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Article  |   February 2019
Hole superiority effect with 3D figures formed by binocular disparity
Author Affiliations
  • Junjun Zhang
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    jjzhang@uestc.edu.cn
  • Jingting Wu
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    511580130@qq.com
  • Xieyi Liu
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    943819188@qq.com
  • Zhenlan Jin
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    jinzl@uestc.edu.cn
  • Ling Li
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    liling@uestc.edu.cn
  • Lin Chen
    CAS Center for Excellence in Brain Science and Intelligence Technology, Shanghai, China
    State Key Laboratory of Brain and Cognitive Science, Institute of Biophysics, Chinese Academy of Sciences, Beijing, China
    MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China
    linchen@bcslab.ibp.ac.cn
Journal of Vision February 2019, Vol.19, 2. doi:10.1167/19.2.2
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      Junjun Zhang, Jingting Wu, Xieyi Liu, Zhenlan Jin, Ling Li, Lin Chen; Hole superiority effect with 3D figures formed by binocular disparity. Journal of Vision 2019;19(2):2. doi: 10.1167/19.2.2.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

The global-first theory of topological perception claims that topological perception is prior to the perception of local features (e.g., Chen, 1982, 2005). Our previous studies demonstrated a hole superiority effect (HSE): Figures with holes are more detectable than figures without holes. Such an HSE was shown with figures formed by either orientation-defined texture (Zhang, 2009) or a black-and-white contrast (Meng, Cui, Zhou, Chen, & Ma, 2012). The present study used binocular disparity as one more organizing factor for testing the abstract nature of the HSE, indicating holes, as a typical kind of topological invariance, are represented in vision independent of the features that were forming the holes. The disparity-forming figures were well controlled for luminance, spatial frequency, subjective contours, and other nontopological factors, which are commonly considered as counter explanations against the topological theory.

Introduction
The theory of topological perception proposes that visual perception proceeds from the “global” to the “local” (for a review, see Chen, 2005). Our visual system extracts the global topological properties rather than the local features at the primitive of visual perception. The most important topological property is characterized by the existence of “hole” stimuli (Pomerantz et al., 2003; S. He, 2008; Casati, 2009; Bertamini & Casati, 2015). For instance, in Figure 1a, there are three figures: an s-shaped figure, an o-shaped figure, and a disk-shaped figure (from left to right). The s-shaped and o-shaped figures have the same area, with similar contour length and spatial frequency components (Chen, Zhang, & Srinivasan, 2003). On the other hand, the s-shaped and disk-shaped figures have different local features but are similar in terms of the existence of a “hole.” Findings show that when these types of stimuli are displayed for a very brief period, it is easier to discriminate between s-shaped and o-shaped figures than to discriminate between s-shaped and disk-shaped figures (Chen, 1982). This sensitivity to the perception of holes has been shown in other tasks, such as with long-range apparent motion perception (Zhuo et al., 2003), multiple-object tracking (K. Zhou, Luo, Zhou, Zhou, & Chen, 2010), numerosity perception (L. X. He, Zhou, Zhou, He, & Chen, 2015), and pattern recognition in bees (Chen et al., 2003). 
Figure 1
 
(a) From left to right: s-shaped figure, o-shaped figure, and disk-shaped figure. (b) An enclosed region (surrounding region) separated the background into two regions: the outer region and the inner region. (c) In a three-dimensional context, the figure-ground relationship of the three regions can be varied to form an o-shaped figure, two-disks figure, or o-shaped hole.
Figure 1
 
