The Misperception of Orientation in Depth When Processing Multiple Pictures With Linear Perspective Cues

Abstract

The leaning tower illusion suggests that combining perspective cues across multiple images can affect the perceived orientation of objects in space. We measured the accuracy of orientation perception when viewing multiple pictures. Across several experiments, 11–16 participants viewed two pictures: a sidewalk and either another sidewalk, a nature scene, or no picture. Participants adjusted an on-screen line to match the remembered orientation of one of the sidewalks. Participants also made a judgment about the parallelism of the sidewalks. Sidewalks perceived as parallel were perceived to have orientations more similar to each other than when they were paired with a nature scene or no picture. The degree of misperception can be approximately twice as large as in the leaning tower illusion, and this effect survived inversion and partially survived alternating presentation of the images. The misperception was eliminated when the participants were cued on which sidewalk they would be judging; however, when forced to process both sidewalks, the misperception reappeared. We conclude that the orientation of objects with perspective cues is misperceived when viewing multiple pictures with perspective cues and this misperception appears to be related at least in part to how parallel those objects are perceived to be.

Keywords

orientation depth perspective perception illusion

The leaning tower illusion (LTI) occurs when two identical images containing linear perspective cues are placed side-by-side (Kingdom et al., 2007). The images are perceived to be nonidentical, with the objects in the image appearing to diverge as they recede in three-dimensional space. Figure 1A shows an example of the LTI using sidewalks. Kingdom et al. (2007) explain the LTI as the result of interpreting the two images as being part of the same visual scene where parallel lines should converge to a single point. However, in the traditional LTI display with two identical images, parallel lines converge at different points for the two images. If the visual system is interpreting the two images as part of one scene, parallel lines converging on different points indicate that the objects are not parallel.

Figure 1.

The leaning tower illusion and the turn in the road illusion. A: A sidewalk version of the leaning tower illusion. When two identical pictures of a sidewalk are placed side-by-side, the sidewalks appear to diverge. B: An illustration of the turn in the road illusion. The left and middle roads appear parallel or nearly parallel. However, the left and right roads are actually identical.

Is perspective necessary for the LTI? Maniatis (2008) suggested that the LTI was better explained as a case of the Jastrow illusion applied to perspective; a simultaneous orientation contrast. Specifically, the right edge of the leaning tower on the left is contrasted to the left edge of the leaning tower on the right. Because these edges diverge and are tilted in opposite directions, the whole objects also appear to diverge. Yoonessi et al. (2008) rejected that explanation because simultaneous orientation contrast would predict the LTI would be present in nonperspective images, but the LTI is not present in nonperspective images.

The necessity of perspective is further supported by recent research. Kingdom et al. (2017) noted that no LTI is experienced for pictures of towers taken at large distances, suggesting that an object receding in depth is necessary for an LTI. Parovel and Costall (2018) showed that increasing either perspective obliqueness of the image or distance between images (up to a point) increases the magnitude of the LTI. They attribute their results as being the result of (a) interpreting the images as part of one visual scene and (b) the visual system creating a new apparent point of observation between the two images which in turn results in new interpretations of the perspective cues in both images. Overall, the research supports perspective as a necessary first factor for the LTI. Parovel and Costall also note that if the images are presented too far apart, each is treated as a separate image, resulting in no LTI (presumably because each image is viewed separately with its own point of observation). Therefore, a second factor, visual integration of the images also appears to be necessary for the LTI.

The Turn in the Road Illusion (TRI) also appears to rely on perspective to create its effect. In the TRI identical schematic drawings of a road receding into the distance appear to be different (Orsten & Pomerantz, 2014). Furthermore, when a third nonidentical road schematic is added, it can appear identical to one of the actually identical roads. Figure 1B illustrates the TRI. Orsten and Pomerantz (2014) explain the TRI as being the result of identical roads not sharing a vanishing point and therefore appear to be nonidentical; roads that do share a vanishing point (the appropriate nonidentical road) appear to be identical. Hiris (2019) introduced the concept of “convergence vectors” to explain aspects of the TRI and LTI. In perspective drawings and pictures, parallel lines converge on a vanishing point. Convergence vectors are vectors that bisect the angle formed by the parallel lines and continue beyond the vanishing point. Hiris noted that nonidentical roads can be perceived as identical even when they do not share a vanishing point, so long as their “convergence vectors” intersect. Hiris also noted that the nonintersection of the convergence vectors in LTI predicts that they would not appear parallel in three-dimensional space and therefore, not identical.

