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Article  |   October 2015
Independence of the completion effect from the noncompletion effect in illusory contour perception
Author Affiliations
  • Junkai Yang
    Department of Psychology, Sun Yat-Sen University, Guangzhou, Guangdong, China
    junkaiyang@hotmail.com
  • Zhenzhu Yue
    Department of Psychology, Sun Yat-Sen University, Guangzhou, Guangdong, China
    yuezhenzhu@gmail.com
  • Xiang Wu
    Department of Psychology, Sun Yat-Sen University, Guangzhou, Guangdong, China
    rwfwuwx@gmail.com
Journal of Vision October 2015, Vol.15, 6. doi:10.1167/15.14.6
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      Junkai Yang, Zhenzhu Yue, Xiang Wu; Independence of the completion effect from the noncompletion effect in illusory contour perception. Journal of Vision 2015;15(14):6. doi: 10.1167/15.14.6.

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

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Abstract

Spatially separated object information can be effortlessly completed in the visual system, as demonstrated by the well-known Kanizsa-type illusory contours. The perception of illusory contours is closely associated with the spatial configuration of contour fragments, leading to the long-lasting difficulty in distinguishing the effect of the completion process that interpolates the contour fragments from the effect of the noncompletion process that analyzes the contour fragments. However, a close relationship does not necessarily imply nonindependence, e.g., two people may show similar behaviors in one situation but may not in another situation. Inspired by this simple common sense, we conducted a contour discrimination task (i.e., discriminating between the interpolated contours) and a fragment discrimination task (i.e., discriminating between the physically-specified contour fragments) for Kanizsa squares and Kanizsa circles. The performance difference between the contour and fragment discrimination tasks was much larger for Kanizsa circles than for Kanizsa squares. This independence of the completion effect—as indicated by the performance in the contour task—from the noncompletion effect—as indicated by the performance in the fragment task—provides new insights into the understanding of the mechanism of visual completion.

Introduction
The visual system recognizes objects even when environmental information is widely separated in space, as revealed by the well-known Kanizsa-type illusory contours, in which an interpolated contour is perceived despite spatially separated inducing contour fragments (Kanizsa, 1976; Figure 1). A Kanizsa-type illusory contour includes physical contour parts that are supported by the inducers and illusory contour parts (i.e., contrast borders are perceived in image regions containing no contrast; Figure 1A, left). To perceive illusory contours, the physically-missing illusory contour parts must be completed via interpolation of a connection between the physical contour parts (Pillow & Rubin, 2002; Treisman, 1999). Obviously, the effect of the completion process that interpolates the physical contour parts is closely associated with the effect of the noncompletion process that analyzes the physical contour parts (Ringach & Shapley, 1996). For example, the deformation of an illusory contour (e.g., thin or fat) is determined by the rotation of the physical contour parts (Ringach & Shapley, 1996), and the clarity of an illusory contour is influenced by the ratio between the physical and illusory contour parts (Shipley & Kellman, 1992). 
Figure 1
 
Illustration of the experimental design and predictions. (A) The examples of a standard (nondeformed) Kanizsa square (left) and the corresponding thin (middle) and fat (right) deformed figures used in the original thin/fat discrimination task (Ringach & Shapley, 1996). The red and deep blue arrows indicate the physical and illusory contour parts of the left contour, respectively. The analyses of the illusory and physical contour parts are considered to reflect the effects of the completion and noncompletion processes, respectively. (B) A variation of the original thin/fat task was used in the present study. The left/right and top/bottom contours of the standard Kanizsa square were varied separately, producing the thin and short deformed figures (Pillow & Rubin, 2002). (C) A Kanizsa circle was adopted in the present study and the thin and short deformations were applied. The green and light blue arrows indicate the physical and illusory contour parts of the left contour, respectively. (D) The predictions of discrimination performances. The discrimination performance is represented by the probability of correct responses as a function of rotation angles of the inducer mouth edges. “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle” represent the performances based on the completion and noncompletion processes for Kanizsa squares and circles, respectively, and are indicated by different colors. (For the purpose of a clear illustration, the rotation angles of the example deformed figures [10° for square figures in A and B and 15° for circle figures in (C)] are larger than the largest rotation angles used in the experiment [indicated in (D); also see Figure S1]).
Figure 1
 