(a) From left to right: s-shaped figure, o-shaped figure, and disk-shaped figure. (b) An enclosed region (surrounding region) separated the background into two regions: the outer region and the inner region. (c) In a three-dimensional context, the figure-ground relationship of the three regions can be varied to form an o-shaped figure, two-disks figure, or o-shaped hole.
The proposition that the visual system is sensitive to the existence of holes implies that figures with holes are more detectable than figures without holes. In fact, we showed in previous studies (Zhang et al., 2009; Meng et al., 2018) that it is easier to segment hole figures than to segment non–hole figures from their background, when the backward masking is the same. Another study (Meng et al., 2012) demonstrated that, even during unconscious perception, hole figures have an advantage during visual processing. Thus, the superiority of hole figures during figure-ground segmentation seems to exist across different experimental paradigms. 
The objective of the current study was to investigate the extent of the hole superiority effect (HSE). Specifically, we investigated whether the HSE is observed with three-dimensional (3D) hole figures formed by binocular disparity to further understand the nature of the HSE with the two following advantages. 
First, studies of topological perception, which use two-dimensional (2D) figures that have different topologies, may be confounded by other nontopological factors, such as luminance and spatial frequency. Thus, it is possible that the HSE is observed as a result of these factors, rather than the topological properties. However, in a 3D context, the figures are formed by random-dot stereogram, that is, a pair of images consisting of random dots. Thus, nontopological factors, such as density and luminance, are well matched across the dots, and the binocular disparity between the two images is the only cue that forms the figures. In this case, the topological difference is generated by the binocular disparity only, whereas other nontopological factors are controlled for. 
Second, in a 3D context, it is easier to manipulate the figure-ground relationships via the depth order. For instance, Figure 1b illustrates an image with a surrounding area that is different in color to that of the inner and outer regions. However, the perception of object-hood that can be extracted from this image may differ. It can be perceived as an o-shaped figure, with the surrounding area as the foreground, and the outer and the inner regions as the background (Figure 1c, left). Alternatively, the figure can be interpreted as a small object on top of a bigger one (Figure 1c, middle) or an o-shaped hole (Figure 1c, right), which is the reversal of the o-shaped figure in depth. Hence, the HSE can be tested with different figure-ground organizations. 
We hypothesized that first, the HSE is still effective with 3D figures formed by binocular disparity, and second, the HSE can be observed only with real 3D holed figures in terms of the figure-ground relationship (Figure 1c, left). To test the above hypotheses, we performed three experiments. A four-mirror stereoscope was used in all the experiments to generate the 3D stimuli. The figure-ground relationships in this study were determined using binocular disparity. An enclosed region could be perceived as an object or as a hole, and such perception can sometimes be ambiguous and affected by different factors. Among the different factors, the depth-order factor is a salient cue for the figure-ground relationship and eliminates this ambiguity (Nelson & Palmer, 2001; Bertamini & Lawson, 2006). In the first experiment, o-shaped and s-shaped figures were used to study the HSE in 3D. In the second and third experiments, the depth order was manipulated to study its effect on the HSE. In the second experiment, the depth order of the inner region and the surrounding region of the o-shaped figure was manipulated, whereas in the third experiment, the o-shaped and disk-shaped figures, and their reversed counterparts in depth, were manipulated. 
Experiment 1
Materials and methods
Subjects
Forty college students (aged 19–27 years, 26 men) participated in Experiment 1. Subjects were paid to participate. All participants were right-handed and had normal or corrected-to-normal vision. This experiment and the following experiments were carried out in accordance with the recommendations of the Guideline for Human Behavior Studies, the Institutional Review Board of UESTC MRI Research Center for Brain Research, with written informed consent from all participants. The protocol was approved by the Institutional Review Board of UESTC MRI Research Center for Brain Research. 
Apparatus
A 23-in. light-emitting diode monitor with a resolution of 1,920 × 1,080 was used in the experiment. A four-mirror stereoscope was placed in front of the monitor at a distance of 57 cm. A chin rest was placed in front of the stereoscope. The height of the chin rest was adjusted to ensure that the participants' eyes were at the same height as the stereoscope. A black box covered the area around the monitor and the stereoscope to ensure that the participants could view the monitor only through the stereoscope. Stimuli in the three experiments were presented using MATLAB with Psychtoolbox (Brainard, 1997). 
Stimuli
Random-dot stereograms were used as stimuli. There were two kinds of stereograms: a blank and a target stereogram. The blank stereogram consisted of a pair of identical images of random dots (for instance, Figure 2a). The target stereogram consisted of a pair of images of certain dots at different positions. Two targets were used: the o-shaped figure (for instance, Figure 2b) and the s-shaped figure (for instance, Figure 2c). Each stereogram extended on the screen for 7° × 7°. The binocular disparity of the figures was set as 12 arcmin. The simulated distance from the observers to the background was 57 cm. The simulated distance from the observers to the figures was approximately 55.3 cm. 
Figure 2
 
The random-dot stereograms for (a) blank stimuli, (b) o-shaped figure, and (c) s-shaped figure.
Figure 2
 
The random-dot stereograms for (a) blank stimuli, (b) o-shaped figure, and (c) s-shaped figure.
Design
The ability to detect the target was measured using a two-alternative forced-choice task with backward masks. Each trial started with a 500-millisecond fixation cross, followed by the first dynamic stimulus, another 500 milliseconds of fixation, and then the second dynamic stimulus (Figure 3a). Each dynamic stimulus consisted of 60 frames, each presented for 17 milliseconds. One dynamic stimulus consisted of 60 frames of blank stereograms. Another dynamic stimulus consisted of two successive target stereograms and 58 blank stereograms. The target stereograms appeared randomly between the 11th and the 20th frames. Thus, the dynamic stimulus consisting of a target started with a 167-ms to 340-ms blank stereogram, followed by a 34-ms target stereogram and then a 628-ms to 800-ms blank stereogram again. At the end of each trial, participants were asked to judge whether the target appeared in the first or the second dynamic stimulus, regardless of the shape of the target. 
Figure 3
 