There is general agreement on a perspective-based explanation of the LTI (Erkelens, 2015; Hiris, 2019; Kingdom et al., 2007; Martinez-Conde, 2018; Orsten & Pomerantz, 2014; Parovel & Costall, 2018, Yoonessi et al., 2008). However, all of these studies rely on demonstrations rather than data collection. Although the demonstrations are convincing, there are no specific quantifications of the size of the LTI (or TRI) and this makes it difficult to arrive at entirely convincing explanations of the LTI and TRI. Except for Hiris (2019) and Orsten and Pomerantz (2014), past studies have focused on presenting identical copies of an image side-by-side. Knowledge that the images are identical, even though they do not appear to be, makes it easy to appreciate the LTI. However, understanding how perspective cues are being used by the visual system might be better explored by using images of varying perspective cues.

Past research has not quantified the LTI beyond a cursory examination of the conditions that determine the size of the illusion. Also, most previous research has focused on observing perceptual effects on identical images. Therefore, in the current studies (Experiments 1 and 2) we sought to (a) establish a method of quantifying the size of the LTI (identical images with perspective cues) and (b) measure the same effect on LTI-like stimuli (any pairing of images with perspective cues). After establishing a way of measuring the LTI and LTI-like effect, we sought to determine what factors influence these effects. Parovel and Costall (2018) showed that large spatial separations between identical images result in no LTI, presumably because the images are processed separately. In Experiments 3 and 4, we sought to explore the necessity of visual integration for the LTI by manipulating attention. Manipulating attention to focus on only one image should reduce or eliminate the LTI (Experiment 3), while requiring processing of both images should result in a full strength of enhanced LTI (Experiment 4). Finally, in Experiment 5, we further explored the necessity of visual integration by determining whether presenting images in alternation would eliminate the LTI and LTI-like effects.

General Method

Participants

Participants received course credit in General Psychology for participating in the study. All participants had normal or corrected to normal vision and were naïve to the hypotheses being tested.

Stimuli and Materials

The stimuli were two pictures presented side-by-side on a 27-in. iMac using Matlab and Psychophysics Toolbox (Brainard, 1997; Kleiner et al., 2007; Pelli, 1997). Each picture was 1,500 pixels wide by 2,025 pixels tall, creating a visual angle of 17.5° by 23.5° at the viewing distance of 57 cm ensured by the use of a head and chin rest. A blank area of 1.8° separated the pictures. All pictures were taken by one of the authors using a Canon PowerShot SX200 mounted on a tripod and cropped to the display size of 1,500 by 2,025 pixels. Each display included one target picture (whose sidewalk orientation would be judged) and one comparison picture (no judgment required). The target pictures were one of three perspective pictures of a sidewalk receding into the distance (see Figure 2). Perspective was created by taking the picture with a tripod placed six feet to the right of the center of the sidewalk, on the center of the sidewalk, or six feet to the left of the center of the sidewalk. We chose to use pictures of sidewalks, rather than towers or some other vertical structure, because we assumed our participants were familiar with sidewalks and our participants (many from rural areas or small towns) were likely less familiar with tall buildings or other tall vertical structures. Pictures taken parallel to the sidewalk create images of an object receding in depth as required for the LTI to occur (Kingdom et al., 2017). Also, Hiris (2019) has demonstrated that LTI-like effects occur using these displays. The comparison picture on each display was one of the three target pictures, a picture of a nature scene with no perspective lines (rightmost picture in Figure 2), or no picture (a blank white screen). By “no perspective lines” we mean no straight (or nearly straight) lines that recede into the distance towards a vanishing point. There are, of course, cues to perspective remaining within the right image in Figure 2, for example, the relative size of the trees in the foreground versus the background. However, there are no straight-line cues to the location of a vanishing point. The no perspective lines picture and no picture comparisons were used as controls. The target picture could either be to the left or right of the fixation point and the comparison picture filled the other location. Because there were three target pictures, two possible locations for the target picture, and five possible comparisons (four pictures and no picture), there were 30 total conditions.