Illustration of the experimental design and predictions. (A) The examples of a standard (nondeformed) Kanizsa square (left) and the corresponding thin (middle) and fat (right) deformed figures used in the original thin/fat discrimination task (Ringach & Shapley, 1996). The red and deep blue arrows indicate the physical and illusory contour parts of the left contour, respectively. The analyses of the illusory and physical contour parts are considered to reflect the effects of the completion and noncompletion processes, respectively. (B) A variation of the original thin/fat task was used in the present study. The left/right and top/bottom contours of the standard Kanizsa square were varied separately, producing the thin and short deformed figures (Pillow & Rubin, 2002). (C) A Kanizsa circle was adopted in the present study and the thin and short deformations were applied. The green and light blue arrows indicate the physical and illusory contour parts of the left contour, respectively. (D) The predictions of discrimination performances. The discrimination performance is represented by the probability of correct responses as a function of rotation angles of the inducer mouth edges. “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle” represent the performances based on the completion and noncompletion processes for Kanizsa squares and circles, respectively, and are indicated by different colors. (For the purpose of a clear illustration, the rotation angles of the example deformed figures [10° for square figures in A and B and 15° for circle figures in (C)] are larger than the largest rotation angles used in the experiment [indicated in (D); also see Figure S1]).
However, the close relationship between the effect of the completion process and the effect of the noncompletion process in illusory contour perception leads to the long-lasting difficulty in distinguishing the former from the latter, as is manifested in the intense debate on whether a thin/fat discrimination task indeed taps into the completion process (for reviews, see Anderson, 2007; Kellman, Garrigan, Shipley, & Keane, 2007). The thin/fat task was first introduced by Ringach and Shapley (1996), in which the inducer mouth edges are rotated to produce either a thin (Figure 1A, middle) or a fat (Figure 1A, right) deformation of a standard Kanizsa square (Figure 1A, left), and the discrimination is considered to reflect the completion process. Since then, this task has become the most widely used objective paradigm to investigate the completion process. The core argument regarding the validity of the task in measuring the completion process is illustrated in Figure 1A. The thin/fat discrimination performance may be determined by processing either the illusory contour parts (Figure 1A, deep blue arrows) or the physical contour parts (Figure 1A, red arrows), because (1) being a thin or fat deformation is determined by the direction of rotation of the inducer mouth edges, and (2) the amount of curvature is determined by the extent of the rotation, i.e., the size of the rotation angle. Therefore, the difficulty in identifying the completion process comes from the fact that the rotation of inducer mouth edges has a strong influence on the processing of illusory and physical contour parts; the discrimination performances based on the completion process (Figure 1D, the deep blue curve) and the noncompletion process (Figure 1D, the red curve) were both influenced by the rotation of inducer mouth edges, although the influence was stronger for the completion than for the noncompletion effect (Ringach & Shapley, 1996). This co-influence implies that the completion effect can be determined, at least in part, by the noncompletion effect. As Anderson (2007) pointed out, the question is “whether there is any compelling evidence to support the claim that performance on the fat-thin task is exclusively (or even primarily) limited by contour completion processes” (page 481 in Anderson, 2007). 
The evidence that is considered to support the validity of the thin/fat task in measuring the completion process has come from several lines of research. First, by employing different control figures that do not produce illusory contours, it has been shown that the performance of discrimination between the thin and fat contours (representing the completion effect) is better than the discrimination performance for the contour fragments (representing the noncompletion effect; Kellman, Yin, & Shipley, 1998; Ringach & Shapley, 1996). Although these results suggest that the completion effect is stronger than the noncompletion effect, as discussed previously, they cannot rule out the possibility that the former is determined by the latter when perceiving illusory contours. Second, an event-related potential (ERP) study (Murray, Imber, Javitt, & Foxe, 2006) showed that in the processing of illusory contour figures, an early ERP component was related to the completion effect and a later ERP component was related to shape discrimination. These results were not observed in the processing of control figures. Although this finding suggests a central role of the completion effect in the processing in the thin/fat task, the noncompletion effect was not explicitly investigated (“Nor were subjects explicitly directed to note the rotation of the inducers;” page 12044 in Murray et al., 2006). Therefore, this study did not clarify to what extent contour fragments were processed when perceiving illusory contours and whether the observed completion effect could be determined by the noncompletion effect. Third, a study using an image classification method showed the involvement of the illusory contour parts in the classification images (Gold, Murray, Bennett, & Sekuler, 2000). While the results suggested that the subjects indeed used the illusory contour parts to recognize contours, it was not clarified whether the processing of the illusory contour parts was determined by the processing of the physical contour parts when perceiving illusory contours. (See the General discussion section for further discussion of retinotopic representations of the illusory and physical contour parts). Together, despite prior results that indicate the validity of the thin/fat task, it remains unclear whether the completion effect is determined by the noncompletion effect. 
Our solution for the so-far seemingly unsolvable issue of distinguishing the completion effect from the noncompletion effect in Kanizsa-type illusory contour perception is inspired by simple common sense; a close relationship does not necessarily imply nonindependence. For example, two people may show similar behaviors in one situation but may not in another situation. Such independence would be revealed more clearly if one of the two people behaves similarly in the two situations whereas the other behaves differently between the two situations, i.e., the former's behavior is totally unrelated to the latter's behavior across different situations. In other words, given similar behaviors of two people, one's behavior is not necessarily determined by the other's behavior, because they can be independent. With respect to the Kanizsa-type illusory contours, the completion and noncompletion effects are closely related for Kanizsa squares (which have been used in most previous studies that employed the thin/fat paradigm), but such close relationship (i.e., the co-influence of the rotation of inducer mouth edges on the completion and noncompletion effects) may not hold for other shapes of Kanizsa figures. It is well known that different shapes of contours (e.g., Kanizsa square and circle) share the common underlying completion rule (Coren, 1972; Murray et al., 2002; Rock & Anson, 1979). However, the processing of the corresponding contour fragments may vary dramatically. For Kanizsa squares, the inducer mouth edges provide clear cues for the discrimination of the contour fragments (Figure 1A, red arrows). For instance, the subjects may easily recognize the thin figure in Figure 1A and B by judging whether one of the two mouth edges of an inducer is nonvertical, or recognize the thin figure in Figure 1B by judging whether the inducer mouth is less than 90°. However, for Kanizsa circles (Figure 1C), such fragment cues should be substantially diminished. Therefore, it might be possible that discrimination performance of contours (representing completion effects)—that is comparable for Kanizsa squares (Figure 1D, the deep blue curve) and circles (Figure 1D, the light blue curve)—is accompanied by discrimination performance of contour fragments (representing noncompletion effects)—that is much poorer for Kanizsa circles (Figure 1D, the solid green curve) than for Kanizsa squares (Figure 1D, the red curve). In other words, the completion effect may not be determined by the noncompletion effect, because both are independent. 
The subjects were required to perform a contour discrimination task (i.e., discriminating between the interpolated contours) and a fragment discrimination task (i.e., discriminating between the physically specified contour fragments) for Kanizsa squares (Figure 1B) and circles (Figure 1C). We employed a variation (Pillow & Rubin, 2002) of the original thin/fat task (Ringach & Shapley, 1996), i.e., discriminating between a deformed (thin or short) and a standard figure. The rationale of the present study was simple: given the close relationship between completion and noncompletion effects for Kanizsa squares, we aimed to test the hypothesis that this relationship is less pronounced for Kanizsa circles (cf. Figure 1D). Particularly, the contour discrimination performance for Kanizsa circles (the light blue curve in Figure 1D) was controlled to be comparable to that for Kanizsa squares (the deep blue curve in Figure 1D; by controlling the range of rotation angles of inducer mouth edges). 
If the inducer mouth edges of Kanizsa circles would not provide any cues for the fragment discrimination, the completion effect would also be totally unrelated to the noncompletion effect, since the fragment discrimination performance would not increase with rotation angles (Figure 1D, the dashed green line). (This manner of independence is for a given specific shape, and the manner of independence across different shapes has been discussed previously). Although this situation does not exist physically, it might exist perceptually: The fragment cues might be “invisible.” Indeed, this is what we observed in some conditions for some subjects, providing additional strong evidence for the independence of the completion effect from the noncompletion effect. 
Methods
Participants
Five subjects (all right-handed, one male, mean age ± SD 22.6 ± 4.5 years), five subjects (all right-handed, one male, mean age ± SD 22.6 ± 1.5 years), and five subjects (all right-handed, three males, mean age ± SD 21.0 ± 2.2 years) participated in the main experiment, control experiment 1, and control experiment 2, respectively. A screen procedure was conducted before the formal experiments to test whether a subject could perform the discrimination task with briefly presented stimuli (117-ms stimuli followed by a mask). The discrimination of contours of Kanizsa squares and circles were used in the screen procedure (See method details below; Pillow & Rubin, 2002). Except for the above subjects who performed the formal experiments, three subjects in the main experiment and three subjects in control experiment 2 reported great difficulty in the screen procedure and thus did not perform the formal experiments. All subjects had normal or corrected-to-normal vision. All subjects were naive to the task and each subject participated in one of the three experiments. The research protocols of this study were approved by Sun Yat-Sen University. All subjects gave written informed consent. A large discrimination performance difference between the contour and fragment tasks for Kanizsa circles was the primary effect predicted by the present design (see the light blue and solid green curves in Figure 1D). Because this effect was consistently observed for each subject in each experiment (see the Results section), five subjects performed the formal tasks in each experiment. In other words, this strong effect we reported in the current study was in terms of individual subjects. 
Stimuli and procedure
All experimental stimuli are listed in Figure S1. The deformed Kanizsa circles were produced by a deformation procedure that was similar to the procedure constructing the deformed Kanizsa squares (i.e., rotating inducer mouth edges of the standard figure; Pillow & Rubin, 2002; Ringach & Shapley, 1996), with an additional smoothing step that was applied to further reduce the nonsmoothness of the inducer mouth (so that the contour fragments of Kanizsa circles provided fewer cues for the discrimination; Figure S2). The left/right and top/bottom contours were varied separately (Pillow & Rubin, 2002). Because the smoothing step was not suitable for a fat or tall deformation (Figure S2B, bottom left), the deformed Kanizsa figures included thin and short shapes. Six rotation angles were used for the deformed figures: 0.4°, 0.8°, 1.2°, 1.6°, 2°, and 2.4° for the square figures; and 1.2°, 2.4°, 3.6°, 4.8°, 6°, and 7.2° for the circle figures. For the deformed square figures, the rotation angle was defined as the deviation angle between the inducer mouth edges of the standard and deformed figures (Pillow & Rubin, 2002; Ringach & Shapley, 1996; Figure S2A). The rotation angle of deformed circle figures was defined in a similar way except that the inducer mouth edges were arcs (Figure S2B). The rotation angles for Kanizsa squares were assigned according to those used in previous studies (Pillow & Rubin, 2002; Ringach & Shapley, 1996) and were pretested for the present design (Figure 2). Because the current study aimed to achieve similar discrimination performance for Kanizsa circles and Kanizsa squares, circles were pretested to determine the rotation angles used in the formal experiments (as shown in Figure S1). The Kanizsa squares and circles were used for the discrimination of contours. The corresponding control figures were used for the discrimination of contour fragments, which were produced by replacing the three pacman inducers other than the top-left one of the Kanizsa figures with full disks. The control figures were such designed for three reasons. First, the Kanizsa figures could also be used for the discrimination of the contour fragments, but in pretesting, the subjects reported that the discrimination of the contour fragments was strongly influenced by the perception of the contours. Second, the control figures could be constructed by rotating all the four inducers by a fixed angle (Ringach & Shapley, 1996), but this arrangement would also produce a global pattern, though not the pattern of an illusory contour. Third, the position of the top-left inducer appears special, because people tend to use the information from the top-left inducer to perform the discrimination task (Gold et al., 2000). 
Figure 2
 