(a) The procedure of a single trial in Experiment 1. The o-shaped figure appeared in the first dynamic stimulus. Conditions with either s-shaped figures or targets that appeared in the second dynamic stimulus position are not shown. (b) Results of Experiment 1. Detecting the o-shaped figure (90.1%) was more accurate than detecting the s-shaped figure (85.6%). Error bars denote standard error.
Figure 3
 
(a) The procedure of a single trial in Experiment 1. The o-shaped figure appeared in the first dynamic stimulus. Conditions with either s-shaped figures or targets that appeared in the second dynamic stimulus position are not shown. (b) Results of Experiment 1. Detecting the o-shaped figure (90.1%) was more accurate than detecting the s-shaped figure (85.6%). Error bars denote standard error.
The dynamic random-dot stereograms form a better display to test target detection, compared with traditional paradigms of backward masking. In the traditional backward masking paradigm, the presented target is followed by a visible mask, so that subjects are aware of the abrupt onset of the mask. In the current study, each pair of stereograms was replaced by another pair of stereograms in a subsequent frame. Thus, participants were not aware of the onset of the mask, but the target was still masked. 
The independent variable was the topology of the figures (o-shaped or s-shaped). Each condition was replicated 48 times. The experiment consisted of three blocks of 32 trials. The appearance of the target in the first or the second dynamic stimulus was counterbalanced. Before the experiment, subjects were asked to perform a 10-trial training session. 
Results
The dependent variable was the accuracy of target detection with the o-shaped and s-shaped figures as stimuli. The accuracies in detecting an o-shaped and s-shaped target were analyzed. An averaged accuracy of 60% was chosen as the criterion. Twelve of the 40 subjects did not meet this criterion. Their data were excluded from further analysis. Accuracies were analyzed using a Wilcoxon signed-rank test. There was a significant difference in detecting o-shaped and s-shaped figures (Z = −3.753, sample size = 27, p < 0.001). The accuracy in detecting o-shaped and s-shaped targets was 91.0% and 85.7%, respectively (Figure 3b). The results suggest that the HSE exists in a 3D context, in which the figure-ground segmentation is determined by the binocular disparity only. 
Experiment 2a
In Experiment 1, the HSE was observed in a 3D context. In Experiment 2, we investigated whether the figure-ground organization had an impact on the HSE. Here, we used a disk-shaped figure, an o-shaped figure, and a two-disks figure (Figure 4a) to evaluate target detection. We hypothesized that if the figure-ground organization has an effect on the HSE, target detection performance will be different for the two-disks and disk-shaped figures. 
Figure 4
 
(a) The three targets in Experiment 2a: disk-shaped figure, o-shaped figure, and two-disks figure. (b) Results of Experiment 2a. Detecting the o-shaped figure (88.7%) was more accurate than detecting the o-shaped figure (81.5%) and the two-disks figure (82.2%). Error bars denote standard error.
Figure 4
 