Figure 2.

Target pictures and no perspective lines picture used in Experiment 1.

Procedure

Participants signed a consent form, were asked if they had any questions about the consent form, and were given a blank copy for their own records. Participants were seated in front of an iMac computer and given instructions on how to use the keyboard to enter responses.

In most experiments, there were three practice sessions. No feedback, beyond what was visible on the screen, was given during any of the practice sessions or in the experiments. In the first practice session, there were two trials. In each trial, a fixation cross appeared at the center of the screen indicating the participant could press the spacebar to start the trial. After the spacebar press, one picture of a sidewalk was presented (all pictures used in the practice sessions were not used in the main experiment). After 3 seconds, a line appeared overlaid on the picture (centered on the sidewalk) at a randomly determined orientation. The participant was instructed to use the “f” key to rotate the line anti-clockwise and the “j” key to rotate the line clockwise until the line matched the orientation of the center of the sidewalk. The participant was instructed to press the return key when they were done adjusting the orientation of the line to match the orientation of the sidewalk. A fixation cross was displayed again to indicate the next practice trial was ready to begin. This first practice session was meant to make it clear that the adjusted line was meant to match the center of sidewalk and to give the participant visual feedback of what that would look like (with both the line and sidewalk present).

In the second practice session, there were also two trials. Each of these trials were the same as those in the first practice session, except when the line appeared, the picture of the sidewalk disappeared. The participant was instructed to adjust the line to the remembered orientation of the sidewalk. Here, the purpose was to allow the participant to practice matching the line to the remembered orientation of the sidewalk.

In the third practice session, there were four trials. Each of these trials were the same as those in the second practice session, except there were two pictures presented side-by-side on each trial. The participant only had to judge the orientation of one of the sidewalks, but which sidewalk was to be judged was only clear to the participant when the pictures disappeared and the response line appeared on the same side of the screen as the picture of the sidewalk that they were supposed to judge. The participant was instructed to adjust the line to the remembered orientation of the sidewalk that had been presented at the location of the line. Except for the pictures used, these trials were the same as the trials in the main experiment. In this final practice session, the purpose was to expose the participant to how the main experiment would run, including seeing multiple pictures simultaneously and having to remember the orientations of both sidewalks.

For the main experiment, the lights were turned off, and the trials started with the display of a fixation cross at the center of the screen. Participants pressed the spacebar on the keyboard to start each trial and the pictures for that trial were displayed. After 3 seconds, the pictures disappeared, then a line appeared at a random orientation in the same location as the target picture (see Figure 3). As in the practice trials, the participant used the “f” and “j” keys to rotate the line to match the orientation of the sidewalk in the target picture. When the participant was satisfied with the orientation of the line, they pressed the return key to indicate they were done adjusting the line. The response was recorded, and the fixation cross for the next trial was displayed. Each of the 30 conditions described above were shown 4 times in random order for a total of 120 trials. In Experiments 4 and 5, only one control condition was used, resulting in 24 conditions and 96 trials.

Figure 3.

Main experiment trials for Experiment 1.

After the main experiment was completed, participants viewed every condition that included two sidewalks twice, resulting in 18 total trials. Instead of making a judgment about the orientation of the sidewalks, participants were asked to make a judgment about how parallel the sidewalks appeared to be in the two pictures. Participants indicated this by pressing “1” for “perfectly parallel,” “2” for “almost parallel,” “3” for “somewhat parallel,” “4” for “not very parallel,” and “5” for “not parallel.” A labeled scale appeared on the screen below the pictures while the participant was making this judgment.

The whole procedure, including the three practice sessions, the main experiment, and the judgments of parallelism, required 30–45 minutes for each participant.