Illustration of the experimental procedure. Each trial contained two intervals, with each interval consisting of a stimulus, a blank, and a mask. In the shown example, a standard figure is shown in the first interval and a deformed (thin) figure is shown in the second interval with the rotation angle being 2.4° for square figures and 7.2° for circle figures (see Figure S1 for all used experimental stimuli). Kanizsa circle figures, control Kanizsa circle figures, Kanizsa square figures, and control Kanizsa square figures are listed from the bottom to the top. The subjects were required to indicate which interval contained the deformed figure. There were two types of discrimination tasks. For the contour task, the discrimination referred to the contours of the Kanizsa figures; for the fragment task, the discrimination referred to the top-left contour fragment of the control figures. A disk mask was used in the main experiment and control experiment 1, and a star mask was used in control experiment 2. The subjects were required to fixate on the central fixation point in the contour task in all experiments and in the fragment task in the main experiment, and to fixate on the top-left inducer in the fragment task in control experiments 1 and 2.
Figure 2
 
Illustration of the experimental procedure. Each trial contained two intervals, with each interval consisting of a stimulus, a blank, and a mask. In the shown example, a standard figure is shown in the first interval and a deformed (thin) figure is shown in the second interval with the rotation angle being 2.4° for square figures and 7.2° for circle figures (see Figure S1 for all used experimental stimuli). Kanizsa circle figures, control Kanizsa circle figures, Kanizsa square figures, and control Kanizsa square figures are listed from the bottom to the top. The subjects were required to indicate which interval contained the deformed figure. There were two types of discrimination tasks. For the contour task, the discrimination referred to the contours of the Kanizsa figures; for the fragment task, the discrimination referred to the top-left contour fragment of the control figures. A disk mask was used in the main experiment and control experiment 1, and a star mask was used in control experiment 2. The subjects were required to fixate on the central fixation point in the contour task in all experiments and in the fragment task in the main experiment, and to fixate on the top-left inducer in the fragment task in control experiments 1 and 2.
The locations of the centers of the four inducer disks were the same for Kanizsa circle and square figures. The support ratio (i.e., the ratio of the physically specified edge length to the total edge length of the contour) was 0.5 for both the standard Kanizsa square and circle figures. The side length of the square in the standard Kanizsa square figure and the diameter of the circle in the standard Kanizsa circle figure subtended visual angles of 15.0° and 21.2°, respectively. The diameter of the inducer disk of Kanizsa square and circle figures subtended visual angles of 7.5° and 8.2°, respectively. The stimuli composed of black (RGB values: 0 0 0; luminance: 0.89 cd/m2) inducers were displayed on a gray (RGB values: 122 122 122; luminance: 19.10 cd/m2) background with a black fixation point permanently displayed at the center of the stimuli. 
The experimental procedure is illustrated in Figure 2, and the data were gathered using a temporal 2AFC (two-alternative forced choices) manner (Klein, 2001). Each trial contained two 417-ms intervals. Each interval was preceded by a 500-ms blank and consisted of a 117-ms stimulus, a 50-ms blank, and a 250-ms mask. A standard or a deformed figure was randomly presented in one of the two intervals. After the presentation of the second interval, the subjects were asked to indicate which interval contained the deformed figure by pressing one of two keys on a computer keyboard. The next trial was triggered after the subjects had made a decision. 
In the main experiment, the thin and short deformed figures were examined in two separate sessions and the order of the two sessions was counterbalanced across the subjects. In each session, the subjects were required to discriminate between the interpolated contours of the deformed and standard Kanizsa figures (the contour task), or discriminate between the physically specified contour fragments of the deformed and standard control figures (the fragment task), i.e., whether a contour or a contour fragment belonged to a deformed figure. To avoid the potential possibility that the subjects explicitly used the cues in contour fragments in the contour task, the contour task was always carried out before the fragment task. Each of the contour and fragment tasks was organized into 10 blocks in which five blocks containing square figures and five blocks containing circle figures were randomly arranged. Each block consisted of 60 trials in which the deformed figures of six rotation angles were randomly measured 10 times (each rotation angle was totally measured 50 times in five blocks). The subjects were required to fixate on the fixation point in both the contour and fragment tasks. The presentation of the stimuli was followed by a disk mask. 
Control experiment 1 was the same as the main experiment with the exception that the subjects were required to fixate on the top-left inducer in the fragment task. Control experiment 2 was the same as control experiment 1 except that a star mask was used instead of the disk mask. 
Data analyses
Each experiment involved four factors: deformation type (thin and short), task type (contour and fragment), shape type (square and circle), and rotation angle (six rotation angles); the percentage of correct responses was subjected to a repeated-measures analysis of variance (ANOVA) with the previously mentioned four factors (Greenhouse-Geisser corrections were applied; Table S1). Because task type and shape type were factors of interest for the present study (see Introduction, Figure 1D), a second ANOVA with the factors task type and shape type was conducted in which the data for deformation types and rotation angles were averaged (Table S2). Post-hoc analyses were performed for the second ANOVA (all t tests were two-tailed; Table S3). Responses were also fitted with a psychometric function (a logit function implemented in Matlab, The Mathworks, Natick, MA; Klein, 2001; Treutwein & Strasburger, 1999). Note that in the current study the discrimination performance for the control Kanizsa circle figures was very poor. The performance threshold derived from the corresponding psychometric function was very large, and could hardly be obtained in some conditions for some subjects because the performance did not increase with rotation angles (see results of control experiment 2; Figure 4C and D). Therefore, the purpose of fitting the data to a psychometric function in the present study was to better illustrate the data rather than to obtain derived performance thresholds. 
Figure 3
 