(a) The three targets in Experiment 2a: disk-shaped figure, o-shaped figure, and two-disks figure. (b) Results of Experiment 2a. Detecting the o-shaped figure (88.7%) was more accurate than detecting the o-shaped figure (81.5%) and the two-disks figure (82.2%). Error bars denote standard error.
Materials and methods
Subjects and apparatus
Twenty-six college students (aged 21–25 years, 12 men) were paid to participate in this experiment. They were right-handed and had normal or corrected-to-normal vision. None of them had participated in Experiment 1. The apparatus was the same as in Experiment 1
Stimuli and design
The paradigm of this experiment was similar to Experiment 1. Targets consisted of a disk-shaped figure, o-shaped figure, and a two-disks figure. The two-disks figure consisted of one small disk on the top of a big one. The size of the small disk was the same as the hole of the o-shaped figure. Thus, the only difference between the o-shaped figure and the two-disks figure was the depth of the inner region. The binocular disparities of the two disks were set as 12 and 25 arcmin. The simulated distance from the observers to the background was 57 cm. The simulated distance from the observers to the disk-shaped figure, o-shaped figure, and the outer region of the two-disks figure was 55.3 cm. The simulated distance from the observers to the inner region of the two-disks figure was 53.6 cm. The independent variable was the target shape (disk, o-shaped, or two-disks). There were three conditions. Each condition was replicated for 36 times. There were three blocks of 36 trials in this experiment. In half of the trials, the target appeared as the first dynamic stimulus, and in the other half, the target appeared as the second stimulus. The order of the trials was randomized. 
In Experiment 1, the accuracy of the target detection varied for each participant. As a result, only 28 of 40 participants met the accuracy criterion. Thus, prior to the experiment, an adaptive session was performed to determine the threshold of target detection (a square). A 2/1 up-down staircase was designed to estimate the threshold at a detecting accuracy of 70.7% for each subject, which was then used in the experiment. 
Results
The average duration of the target detection was 29 ms (17 ms for 12 subjects, 34 ms for seven subjects, and 50 ms for seven subjects). The same criterion (averaged accuracy greater than 60%) was applied to the experiment, and none of the data were excluded. A Wilcoxon signed-rank test showed that the accuracy in detecting the o-shaped figure was significantly higher than detecting the disk figure (Z = –3.811, sample size = 21, p < 0.001). The finding is consistent with those of Experiment 1, showing HSE for 3D images. In addition, we found that the accuracy in detecting the o-shaped figure was significantly higher than detecting the two-disks figure (Z = –3.425, sample size = 24, p < 0.01), suggesting that the figure-ground organization has an impact on the HSE. However, there were no significant differences between the detection accuracy of the disk-shaped and two-disks figures (Z = –0.602, sample size = 22, p = 0.547). The detection accuracies of the o-shaped, disk-shaped, and two-disks figures were 88.7%, 81.5%, and 82.2%, respectively (Figure 4b). 
Experiment 2b
In Experiment 2a, there were differences between the range of disparity of the o-shaped and two-disk figures. It is possible that the difference in detection was simply due to the range of the disparity and not the topological structure. In the current experiment, the range of the disparity was matched for the two stimuli. The binocular disparities were set as 9 and 19 arcmin. For the o-shaped figure, the simulated distances from the observers to the outer and the inner regions were 54.4 cm and 55.7 cm, respectively. For the two-disk figure, the simulated distances from the observers to the outer and the inner regions were 55.7 cm and 54.4 cm, respectively (Figure 5a). The simulated distance from the observers to the background was 57 cm. Thus, the range of the disparity of the o-shaped and two-disk figures was identical. The setup of this experiment was the same as in Experiment 2a, and each condition was tested 36 times. 
Figure 5
 
(a) The two targets in Experiment 2b. (b) Results of Experiment 2b. Detecting the o-shaped figure (91.1%) was more accurate than detecting the two-disks figure (85.1%). Error bars denote standard error.
Figure 5
 
(a) The two targets in Experiment 2b. (b) Results of Experiment 2b. Detecting the o-shaped figure (91.1%) was more accurate than detecting the two-disks figure (85.1%). Error bars denote standard error.
Fourteen college students (aged 22–26 years, seven men) were paid to participate in the experiment. The accuracies for detecting the o-shaped figure and two-disk figure were analyzed (Figure 5b). A Wilcoxon signed-rank test showed a significant difference between the detection accuracy of the o-shaped and the two-disk figure (Z = –2.866, sample size = 11, p < 0.01). The detection accuracy of the two-disk figure (85.1%) was lower than that of the o-shaped figure (91.1%). This finding demonstrates that the difference in detection is not due to the range of the disparity. 
Experiment 3
Materials and methods
Subjects and apparatus
Twenty-six college students (aged 20–26 years, 14 men) were paid to participate in the experiment. They were right-handed and had normal or corrected-to-normal vision. None of the subjects had participated in Experiments 1 or 2. The apparatus was the same as in Experiment 1
Stimuli and design
Four different targets were used. Two targets consisted of the same o-shaped and disk-shaped figures that were used in Experiment 2. The other two targets consisted of the depth reversal of the figures, that is, an o-shaped hole and a disk-shaped hole (Figure 6a). The paradigm of this experiment was similar to that in Experiment 2. The binocular disparity was set the same as in Experiment 2a. The simulated distance from the observers to the figures and the holes were 55.3 cm and 58.7 cm, respectively. The simulated distance from the observers to the background was 57 cm. 
Figure 6
 
(a) The targets in Experiment 3: o-shaped figure, disk-shaped figure, o-shaped hole, and disk-shaped hole. Random-dot stereogram of those figures were the same as in Figure 4a. (b) Results of Experiment 3. Detecting figures (92.5% for o-shaped figure, 88.8% for disk-shaped figure) was more accurate than detecting holes (72.1% for o-shaped hole, 74.7% for disk-shaped hole). Error bars denote standard error.
Figure 6
 