Data Validation

Data were analyzed in two ways: (1) after data were validated and (2) after data were validated and marked cases dropped. Data were validated for each participant using the following procedure: If a condition had a standard deviation (SD) greater than 12.5°, the score that deviated the most from the mean for that condition was removed. If the SD was then below 10°, the new mean was used for that condition. These criteria were used to capture and correct those participants that had one data point for a condition that was substantially different than their other data points. The authors believe such cases were the result of the participant forgetting which picture was to be judged, a single trial lapse of attention, and/or an instance of pressing the return key before the judgment was actually complete. If the SD was still above 10 after dropping the most deviant case, the participant’s data were marked to drop from the study. In this case, there was not a single data point for the condition that was creating the high variability. In these cases, the authors believe that extended inattention to the task was indicated. Data analyses were run on (1) validated data with no cases dropped and (2) validated data after dropping all marked cases.

Table 1 shows the total number of participants for each experiment, the number of participants marked for removal (and their average number of conditions with a removed score), and the number of participants remaining after validation and dropping marked cases (and the remaining participants average number of conditions with a removed score). Because the analyses without marked participants remove unwanted “noise” (the conditions that still had high variability, a SD greater than 10), we focus on the analyses after dropping all marked cases. When statistical decisions differ between the full validated data set and after dropping marked cases, those differences are noted in the relevant results section. Although the number of participants marked for removal was large in Experiment 1, the statistical analyses were largely the same before and after removing the marked participants.

Table 1.

Participants Before and After Data Validation.

Experiment	Total participants	Marked participants (average number of removed scores)	Participants after validation (average number of removed scores)
Experiment 1	31	20 (6.1)	11 (2.1)
Inversion	10	5 (5.8)	5 (1.8)
Experiment 2	15	4 (6.3)	11 (1.5)
Experiment 3	15	2 (4.0)	13 (1.1)
Experiment 4	21	9 (5.8)	12 (3.2)
Experiment 5	20	4 (9.8)	16 (2.2)

Initial Data Processing

In most experiments reported here, two control conditions were created by pairing each sidewalk with either no picture or a picture without perspective lines. For those experiments, six paired samples t-tests were run to compare the perceived orientation of each target picture/location combination when it was paired with no picture and when it was paired with the no perspective lines picture to determine if the control conditions differed. For example, one paired samples t-test compared the judgment of the left sidewalk stimulus in the left location paired with no picture versus the judgment of the left sidewalk stimulus in the left location paired with the no perspective lines picture. Except where noted, none of the paired samples t-tests showed a significant difference, with validated data or validated data after dropping marked cases.

Given that there were no significant differences between the control conditions in almost every case, the average of these control conditions was used as a baseline. The deviation of adjustments for sidewalk pictures presented with other sidewalk pictures from the average of the appropriate control conditions was used as the data of interest in the main analysis reported for each experiment (see Figure 4 for an illustration of how these deviation scores were calculated). This gave a measure of how much the perspective lines in the other picture influenced the orientation judgment compared to the average of the control conditions—in other words, the deviation score gives the magnitude and direction of the LTI-like illusion. For Experiments 4 and 5, the single control condition was subtracted to obtain the deviation score. For each experiment, a table gives the exact values of the deviation scores that served as the dependent variable in the repeated measures analysis of variance (ANOVA; Greenhouse-Geisser-corrected values are reported in all results sections).

Figure 4.

Illustration of the calculation of deviation scores.

Experiment 1—Quantifying the Leaning Tower Illusion

Previous research on LTI-like stimuli have not measured the degree of misperception that occurs in such stimuli. Furthermore, previous research has been almost exclusively on presenting the same stimuli side-by-side. In Experiment 1, we sought to measure the misperception that occurs in LTI-like stimuli. We presented pictures of sidewalks side-by-side and determined how orientation judgments under those conditions differed from orientation judgments made when the picture was presented alone or with a picture that did not contain perspective lines. In order to determine whether misperception of orientation generally occurs in such stimuli, we presented several combinations of pictures, rather than just presenting the same stimuli side-by-side. After all orientation judgments were complete, we also measured participants perception of how parallel the sidewalks appeared in stimulus combinations containing two sidewalks. There were 11 participants after data validation procedures (see Table 1).

