system attempts to identify corresponding retinal points in order to fuse different 2D interocular images as a single 3D object (Westheimer, 1979). This 2D spatial correspondence limit creates a 3D volume along the horopter known as Panum’s Fusional Area (Panum, 1858). Outside Panum’s Fusional Area, there is a loss of stereoscopic depth perception and either double vision (diplopia) may be experienced, or single vision may occur if the image from one eye is partly suppressed (Georgeson and Wallis, 2014; Ono et al., 1977; Spiegel et al., 2016; Stidwill and Fletcher, 2010). The spatial extent of Panum’s Fusional Area depends on the spatial frequency of the stimuli (Maiello et al., 2020; Pulliam, 1981; Reynaud and Hess, 2017; Wilcox and Allison, 2009; Yang and Blake, 1991) and increases with eccentricity (Hampton and Kertesz, 1983; Harrold and Grove, 2019; Qin et al., 2006).

It is possible that differences between fusion and depth perception within Panum’s Fusional Area versus diplopia, and/or local suppression for single vision, outside of it can explain the patterns of results observed between studies. Small disparity differences between target and flankers create differences in perceived depth that can alleviate the effects of crowding, potentially through ungrouping of target and flanking elements (Herzog et al., 2015; Herzog and Manassi, 2015; Manassi et al., 2012) or by independent processing of target and flankers in different depth-selective channels (Norcia et al., 1985; Pulliam, 1981; Reynaud and Hess, 2017; Tyler et al., 1994; Wilcox and Allison, 2009; Yang and Blake, 1991) by any of the computational models of crowding based on texture processing and feature integration (Balas et al., 2009; Freeman and Simoncelli, 2011; Parkes et al., 2001; van den Berg et al., 2012; Wallis and Bex, 2012), sampling errors (Ester et al., 2015; Ester et al., 2014; Harrison and Bex, 2017; Harrison and Bex, 2016; Harrison and Bex, 2015) attentional resolution limits (He et al., 1996) or saccade properties (Nandy and Tjan, 2012). Large interocular disparity differences on the other hand can induce diplopia that could increase the perceived number of flankers (Eberhardt and Huckauf, 2019). In theory, this perceived increase in the number of flanking elements could result in higher perceptual error because increasing the number of flankers is known to increase crowding under certain conditions (Chanceaux et al., 2014; Manassi et al., 2012; Pluháček et al., 2021). It is however worth noting that the opposite can occur, that is reduced crowding with increasing number of flankers, in cases where the additional flankers are grouped together (Manassi et al., 2013; Manassi et al., 2012). Surprisingly, when asked, only a few of the naive observers reported experiencing diplopia, and those that did reported only experiencing it in a minority of presentations for which they selected the ‘unsure or no ring’ option (see Methods) when reporting the perceived location of the target (Figure 8—figure supplements 1E and 2E, and Figure 9—figure supplements 1E and 2E). However, among the four experienced observers, three verbally reported experiencing diplopia during some of the conditions for which they either selected the ‘unsure or no ring’ option (Figure 10—figure supplement 2E and Figure 11—figure supplement 2E), or in cases when the diplopia was barely visible, they chose the option that was the closest match to the clearest stimulus image. The fact that the experienced observers were more likely to report experiencing diplopia, possibly because they were better at recognizing it, raises the possibility that diplopia may have been more common among the naive observers than was indicated by asking them. However, it is worth noting that one of the four experienced observers reported that they never experienced diplopia in any of the experiments, which is more consistent with the majority of naive observers. It is possible that the short presentation time of the stimulus was too fast for most observers to notice diplopia consciously (i.e. diplopia did not enter awareness), or that diplopia was suppressed entirely by local suppression to maintain single vision. Attention effects such as inattentional blindness (Bredemeier and Simons, 2012; Simons and Chabris, 1999) could also play a role in explaining why so few observers reported diplopia in the main experiments. There is conflicting evidence as to whether conscious awareness of a flanker is necessary for it to induce crowding (compare Ho and Cheung, 2011 vs Wallis and Bex, 2011), and thus whether ‘unconscious diplopia’ could have increased crowding in this study due to the reason highlighted above is a matter for debate and beyond the scope of our findings. In addition, it is worth noting that due to the lack of binocular fusion of stimulus areas outside Panum’s Fusional Area, we can’t rule out the possible involvement of binocular rivalry which has been shown to interfere with object recognition not just in isolation but also when combined with crowding (Kim et al., 2013).