(a) The targets in Experiment 3: o-shaped figure, disk-shaped figure, o-shaped hole, and disk-shaped hole. Random-dot stereogram of those figures were the same as in Figure 4a. (b) Results of Experiment 3. Detecting figures (92.5% for o-shaped figure, 88.8% for disk-shaped figure) was more accurate than detecting holes (72.1% for o-shaped hole, 74.7% for disk-shaped hole). Error bars denote standard error.
The independent variables were the topology (o-shaped or disk-shaped) and the depth order (figure or hole), resulting in a total of four conditions. Each condition was replicated 32 times. The current experiment consisted of four blocks of 32 trials. The same adaptive session that was used in Experiment 2 was performed prior to the experiment, in order to determine the detection threshold for each subject. 
Results
All subjects met the criterion of the detection accuracy (60%). The average duration of the target was 57 ms (17 ms for seven subjects, 34 ms for six subjects, 50 ms for four subjects, 67 ms for four subjects, 100 ms for four subjects, and 117 ms for one subject). First, a Shapiro-Wilk test was applied and confirmed that the accuracies for each condition were normally distributed. A repeated analysis of variance was then applied and found a significant main effect for the depth order, F(2, 50) = 40.711, p < 0.001, and a significant depth × topology interaction, F(4, 100) = 7.246, p < 0.05 (Figure 6b). A Wilcoxon signed-rank test found that the detection accuracy of the o-shaped figure (92.5%) was significantly higher than that of the disk-shaped figure (88.8%), Z = −4.200, sample size = 24, p < 0.001. There was no significant difference between the detection accuracy of the o-shaped hole (72.1%) and the s-shaped hole (74.7%). 
General discussion
The HSE was first observed in a 2D context showing that figures with holes were more detectable than figures without holes (Zhang et al., 2009; Meng et al., 2012, 2018). In the current study, we showed that the HSE is also effective in a 3D context but only applies to real holed figures, in which holed figures were defined as objects surrounding a region, through which a further background is visible. In all experiments, we used random-dot stereograms and binocular disparity as the only cue for the figure-ground relationship. Our previous studies showed the HSE with figures formed by orientation-defined texture (Zhang et al., 2009) and black-white contrast (Meng et al., 2012, 2018). Here, we further showed that the HSE is also effective for 3D disparity segmentation (Experiment 1). These findings suggest that the HSE is a general figure-ground segmentation rule regardless of the underlying low-level features. 
In Experiments 2 and 3, different figure-ground relationships of an o-shaped figure were manipulated using binocular disparity. In Experiment 2, the o-shaped figure was more detectable than the disk-shaped figure, supporting the proposition of a 3D HSE. The two-disk figure differed from the o-shaped figure in terms of the depth of the inner region and showed lower accuracy for target detection. In Experiment 3, the o-shaped figure and the disk-shaped figure were reversed in depth. We found that the detection of figures was easier than the detection of holes and that the HSE was effective only for the figures. Taken together, Experiments 2 and 3 showed that different figure-ground segmentation has an impact on the HSE. Thus, the hole figure has to be perceived as a real hole in a 3D context in order for the figure-ground segmentation superiority effect to take place. 
It can be argued that the HSE is due to the detection of the hole itself and not the figure surrounding the hole. If this was the case, the disk-shaped hole should have been detected easily. However, our results show otherwise (Experiment 3), further supporting evidence that the HSE is effective only for the hole figure that has two closed contours. 
Border ownership and the formation of a hole
To segment a figure from its background, the boundaries need to be detected and then the surface needs to be segregated (Appelbaum, Wade, Vildavski, Pettet, & Norcia, 2006; Scholte, Jolij, Fahrenfort, & Lamme, 2008; Machilsen & Wagemans, 2011; Layton, Mingolla, & Yazdanbakhsh, 2014). The integration of these two steps is based on the formation of border ownership (Komatsu & Ideura, 1993; von der Heydt, 2015) that determines which surface is integrated with the contour to form a figure. Physiological studies found that V1 and V2 are responsible for boundary detection (Rossi, Desimone, & Ungerleider, 2001; Marcus & Van Essen, 2002), whereas neurons in V2 and V4 areas selectively respond to border ownership (H. Zhou, Friedman, & von der Heydt, 2000), and such selectivity arises via feedback projection from higher visual cortex (Jehee, Lamme, & Roelfsema, 2007; Layton et al., 2014). On the other hand, an electroencephalogram (Scholte et al., 2008) and a transcranial magnetic stimulation study (Heinen, Jolij, & Lamme, 2005) found that neural correlates of surface segregation first appear in temporal areas and back propagate to occipital areas. These studies suggested that local and global information of figure-ground segregation proceed along the visual ventral pathway. Boundary