Results

The dependent variable in the three-way repeated measures ANOVA was the deviation score (described in the General Method). The independent variables were screen location of the judged sidewalk (left or right), the sidewalk picture in the left location (left, straight, or right sidewalk; see Figure 2), and the sidewalk picture in the right location (left, straight, or right). All statistical tests were significant except for the main effect of the left location stimulus and the interaction of the left location stimulus and right location stimulus (this interaction was statistically significant in the validated data set before cases were dropped). There was a main effect of location judged, F(1, 10) = 14.871, p = .003, η_p² = .598, and a main effect of what the right location stimulus was, F(1.563, 15.631) = 8.282, p = .006, η_p² = .453. Also, there a significant interaction between location judged and the left location stimulus, F(1.712, 17.116) = 15.388, p < .001, η_p² = .605, and a significant interaction between location judged and the right location stimulus F(1.488, 14.878) = 7.859, p = .008, η_p² = .440. Finally, there was a statistically significant three-way interaction between the location of the judged stimulus, what the left location stimulus was, and what the right location stimulus was, F(1.948, 19.476) = 4.422, p = .027, η_p² = .307. Table 2 summarizes the main results of the study.

Table 2.

Experiment 1 Results Given as Left Side Misperception/Right Side Misperception (Average Parallel Judgment).

Right side sidewalk stimulus	Left side sidewalk stimulus
Right side sidewalk stimulus	Left \	Straight \|	Right /
Left \	\ \ 2.2°/5.6° (3.50)	\| \ –0.8°/5.6° (2.77)	/ \ –9.3°/10.9° (1.41)
Straight \|	\ \| –1.4°/0.8° (4.27)	\| \| –4.0°/3.0° (3.05)	/ \| –6.8°/1.6° (2.09)
Right /	\ / –3.8°/1.3° (4.82)	\| / –1.1°/–0.2° (4.32)	/ / –6.0°/–1.6° (3.68)

Because the three-way interaction was significant, we focus our explanations there. When the left stimulus location was the sidewalk receding to the right, it was judged to be rotated anticlockwise relative to the control condition (see the negative values on left side of the “/” in the rightmost column of Table 2). However, when the right stimulus location was the sidewalk receding to the left, it was judged to be rotated clockwise relative to the control condition (see the positive values on the right side of the “/” in the uppermost row of Table 2). In general, these highlighted conditions are where the largest deviations between the control conditions and the conditions with two sidewalks were present. In particular note that in the upper right corner of Table 2, where two sidewalks recede towards each other in the distance, the largest deviations (misperceptions) from the control conditions occur (–9.3° and 10.9°). Note also that the deviation is larger than any of the deviations resulting from the traditional LTI where the same stimuli are presented side-by-side (diagonal from upper left to lower right in Table 2). The conditions where two sidewalks recede towards each other in the distance are also perceived as most parallel as shown by the analysis of parallel judgments described next (see the values within parentheses in Table 2).

The parallel judgment data were analyzed using a two-way repeated measures ANOVA, with parallelism judgments as the dependent variable (1 = perfectly parallel, 5 = not parallel) and which sidewalk picture was in the left and right locations as the independent variables. There was a significant effect of the left location stimulus on the perceived parallelism of the sidewalks, F(1.798, 17.985) = 62.986, p < .001, η_p² = .863, and there was a significant effect of the right stimulus on the perceived parallelism of the sidewalks, F(1.217, 12.171) = 109.602, p < .001, η_p² = .916. There was also a significant statistical interaction of the left location and right location stimulus, F(2.477, 24.773) = 3.284, p = .045, η_p² = .247.

Based on Bonferroni-corrected pairwise comparisons, all left stimulus position conditions were statistically different from each other. Specifically, when the left sidewalk was the left stimulus, the sidewalks were perceived as less parallel (M = 4.20) than when the straight sidewalk was the left stimulus (M = 3.38, p = .002) or when the right sidewalk was the left stimulus (M = 2.39, p < .001). The sidewalks were perceived as less parallel when the left stimulus was the straight sidewalk (M = 3.38) than when it was the right sidewalk (M = 2.39, p = .001). In general, to create an overall image where the sidewalks might appear parallel, the left stimulus must be a sidewalk that is receding to the right.