Results of the main experiment. The data for the thin and short deformed figures are shown in (A) and (B), respectively. Both the average responses of all subjects (left) and the responses of individual subjects (right) are presented. The small marks represent the data for individual rotation angles of deformed figures (the 0 degree refers to the standard figures). The performances of the contour task (representing the effect of the completion process) and the fragment task (representing the effect of the noncompletion process) for Kanizsa squares and circles are represented using different colors, and are indicated by “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle,” respectively. The axes for the response images, the sample deformed figures for investigating the completion and noncompletion effects for Kanizsa squares and circles, and the predictions of the present design (also see Figure 1D) are shown at the bottom. For the purposes of a clear illustration of the data and a convenient comparison between the data and the predictions, the responses were fitted with a logit psychometric function.
Figure 3
 
Results of the main experiment. The data for the thin and short deformed figures are shown in (A) and (B), respectively. Both the average responses of all subjects (left) and the responses of individual subjects (right) are presented. The small marks represent the data for individual rotation angles of deformed figures (the 0 degree refers to the standard figures). The performances of the contour task (representing the effect of the completion process) and the fragment task (representing the effect of the noncompletion process) for Kanizsa squares and circles are represented using different colors, and are indicated by “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle,” respectively. The axes for the response images, the sample deformed figures for investigating the completion and noncompletion effects for Kanizsa squares and circles, and the predictions of the present design (also see Figure 1D) are shown at the bottom. For the purposes of a clear illustration of the data and a convenient comparison between the data and the predictions, the responses were fitted with a logit psychometric function.
Figure 4
 
Results of control experiments. (A) and (B) show the results of control experiment 1; and (C) and (D) show the results of control experiment 2. The experimental settings in control experiment 1 were the same as those in the main experiment except that the subjects were asked to fixate on the top-left inducer in the fragment task. The experimental settings in control experiment 2 were the same as those in control experiment 1 except that a star mask was used instead of the disk mask. The conventions are as in Figure 3.
Figure 4
 