detection can be generated from different cues, such as color contrast, texture orientation, and, in this case, binocular disparity, which can also be detected in the V1 and V2 areas (Prince, Cumming, & Parker, 2002; Prince, Pointon, Cumming, & Parker, 2002; Parker, 2007). In the current study, it may be argued that to identify an object, one needs to detect the local boundary that is defined by the binocular disparity. In other words, the global structure is apparent only after the local feature has been extracted. This seems to contradict the proposal that global information proceeds from local information in visual perception. However, we argue that there is a distinction between psychological perception and the underlying physiological process. Thus, even though boundary detection is believed to be the first stage in the physiological process, it may not be sufficient to generate the psychological perception of the object, or even the boundary itself. To identify an object, the complete process of the figure-ground segregation is required, including border ownership assignment and surface segregation. With regard to the random-dot stereograms that were used in the current study, the visual system is required to pair all the dots in one eye with the corresponding dots in another eye, a process known as the stereo-correspondence problem (Julesz, 1964). Thus, even when the local boundary is detected within areas V1 and V2, the stereo-correspondence problem remains unsolved (Verhoef, Vogels, & Janssen, 2016) and can be solved only in the temporal visual cortex (Janssen, Vogels, Liu, & Orban, 2003), so that the successful perception of the 3D structure can be formed only after all the corresponding dots are matched. 
Because the HSE is effective at the figure-ground segmentation stage, it is important to determine which factor is critical: contour detection, surface segregation, or border ownership. In Figure 1, each of the three figures (the o-shaped figure, two-disk figure, and o-shaped hole) has two closed contours; thus, the boundary detection for the three figures is identical. The surface segregation of the three figures is also identical, because the surrounding region is segregated from the outer and inner region. We found that the detection of the o-shaped figure was more accurate than the two-disk figure (Experiment 2) and o-shaped hole (Experiment 3). Thus, contour detection and surface segregation do not seem to be factors that affect the HSE. 
Our study suggests that the only factor that seems to be critical for the HSE is border ownership. In the current study, the o-shaped figure has two closed contours that are owned by the surrounding region and form the boundary of the figure. The two-disks figure has one contour that is owned by the surrounding region and another that is owned by the inner region. The o-shaped hole has one contour that is owned by the outer region and one that is owned by the inner region. Thus, the o-shaped figure is the only figure that has two closed borders and that demonstrates the HSE. In addition, we found that detecting the o-shaped figure was easier than detecting the disk-shaped figure, but this was not the case for their reversed counterpart in depth (Experiment 3). The difference between the figure and the hole is that the figure owns borders but the hole does not. This is consistent with a reinterpretation of the hole concept (Casati, 2009), which proposes that the necessary condition for a figure to have a hole is that it has two complete boundaries. 
Border ownership is regarded as a process that forms an early representation of objects (Kogo & Ee, 2015; von der Heydt, 2015). Our results demonstrated that border ownership selectively formed the real 3D holed figures, which exhibited the HSE exclusively. This is supported by the proposition that the formation of an object, and not its physical stimulus features, is the unit of perceptual experience (Wagemans, 2016). 
The HSE and hole figures
Differences in perception of holes versus objects lead to changes in performance in tasks such as visual searching (Hulleman & Humphreys, 2005; Bertamini & Lawson, 2006) and position judgment (Bertamini & Croucher, 2003). Previous studies (Bertamini & Mosca, 2004; Bertamini & Farrant, 2006; Bertamini & Hulleman, 2006; Bertamini & Lawson, 2006; Bertamini & Helmy, 2012) used similar methodologies as those in our study and showed that the reaction time in detecting the shape of a barrel-shaped figure was faster than that of a figure with a barrel-shaped hole (Bertamini & Mosca, 2004). These findings seem to contradict our results, which showed that detecting a holed figure is easier than a non–holed figure. These differences may arise due to several reasons. First, it is possible to detect a barrel-shaped figure regardless of the exact position of the vertex. Second, the two vertices of the barrel-shaped figure are convex, whereas the two vertices of the figure with a barrel-shaped hole are concave. This difference in the curvature polarity may have resulted in prolonged reaction times. In addition, the HSE is apparent only during the figure-ground segmentation stage and does not necessarily show further superiority effects at later stages of perception. 