Likewise, all right stimulus position conditions were statistically significantly different from each other. When the right stimulus was the left sidewalk, the sidewalks were perceived as more parallel (M = 2.56) than when it was the straight sidewalk (M = 3.14, p = .001) or the right sidewalk (M = 4.27, p < .001). When the right stimulus was the straight sidewalk, it was perceived as more parallel (M = 3.14) than when it was the right sidewalk (M = 4.27, p < .001). In general, to create an overall image where the sidewalks might appear parallel, the right stimulus must be a sidewalk that is receding to the left. The interaction suggests that these main effects are not entirely additive. However, the top right cell in Table 2 does result in the perception of being most parallel as one would expect based on the main effects.

Figure 5 overlays the results of Experiment 1 on the stimuli. Note that images in Figure 5 are not the full images presented in the actual experiment and are useful only in helping to visualize the data in relation to the stimulus conditions. Figure 5A corresponds to the left column of Table 2, Figure 5B corresponds to the middle column of Table 2, and Figure 5C corresponds to the right column of Table 2. Note that in all control conditions, the orientation adjustments are always in error towards 90°. This is consistent with what one would expect if the participant was adjusting the line to match their three-dimensional perception of the sidewalk orientation rather than the two-dimensional orientation on the screen. This is tested and discussed further in Experiment 2.

Figure 5.

Results from the Experiment 1. A: Results from conditions with left leaning sidewalk as the left stimulus. B: Results from conditions with straight sidewalk as the left stimulus. C: Results from conditions with right leaning sidewalk as the left stimulus.

Discussion

Experiment 1 shows that the misperception of orientation created by LTI-like stimuli can be measured. Furthermore, measurements show that the traditional LTI stimuli created by placing two copies of a stimulus side-by-side creates only a medium-strength version of the LTI effect. Stimuli that in reality converge (a sidewalk receding to the right in the left location and sidewalk receding to the left in the right location) create a misperception that is more than twice as large as the traditional LTI stimuli (compare upper right corner of Table 2 to the middle of Table 2). These results also make it clear that misperception of orientation when presented with multiple pictures containing perspective lines occurs in a wide variety of stimulus conditions. Although the traditional LTI stimuli make it easy to perceive the misperception of orientation because two identical stimuli do not appear identical, other stimulus combinations actually result in a greater degree of misperception.

We also explored the effect of inverting the stimuli with five (after data validation procedures, see Table 1) naive participants. Analyses were the same as in Experiment 1. A three-way repeated measures ANOVA showed a significant three-way interaction between the location of the picture being judged, the left location stimulus, and the right location stimulus, F(1.415, 5.661) = 9.508, p = .019, η_p² =.704. The interaction between location judged and the right location stimulus was also significant, F(1.440, 5.759) = 8.843, p = .021, η_p² =.689. In the analysis before cases were dropped, the main effect of location and main effect of the right location stimulus were statistically significant as well. Table 3 shows the results, note the difference in the schematics of the table and the predictable reversal of the sign of the deviation scores compared to Table 2. Interestingly, the straight–straight condition appears to give no illusion when inverted. However, the right–left condition appears to still result in the illusion when inverted. Inversion is known to disrupt the perception of depth in photographs (Fujita, 1996), but it is unclear why this would only affect the straight–straight condition. Table 3 also shows that for inverted stimuli, the straight–straight condition, with actually parallel sidewalks are perceived as most parallel (unlike upright displays, compare with Table 2). This provides further evidence that inversion of the stimuli is disrupting depth perception, but perhaps only for the straight–straight stimuli. Figure 6 allows the reader to experience these effects. The effect of inversion on the misperception of LTI-like stimuli needs further investigation, but is beyond the scope of this study.

Table 3.

Inversion results given as Left Side Misperception/Right Side Misperception (Average Parallel Judgement).

Right side sidewalk stimulus	Left side sidewalk stimulus
Right side sidewalk stimulus	Inverted Left /	Inverted Straight \|	Inverted Right \
Inverted Left /	/ / 2.3°/–2.8° (2.50)	\| / 0.7°/–6.4° (2.13)	\ / 9.9°/–11.4° (3.50)
Inverted Straight \|	/ \| 1.1°/–0.5° (4.50)	\| \| –0.1°/0.4° (1.38)	\ \| 1.8°/–1.0° (2.50)
Inverted Right \	/ \ 4.4°/–4.3° (5.00)	\| \ –1.0°/–3.2° (4.38)	\ \ 0.6°/1.2° (2.25)

Note. The sky is at the bottom of each schematic. Negative values indicate an anti-clockwise difference score. For parallel judgments, 1 = perfectly parallel and 5 = not parallel.