Results of control experiments. (A) and (B) show the results of control experiment 1; and (C) and (D) show the results of control experiment 2. The experimental settings in control experiment 1 were the same as those in the main experiment except that the subjects were asked to fixate on the top-left inducer in the fragment task. The experimental settings in control experiment 2 were the same as those in control experiment 1 except that a star mask was used instead of the disk mask. The conventions are as in Figure 3.
Results
Main experiment
The results of the main experiment are illustrated in Figure 3. The experiment involved the factors deformation type (thin and short), task type (contour and fragment), shape type (square and circle), and rotation angle (six rotation angles). The ANOVA results with the four factors are listed in Table S1. Here we focused on the comparisons of interest between the performance in the contour task (representing the effect of the completion process) and in the fragment task (representing the effect of the noncompletion process) for square and circle figures (see predictions; Figure 1D), with data averaged across deformation types and rotation angles. The detailed ANOVA results with the two factors task type and shape type are listed in Table S2 and the corresponding post-hoc results are listed in Table S3. Consistent with previous results (Murray et al., 2006; Ringach & Shapley, 1996), the percentage of correct responses was greater in the contour task (mean = 0.868, 95% CI = [0.836–0.900]) than in the fragment task (mean = 0.763, 95% CI = [0.668–0.857]) for the square figures (mean difference = 0.105, 95% CI = [0.037–0.174], t4 = 4.269, p = 0.013, η2 = 0.820). In accordance with the predictions of the present study, the percentage of correct responses was also greater in the contour task (mean = 0.856, 95% CI = [0.827–0.884]) than in the fragment task (mean = 0.632, 95% CI = [0.519–0.745]) for the circle figures (mean difference = 0.223, 95% CI = [0.109–0.338], t4 = 5.420, p = 0.006, η2 = 0.880). Importantly, the discrimination performance difference between the contour and fragment tasks was much larger for the circle than for the square figures (mean difference = 0.118, 95% CI = [0.015–0.221], F(1, 4) = 10.052, p = 0.034, partial η2 = 0.715); and the percentage of correct responses in the contour task was comparable (no statistical difference) for the square and circle figures. (In addition, for the circle figures, the percentage of correct responses in the fragment task was greater for the thin than for the short figures for four out of the five subjects, but this did not seem to be a strong effect (mean difference = 0.093, 95% CI = [−0.004–0.190], t4 = 2.662, p = 0.056, η2 = 0.639) and was not observed in the following control experiments 1 and 2). Therefore, as has been discussed in the Introduction, these results strongly suggest that the completion effect is independent of the noncompletion effect. 
Control experiment 1
The discrimination performance in the fragment task has been consistently found to be poorer than the discrimination performance in the contour task for square figures (Murray et al., 2006; Ringach & Shapley, 1996), which was also observed in the main experiment of the present study. This contour over fragment advantage in the discrimination performance has been taken as the evidence to either support the view that the completion effect is different from the noncompletion effect (given that the performances for the contours and fragments were different; Ringach & Shapley, 1996), or support the opposite view that the completion effect is related to the noncompletion effect (given that the performances for the contours and fragments were both influenced by rotation of the inducer mouth edges; Anderson, 2007). In the present study, we addressed the relationship between the completion and noncompletion effects by introducing the circle figures and showing the independence of the completion effect from the noncompletion effect in the main experiment. From the current independence view, the fragment discrimination performance would not be fixed, but rather would be related to the amount of cues provided by the contour fragments. As has been discussed in the Introduction, the contour fragments of Kanizsa square figures provide clear cues for the discrimination, and the consistently observed contour over fragment advantage in the discrimination performance for square figures may thus look confusing. Although the target inducer in the fragment task was the top-left inducer (Ringach & Shapley, 1996; and in the current main experiment) or unspecified (Murray et al., 2006), the subjects were required to fixate on the central fixation point in the fragment task as in the contour task. The local information is supposed to be better processed using foveal vision (Grill-Spector & Malach, 2004). Thus, the central fixation is appropriate for the processing of contours but may be inappropriate for the processing of local contour fragments, especially when they were to be compared. In fact, it has been shown that subjects tend to use the information from the top-left inducer to perform the discrimination task (Gold et al., 2000). Therefore, the contour over fragment advantage in the discrimination performance for square figures may be diminished if the subjects were asked to fixate on the top-left inducer in the fragment task, which would also be a support for the independence of the completion effect from the noncompletion effect. This was investigated in control experiment 1, which was the same as the main experiment with the exception that the subjects were asked to fixate on the top-left inducer in the fragment task. 
The results of control experiment 1 are illustrated in Figure 4A and B. Consistent with the results of the main experiment, the percentage of correct responses was greater in the contour task (mean = 0.810, 95% CI = [0.778–0.841]) than in the fragment task (mean = 0.619, 95% CI = [0.543–0.695]) for the circle figures (mean difference = 0.190, 95% CI = [0.128–0.253], t4 = 8.413, p = 0.001, η2 = 0.947), and the percentage of correct responses in the contour task was comparable for the square figures (mean = 0.832, 95% CI = [0.791–0.873]) and the circle figures. As predicted by the arrangement of fixation on the top-left inducer in the fragment task, the fragment discrimination performance for the square figures was substantially improved. The percentage of correct responses in the fragment task (mean = 0.836, 95% CI = [0.797–0.875]) was comparable to that in the contour task (mean = 0.847, 95% CI = [0.790–0.904]) for the thin square figures; and the percentage of correct responses in the fragment task (mean = 0.874, 95% CI = [0.844–0.905]) was even greater than that in the contour task (mean = 0.817, 95% CI = [0.789–0.844]) for the short square figures (mean difference = 0.058, 95% CI = [0.005–0.110], t4 = 3.059, p = 0.038, η2 = 0.701). Note that the fragment discrimination performance for the circle figures was not obviously influenced by the manipulation of fixation position in the fragment task (the large discrimination performance difference between the contour and fragment tasks for the circle figures was observed as in the main experiment). This could be because the cues provided by the contour fragments of Kanizsa circles were substantially diminished in the current design, thus the fragment discrimination performance was insensitive to the manipulation of fixation position. 
Control experiment 2