The differentiation between holed and closed figures
The term closure was used in a number of studies, in which it was demonstrated that closed figures are easier to detect and discriminate (Elder & Zucker, 1993, 1994; Mathes & Fahle, 2007; Hadad & Kimchi, 2008; Gerhardstein, Tse, Dickerson, Hipp, & Moser, 2012; Kanbe, 2013). Here, we wanted to make the distinction between a holed figure and a closed figure. 
According to the classical Gestalt principle, elements that form a closed figure tend to be grouped together. It was proposed that a closed figure forms the boundary of a visual object, thus facilitating perception (Elder, 2015). Studies showed that contour closure speeds up the discrimination of 2D shapes (Elder & Zucker, 1993, 1994; Elder & Goldberg, 2002). Other studies also found that closure forms the contour of a visual object, thus facilitating object perception (Mathes & Fahle, 2007; Hadad & Kimchi, 2008; Gerhardstein et al., 2012; Kanbe, 2013). In a closed figure, the region that is surrounded by a contour becomes the surface of the figure that owns the contour. Thus, both the contour and the surface become part of the figure and are in the same depth plane. However, this is not the case in a holed figure. For instance, in Figure 1b, the inner region of the o-shaped figure belongs to the background, not the figure. The surrounding region and the inner region of the o-shaped figure are in different depth planes. Hence, the closure effect can be explained as the emergence of the formation of an object, and thus it cannot be applied to the HSE. 
In a 2D context, the terms hole and closure are often undifferentiated (Pomerantz et al., 2003; S. He, 2008), although they are perceived differently when depth information is introduced. One study found a way to dissociate the contour and the surrounding region (Bertamini & Farrant, 2006) by using random-dot stereograms to form depth, as in the current paradigm. Here, a thin (wire-shaped) object was used that has the same contour as a figure, with the surrounding region as the background, essentially becoming a hole. The results showed that the performance using this thin object (hole) is different from that of a figure with the same outline (closure). Thus, the well-established model of closure contours (Elder, 2015) cannot be applied to the HSE, although the two effects may share the same underlying mechanisms. 
The significance of HSE
The HSE provides an explanation for topological perception and the sensitivity of primary visual perception to hole stimuli. We propose that HSE may be considered a global property in perceptual organization. The current findings provided two main critical evidences for the significance of the HSE: the importance of the object formation in HSE and the global property of the HSE. 
As proposed by the Berlin school of Gestalt psychology, the units of experience are objects, not image features (Wagemans, 2016). The purpose of the principles of perceptual organization is to compose objects in a scene. Thus, when there is no object formation, there is no reason for the rules of perceptual organization to be effective. The major difference between the o-shaped figure and the o-shaped hole is that the holes share the identical image features but still do not form an object per se. In Experiment 3, we showed that the HSE is demonstrated for o-shaped figures but not for o-shaped holes. The results suggest that the HSE is based on object formation and not on the image features. That is, object formation is required for HSE to be effective, supporting the proposal of HSE as a rule in perceptual organization. 
Topological property is proposed to be global and is thought to proceed other local features in visual perception. A property is considered more global the more stable it is after a transformation (Chen, 2005; Todd, Weismantel, & Kallie, 2014). It was demonstrated that observers are more sensitive to changes in topological properties than to changes in projective, affine, and Euclidean properties (Todd et al., 2014), suggesting that the topology is the most stable property. In Experiment 2, the two-disks condition is detected in a 3D context only when occlusion occurs. Thus, our findings demonstrate that the HSE does not apply to the detection of two-disks figures, suggesting that HSE is a global property. 
To understand what the hole perception may mean for everyday vision, let us examine, for example, the Gestalt determinant of “surroundedness” for figure and ground segregation, illustrated in Figure 7. In everyday vision, it is important to establish figure/ground at the very beginning. “Surroundedness” refers to a common phenomenon that a surrounded region is likely to be seen as a figure, while the corresponding surrounding region, ground. It is interesting to notice that, as the irregular shape of and the random location of the surrounded region in Figure 7 indicate, the relationship of surroundedness seems to have nothing to do directly with featural properties such as shape, size, location, and orientation. Nevertheless, exactly what does surroundedness mean? Such global invariant of surroundedness may be formally described in terms of topological invariants in nature, such as holes (Chen, 2005). 
Figure 7
 