Figure 6.

Illustration of differences in inversion effects. Inverting A, the straight–straight condition results in the illusion largely disappearing (see B). Inverting C, the right–left condition results in the sidewalks still appearing parallel (see D).

Experiment 2—Accuracy with Lines

In Experiment 1, the control data for the sidewalk receding to the left and the sidewalk receding to the right do not fall on a line bisecting the sidewalk as one might expect (see Figure 5). To be certain this was not a byproduct of our method of measuring perceived orientation and instead reflected the perception of three-dimensional depth of the sidewalk pictures, a new group of naïve participants viewed lines instead of sidewalks. When viewing lines, which should not have a three-dimensional interpretation for naïve participants, we would expect perception to be accurate. Furthermore, one would not expect the lines to interact in the same way as images of sidewalks, given that lines would not normally be interpreted as receding in three-dimensional space nor be interpreted as perspective lines.

There were 11 participants after data validation procedures (see Table 1). The methods were the same as those given in the General Method with the following changes: Target pictures were three pictures of a single black line on a white background. The line in each picture matched the length, position, and orientation of the center of the sidewalk in the corresponding picture from Experiment 1 (see Figure 7). Practice sessions now used the target pictures described here.

Figure 7.

Target pictures used in Experiment 2.

Results

In the initial data processing (see General Method), the two control conditions were compared using six paired-samples t-tests. Only one uncorrected p-value was less than .05, and therefore, the average of the control conditions was still used as a baseline. Table 4 gives the exact values of the deviations from the average of the control conditions and the statistical analysis was the same as described for Experiment 1.

Table 4.

Experiment 2 Results Given as Left Side Misperception/Right Side Misperception (Average Parallel Judgement).

Right side line stimulus	Left side line stimulus
Right side line stimulus	Left \	Straight \|	Right /
Left \	\ \ 0.5°/0.7° (1.27)	\| \ 0.2°/–0.2° (4.41)	/ \ –0.9°/0.2° (5.00)
Straight \|	\ \| –0.6°/–1.3° (4.55)	\| \| 0.2°/–0.6° (1.32)	/ \| –0.8°/–0.2° (4.59)
Right /	\ / 0.2°/–1.6° (4.95)	\| / 0.3°/–0.5° (4.59)	/ / 0.8°/–0.8° (1.27)

Note. Negative values indicate an anti-clockwise difference score. For parallel judgments, 1 = perfectly parallel and 5 = not parallel.

There were no significant main effects nor interactions in Experiment 2 (in either the before or after dropping cases analyses). Specifically, there was no significant main effect of location judged, F(1, 10) = 1.068, p = .326, η_p² = .097, there was no significant main effect of the line picture in the left location, F(1.648, 16.484) = 0.168, p = .806, η_p² = .097, and there was no significant main effect of the line picture in the right location, F(1.758, 17.577) = 0.917, p = .406, η_p² = .084. There was no significant interaction between location judged and the line picture in the left location, F(1.439, 14.394) = 0.577, p = .529, η_p² = .053, and there was no significant interaction between location judged and the line picture in the right location, F(1.876, 18.763) = 1.342, p = .284, η_p² = .118. There was no significant interaction between the line picture in the left location and the line picture in the right location, F(2.804, 28.045) = 1.151, p = .344, η_p² = .103. There was no statistically significant three-way interaction between location judged, left stimulus, and right stimulus, F(2.355, 23.547) = 0.369, p = .729, η_p² = .036. These results show that the lines, unlike sidewalks, were not influenced by the presence of another line, the location of the line stimulus, nor any combination of those factors.