In control experiment 1, the improvement of the fragment discrimination performance for the square figures was influenced by the type of deformation; the percentage of correct responses in the fragment task was greater than that in the contour task for the short but not for the thin figures. To address this bias of deformation type, we carried out control experiment 2, which was the same as experiment 1 except that the disk mask was replaced by a star mask (Figure 2). This arrangement was inspired by the subjective reports from two subjects in control experiment 1 (and by suggestion of author Junkai Yang, who performed the study) that the discrimination of the fragments of Kanizsa squares could be influenced by the mask. This was confirmed in the results of control experiment 2 (Figure 4C and D), which did not show the bias of deformation type on the improvement of the fragment discrimination performance for the square figures. For the thin square figures, the mean percentage of correct responses in the fragment task was 0.788 (95% CI = [0.720–0.857]) and in the contour task was 0.799 (95% CI = [0.744–0.855]). For the short square figures, the mean percentage of correct responses in the fragment task was 0.786 (95% CI = [0.669–0.903]) and in the contour task was 0.804 (95% CI = [0.752–0.856]). In addition, consistent with the results of the main experiment and control experiment 1, the percentage of correct responses was greater in the contour task (mean = 0.830, 95% CI = [0.777–0.883]) than in the fragment task (mean = 0.641, 95% CI = [0.526–0.756]) for the circle figures (mean difference = 0.189, 95% CI = [0.060–0.318], t4 = 4.057, p = 0.015, η2 = 0.804). The percentage of correct responses in the contour task was also comparable for the square figures (mean = 0.802, 95% CI = [0.768–0.835]) and the circle figures. 
Pillow & Rubin (2002) reported a bias of deformation type on the contour discrimination performance for square figures, but this bias was not observed for naive subjects in a later study (Zhou, Tjan, Zhou, & Liu, 2008). The subjects participating in the present study were all naive to the tasks and the bias was also not evidently observed for both square and circle figures in all the three experiments. The current results were consistent with the results from the study of Zhou et al. (2008). In addition, for the thin figures in control experiment 2, the percentage of correct responses in the contour task was greater for the circle than for the square figures for four out of the five subjects, but the effect was weak (mean difference = 0.040, 95% CI = [−0.004–0.084], t4 = 2.529, p = 0.065, η2 = 0.615) and was not observed in the main experiment and control experiment 1. 
Moreover, in control experiment 2, the discrimination performance for the control Kanizsa circle figures did not significantly increase with rotation angles for three subjects (subject 1 for the thin figures and subjects 2 and 5 for the short figures). As has been discussed in the Introduction (Figure 1D, the dashed green line), such results indicate that the cues in the contour fragments of circle figures could be “invisible” to these subjects and were not effectively utilized in the fragment discrimination task. 
General discussion
Since its first adoption in the literature of visual completion (Ringach & Shapley, 1996), the thin/fat discrimination task has become the most widely used objective paradigm to assess the completion process in Kanizsa-type illusory contour perception (for reviews, see Anderson, 2007; Kellman et al., 2007). However, the validity of this task in investigating the completion process has been under suspicion and those studies employing the task would thus deserve to be re-evaluated; “a large body of data is rendered irrelevant to understanding the relationship between modal and amodal completion” (Anderson, 2007, p. 483). The current finding therefore provides a key answer to the methodological concern of the validity of the thin/fat task: The performance of the thin/fat task indeed reflects the effect of the completion process, which is independent of the effect of the noncompletion process. 
It should be pointed out that the difficulty in identifying the completion process does not only exist for the thin/fat behavioral paradigm. A basic logic of neuroimaging studies to identify the neural mechanism underlying the completion process in Kanizsa-type illusory contour perception is to distinguish neural response to the illusory contour parts from that to the physical contour parts (Treisman, 1999), and such separate neural responses in V1 have been observed in studies using functional magnetic resonance imaging retinotopic methods (Maertens, 2008; Wu et al., 2012). However, the separate V1 activations to the illusory and physical contour parts could not prove that the activation to the illusory contour parts does not reflect the processing of the physical contour parts, given the close relationship between the processing of the illusory and physical contour parts. Accordingly, shortly after the invention of the thin/fat paradigm, an image classification method demonstrated spatially separate processing of illusory and physical contour parts (Gold et al., 2000). These results reveal the fact that the processing of the illusory and physical contour parts both contribute to the perception of illusory contours, whereas it remains unclear whether the processing of the illusory contour parts indeed reflects the completion process (Anderson, 2007). Therefore, the current finding of the independence of the effect of the completion process from the effect of the noncompletion process also provides a key support for the identification of the neural mechanism of the completion process. Moreover, the basic design of the comparison between an illusory contour condition and a control condition (rotating contour fragments so that illusory contours disappear) has been widely used in the research of illusory contour perception, including (but not limited to) studies investigating attentional effects (Conci, Müller, & Elliott, 2007a, 2007b; Davis & Driver, 1994; Gurnsey, Poirier, & Gascon, 1996; Li, Cave, & Wolfe, 2008; Wu, Zhou, Qian, Gan, & Zhang, 2015), awareness modulations (Lau & Cheung, 2012; Wang, Weng, & He, 2012), the effect of inducer contrast (Lesher & Mingolla, 1993; Maertens & Shapley, 2008), feed-forward and feed-back processing (Ffytche & Zeki, 1996; Murray et al., 2002; Stanley & Rubin, 2003), and separate processes at different processing stages (Barlasov-Ioffe & Hochstein, 2008; Foxe, Murray, & Javitt, 2005; Murray, Foxe, Javitt, & Foxe, 2004; Murray et al., 2006; also see Seghier & Vuilleumier, 2006 for a review of neuroimaging studies). Although such a design is supposed to control for the effect of the processing of the contour fragments, it remains unclear whether the comparison indeed reveals the effect of the interpolation processing when perceiving illusory contours (Seghier & Vuilleumier, 2006). Therefore, the independence of the completion effect from the noncompletion effect as demonstrated in the present study provides a support for the identification of the completion process in a broad research background. 
Conclusions
The identification of the completion process in Kanizsa-type illusory contour perception, i.e., distinguishing the effect of the completion process from the effect of the noncompletion process, has been a long-lasting issue. The current results demonstrate that the completion effect is independent of the noncompletion effect. Therefore, although the completion effect is closely related to the noncompletion effect, the former is not determined by the latter. This finding makes both methodological and theoretical contributions to the research of how the visual system completes spatially separated information to form coherent object perception. 
Acknowledgments
This work was supported by National Natural Science Foundation of China (31371129), 985-3 Project of Sun Yat-Sen University (16110-3281303), and Philosophical and Social Science Project of Guangdong Province (GD12YXL02). Junkai Yang and Xiang Wu designed the research; Junkai Yang performed the research; Junkai Yang and Zhenzhu Yue analyzed the data; and Xiang Wu wrote the manuscript. All authors commented on and edited the manuscript. We thank Cheng Li, Zhiyin Luo, and Liang Zhou for their help in producing the deformed Kanizsa figures, and we thank Peng Ye for his help in measuring stimulus luminance. The authors declare no competing financial interests. 
Commercial relationships: none. 
Corresponding author: Xiang Wu. 
Email: rwfwuwx@gmail.com. 
Address: Department of Psychology, Sun Yat-Sen University, Guangzhou, Guangdong, China. 
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Figure 1
 