An illustration of surroundedness as a principle of perceptual organization. Such surroundedness can be described in terms of holes. (Reproduced from Chen, 2005.)
Figure 7
 
An illustration of surroundedness as a principle of perceptual organization. Such surroundedness can be described in terms of holes. (Reproduced from Chen, 2005.)
Conclusion
In summary, we found that hole superiority is effective with 3D figures, which are formed using binocular disparity, and that in a 3D context, the HSE depends on the figure-ground organization. Our findings demonstrated the abstract nature of the HSE, showing that holes are represented in vision independent of the features forming these holes. 
Acknowledgments
This research was supported by grants from the National Natural Science Foundation of China (61773096, 61673087, 61773092), 111 project (B12027), and the Fundamental Research Funds for the Central Universities. 
Commercial relationships: none. 
Corresponding authors: Junjun Zhang; Ling Li. 
Address: MOE Key Lab for Neuroinformation, The Clinical Hospital of Chengdu Brain Science Institute, University of Electronic Science and Technology of China, Chengdu, China. 
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Figure 1
 
(a) From left to right: s-shaped figure, o-shaped figure, and disk-shaped figure. (b) An enclosed region (surrounding region) separated the background into two regions: the outer region and the inner region. (c) In a three-dimensional context, the figure-ground relationship of the three regions can be varied to form an o-shaped figure, two-disks figure, or o-shaped hole.
Figure 1
 
(a) From left to right: s-shaped figure, o-shaped figure, and disk-shaped figure. (b) An enclosed region (surrounding region) separated the background into two regions: the outer region and the inner region. (c) In a three-dimensional context, the figure-ground relationship of the three regions can be varied to form an o-shaped figure, two-disks figure, or o-shaped hole.
Figure 2
 
The random-dot stereograms for (a) blank stimuli, (b) o-shaped figure, and (c) s-shaped figure.
Figure 2
 
The random-dot stereograms for (a) blank stimuli, (b) o-shaped figure, and (c) s-shaped figure.
Figure 3
 
(a) The procedure of a single trial in Experiment 1. The o-shaped figure appeared in the first dynamic stimulus. Conditions with either s-shaped figures or targets that appeared in the second dynamic stimulus position are not shown. (b) Results of Experiment 1. Detecting the o-shaped figure (90.1%) was more accurate than detecting the s-shaped figure (85.6%). Error bars denote standard error.
Figure 3
 
(a) The procedure of a single trial in Experiment 1. The o-shaped figure appeared in the first dynamic stimulus. Conditions with either s-shaped figures or targets that appeared in the second dynamic stimulus position are not shown. (b) Results of Experiment 1. Detecting the o-shaped figure (90.1%) was more accurate than detecting the s-shaped figure (85.6%). Error bars denote standard error.
Figure 4
 
(a) The three targets in Experiment 2a: disk-shaped figure, o-shaped figure, and two-disks figure. (b) Results of Experiment 2a. Detecting the o-shaped figure (88.7%) was more accurate than detecting the o-shaped figure (81.5%) and the two-disks figure (82.2%). Error bars denote standard error.
Figure 4
 
(a) The three targets in Experiment 2a: disk-shaped figure, o-shaped figure, and two-disks figure. (b) Results of Experiment 2a. Detecting the o-shaped figure (88.7%) was more accurate than detecting the o-shaped figure (81.5%) and the two-disks figure (82.2%). Error bars denote standard error.
Figure 5
 
(a) The two targets in Experiment 2b. (b) Results of Experiment 2b. Detecting the o-shaped figure (91.1%) was more accurate than detecting the two-disks figure (85.1%). Error bars denote standard error.
Figure 5
 
(a) The two targets in Experiment 2b. (b) Results of Experiment 2b. Detecting the o-shaped figure (91.1%) was more accurate than detecting the two-disks figure (85.1%). Error bars denote standard error.
Figure 6
 
(a) The targets in Experiment 3: o-shaped figure, disk-shaped figure, o-shaped hole, and disk-shaped hole. Random-dot stereogram of those figures were the same as in Figure 4a. (b) Results of Experiment 3. Detecting figures (92.5% for o-shaped figure, 88.8% for disk-shaped figure) was more accurate than detecting holes (72.1% for o-shaped hole, 74.7% for disk-shaped hole). Error bars denote standard error.
Figure 6
 
(a) The targets in Experiment 3: o-shaped figure, disk-shaped figure, o-shaped hole, and disk-shaped hole. Random-dot stereogram of those figures were the same as in Figure 4a. (b) Results of Experiment 3. Detecting figures (92.5% for o-shaped figure, 88.8% for disk-shaped figure) was more accurate than detecting holes (72.1% for o-shaped hole, 74.7% for disk-shaped hole). Error bars denote standard error.
Figure 7
 
An illustration of surroundedness as a principle of perceptual organization. Such surroundedness can be described in terms of holes. (Reproduced from Chen, 2005.)
Figure 7
 
An illustration of surroundedness as a principle of perceptual organization. Such surroundedness can be described in terms of holes. (Reproduced from Chen, 2005.)
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