Another explanation for higher perceptual error with increasing target-flanker depth differences could be perceived target misalignment. As explained in the Methods, at the start of Experiments 1–4 each observer performed a subjective spatial calibration to ensure that the angular positions of the stimuli and fixation point relative to primary gaze were consistent across all three depth planes. Although the main experiments were performed under binocular viewing conditions, this spatial calibration had to be performed monocularly using the observer’s dominant eye to avoid confusion caused by diplopia or rivalry (see Methods). This means that the screens were imperfectly aligned for the non-dominant eye. Therefore, as in the real world, at certain flanker sizes and separations there may be occlusions between target and flanker features that could affect target report accuracy, which is not the same mechanism as crowding. In our study, such misalignment could result from local suppression of the calibrated eye to maintain single vision, and/or head movements following the spatial calibration. To examine how target misalignment affected the overall results, we recalculated perceptual error for the main experiments with naive observers using only trials in which the observer reported seeing the target inside the flanker ring. We then reanalyzed these data the same way as for perceptual error calculated from the full data set (see Methods). Apart from Experiment 2, the effect of flanker and/or target depth remained statistically significant (see Figure 5—figure supplement 1 and Figure 6—figure supplement 1 for plots and analysis results). Therefore, across the majority of experiments, misalignment or occlusion of the target by the flanker ring is not enough to explain the overall results. This supports the suggestion that the increase in perceptual error when the target and flankers are at different depths is being driven by an increase in crowding.

This current study is the first to investigate how crowding is affected by large, real differences in depth between a target and flanking features. This is important because objects in the real world are often flanked by visual features that vary greatly in their distance from an observer, and many will fall outside the limits of Panum’s Fusional Area (Figure 1). A limitation of our approach is that the use of relatively simple stimuli in a tightly controlled experiment limits the generalizability of our findings to the real world where clutter is abundant and more complex. Future research should therefore aim to utilize stimuli that better capture the complexity and heterogeneity of natural scenes. Future work should also investigate if the reported effects of depth on crowding in our study hold at different target eccentricities, particularly given that the range of Panum’s Fusional Area changes with eccentricity (Hampton and Kertesz, 1983; Harrold and Grove, 2019; Qin et al., 2006). Nevertheless, our findings still show that crowding from clutter outside Panum’s Fusional Area has the potential to significantly impact object recognition and visual perception in the peripheral field. Our findings therefore do not support the view that depth differences between targets and flankers necessarily reduce crowding, instead the effect of depth on crowding appears to be more complex than originally thought. Furthermore, data collected from experienced participants shows that the overall trends at the population level may not always be apparent at the individual level. Nonetheless, our results, alongside those of previous studies, suggest that small differences in depth between targets and flankers do not have the same effect on crowding as larger differences in depth in which either the target or flankers are presented outside the limits of binocular fusion. This finding confirms the potential importance and relevance of crowding in three-dimensional scenes.

All data and code required to replicate the analyses in this paper is available on Zenodo.

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Author details

1. Samuel P Smithers

   Department of Psychology, Northeastern University, Boston, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   s.smithers@northeastern.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-2781-7067

2. Yulong Shao

   Department of Psychology, Northeastern University, Boston, United States

   Contribution

   Investigation

   Competing interests

   No competing interests declared

3. James Altham

   Department of Psychology, Northeastern University, Boston, United States

   Contribution

   Investigation

   Competing interests

   No competing interests declared

4. Peter J Bex

   Department of Psychology, Northeastern University, Boston, United States

   Contribution

   Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Methodology, Writing – original draft, Project administration, Writing – review and editing

   For correspondence

   p.bex@northeastern.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-7561-7695

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