Illustration of the experimental design and predictions. (A) The examples of a standard (nondeformed) Kanizsa square (left) and the corresponding thin (middle) and fat (right) deformed figures used in the original thin/fat discrimination task (Ringach & Shapley, 1996). The red and deep blue arrows indicate the physical and illusory contour parts of the left contour, respectively. The analyses of the illusory and physical contour parts are considered to reflect the effects of the completion and noncompletion processes, respectively. (B) A variation of the original thin/fat task was used in the present study. The left/right and top/bottom contours of the standard Kanizsa square were varied separately, producing the thin and short deformed figures (Pillow & Rubin, 2002). (C) A Kanizsa circle was adopted in the present study and the thin and short deformations were applied. The green and light blue arrows indicate the physical and illusory contour parts of the left contour, respectively. (D) The predictions of discrimination performances. The discrimination performance is represented by the probability of correct responses as a function of rotation angles of the inducer mouth edges. “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle” represent the performances based on the completion and noncompletion processes for Kanizsa squares and circles, respectively, and are indicated by different colors. (For the purpose of a clear illustration, the rotation angles of the example deformed figures [10° for square figures in A and B and 15° for circle figures in (C)] are larger than the largest rotation angles used in the experiment [indicated in (D); also see Figure S1]).
Figure 1
 
Illustration of the experimental design and predictions. (A) The examples of a standard (nondeformed) Kanizsa square (left) and the corresponding thin (middle) and fat (right) deformed figures used in the original thin/fat discrimination task (Ringach & Shapley, 1996). The red and deep blue arrows indicate the physical and illusory contour parts of the left contour, respectively. The analyses of the illusory and physical contour parts are considered to reflect the effects of the completion and noncompletion processes, respectively. (B) A variation of the original thin/fat task was used in the present study. The left/right and top/bottom contours of the standard Kanizsa square were varied separately, producing the thin and short deformed figures (Pillow & Rubin, 2002). (C) A Kanizsa circle was adopted in the present study and the thin and short deformations were applied. The green and light blue arrows indicate the physical and illusory contour parts of the left contour, respectively. (D) The predictions of discrimination performances. The discrimination performance is represented by the probability of correct responses as a function of rotation angles of the inducer mouth edges. “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle” represent the performances based on the completion and noncompletion processes for Kanizsa squares and circles, respectively, and are indicated by different colors. (For the purpose of a clear illustration, the rotation angles of the example deformed figures [10° for square figures in A and B and 15° for circle figures in (C)] are larger than the largest rotation angles used in the experiment [indicated in (D); also see Figure S1]).
Figure 2
 
Illustration of the experimental procedure. Each trial contained two intervals, with each interval consisting of a stimulus, a blank, and a mask. In the shown example, a standard figure is shown in the first interval and a deformed (thin) figure is shown in the second interval with the rotation angle being 2.4° for square figures and 7.2° for circle figures (see Figure S1 for all used experimental stimuli). Kanizsa circle figures, control Kanizsa circle figures, Kanizsa square figures, and control Kanizsa square figures are listed from the bottom to the top. The subjects were required to indicate which interval contained the deformed figure. There were two types of discrimination tasks. For the contour task, the discrimination referred to the contours of the Kanizsa figures; for the fragment task, the discrimination referred to the top-left contour fragment of the control figures. A disk mask was used in the main experiment and control experiment 1, and a star mask was used in control experiment 2. The subjects were required to fixate on the central fixation point in the contour task in all experiments and in the fragment task in the main experiment, and to fixate on the top-left inducer in the fragment task in control experiments 1 and 2.
Figure 2
 
Illustration of the experimental procedure. Each trial contained two intervals, with each interval consisting of a stimulus, a blank, and a mask. In the shown example, a standard figure is shown in the first interval and a deformed (thin) figure is shown in the second interval with the rotation angle being 2.4° for square figures and 7.2° for circle figures (see Figure S1 for all used experimental stimuli). Kanizsa circle figures, control Kanizsa circle figures, Kanizsa square figures, and control Kanizsa square figures are listed from the bottom to the top. The subjects were required to indicate which interval contained the deformed figure. There were two types of discrimination tasks. For the contour task, the discrimination referred to the contours of the Kanizsa figures; for the fragment task, the discrimination referred to the top-left contour fragment of the control figures. A disk mask was used in the main experiment and control experiment 1, and a star mask was used in control experiment 2. The subjects were required to fixate on the central fixation point in the contour task in all experiments and in the fragment task in the main experiment, and to fixate on the top-left inducer in the fragment task in control experiments 1 and 2.
Figure 3
 
Results of the main experiment. The data for the thin and short deformed figures are shown in (A) and (B), respectively. Both the average responses of all subjects (left) and the responses of individual subjects (right) are presented. The small marks represent the data for individual rotation angles of deformed figures (the 0 degree refers to the standard figures). The performances of the contour task (representing the effect of the completion process) and the fragment task (representing the effect of the noncompletion process) for Kanizsa squares and circles are represented using different colors, and are indicated by “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle,” respectively. The axes for the response images, the sample deformed figures for investigating the completion and noncompletion effects for Kanizsa squares and circles, and the predictions of the present design (also see Figure 1D) are shown at the bottom. For the purposes of a clear illustration of the data and a convenient comparison between the data and the predictions, the responses were fitted with a logit psychometric function.
Figure 3
 
Results of the main experiment. The data for the thin and short deformed figures are shown in (A) and (B), respectively. Both the average responses of all subjects (left) and the responses of individual subjects (right) are presented. The small marks represent the data for individual rotation angles of deformed figures (the 0 degree refers to the standard figures). The performances of the contour task (representing the effect of the completion process) and the fragment task (representing the effect of the noncompletion process) for Kanizsa squares and circles are represented using different colors, and are indicated by “Completion Square,” “Completion Circle,” “Noncompletion Square,” and “Noncompletion Circle,” respectively. The axes for the response images, the sample deformed figures for investigating the completion and noncompletion effects for Kanizsa squares and circles, and the predictions of the present design (also see Figure 1D) are shown at the bottom. For the purposes of a clear illustration of the data and a convenient comparison between the data and the predictions, the responses were fitted with a logit psychometric function.
Figure 4
 
Results of control experiments. (A) and (B) show the results of control experiment 1; and (C) and (D) show the results of control experiment 2. The experimental settings in control experiment 1 were the same as those in the main experiment except that the subjects were asked to fixate on the top-left inducer in the fragment task. The experimental settings in control experiment 2 were the same as those in control experiment 1 except that a star mask was used instead of the disk mask. The conventions are as in Figure 3.
Figure 4
 
Results of control experiments. (A) and (B) show the results of control experiment 1; and (C) and (D) show the results of control experiment 2. The experimental settings in control experiment 1 were the same as those in the main experiment except that the subjects were asked to fixate on the top-left inducer in the fragment task. The experimental settings in control experiment 2 were the same as those in control experiment 1 except that a star mask was used instead of the disk mask. The conventions are as in Figure 3.
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