Similar to Experiment 1, the parallel judgment data were analyzed using a two-way repeated measures ANOVA, with parallelism judgments as the dependent variable and which sidewalk pictures were in the left and right positions as the independent variables. There was no significant effect of the left position stimulus on the perceived parallelism of the sidewalks, F(1.566, 15.657) = 2.060, p = .166, η_p² = .171, and there was no significant effect of the right position stimulus on the perceived parallelism of the sidewalks, F(1.407, 14.067) = 1.186, p = .316, η_p² = .106. However, there was a statistically significant interaction between the left position stimulus and the right position stimulus, F(1.863, 18.632) = 453.241, p < .001, η_p² = .978. As Table 4 shows in the values in parentheses, the lines were judged most parallel when the lines were the same on the left and right side of the screen. Recall that when sidewalks were presented in Experiment 1 (Table 2), sidewalks were judged as more parallel when the left stimulus was a sidewalk receding to the right and/or when the right stimulus was a sidewalk receding to the left.

Discussion

In Experiment 1, data from the control conditions did not match the orientation of the sidewalk stimuli. However, in Experiment 2, data from the control condition do match the orientation of the line stimulus—see Supplemental Figure 1. This suggests that the control condition results in Experiment 1 are not a byproduct of our method of presenting stimuli or of measuring perceived orientation. The control condition orientation “misperceptions” in Experiment 1 may be the result of representing three-dimensional space on a screen. Osa et al. (2011) showed that angles in an actual road scene or a projection of that scene on a screen are grossly underestimated (see also: Erkelens, 2015). This underestimation of the angle likely is caused by the misperception of the orientation of the lines/edges in a scene representing three-dimensional space. A similar misperception may be occurring for the sidewalks in our displays, resulting in the control condition “mismatch” in Experiment 1. Because there was no three-dimensional interpretation to the displays in Experiment 2, control conditions were perceived veridically. Also note that there was no influence of the presence of another line on the perception of orientation. This was expected given that there is no reason to interpret the lines as representing three-dimensional space, and the nonoverlapping stimuli would not be expected to cause orientation repulsion (Blakemore et al., 1970). Recall that in Experiment 1 the data are the deviation from the control condition. Therefore, above and beyond the control condition “mismatch” in Experiment 1, there was an effect of the presence of another sidewalk on the perception of orientation in Experiment 1.

Parallel judgments also greatly differed between Experiment 1 and 2. In Experiment 2, actually parallel lines (copies of the same image placed side-by-side) were perceived as most parallel. In Experiment 1, sidewalks that converged in the distance were perceived as most parallel, not copies of the same image placed side-by-side. These results reflect the lack of any three-dimensional interpretation given to the lines presented in Experiment 2, and the three-dimensional interpretation given to the sidewalks presented in Experiment 1.

Experiment 3—The Role of Attention in the Leaning Tower Illusion

Experiment 1 established that we can robustly measure the misperception that occurs in LTI-like stimuli and that the strongest misperception occurs when the stimuli appear most parallel. Experiment 2 showed that these results were not due to our presentation method nor our method of measuring the perceived orientation of the sidewalk stimuli. In Experiment 3, we sought to determine whether directing the participants attention to only one of the two stimuli could influence the size of the misperception. Parovel and Costall (2018) have shown that as the distance between the stimuli in an LTI-like display increases, the magnitude of the misperception increases, up to a point where the illusion breaks down completely. One explanation Parovel and Costall offer for this result is that at large distances, the two stimuli are processed independently. In Experiment 3, we sought to create this independence of processing through an attentional cue.

In the current experiment, we used a visual cue (a small square above the image) to indicate which sidewalk participants would judge after the images disappeared. Therefore, participants would not need to remember, nor even process, the other image on the screen to perform well on the task. Recall that in all previous experiments, participants did need to process and remember both stimuli given that the participants did not know which stimuli would be judged until after the stimuli disappeared. In the current experiment, we would expect the participants not to attend to nor process the noncued stimuli. Therefore, the misperception of orientation should be eliminated or at least minimized.

There were 13 participants after data validation procedures (see Table 1). The methods were the same as those given in the General Method with the following changes: In the last practice session and in the main experiment, there was a black square above the picture that the participant would judge. The participants were told “a black square will appear above the picture you will be judging.” The black square and picture disappeared at the same time, after 3 seconds, when the line for the participant to adjust appeared.

Results

Table 5 gives the exact values of the deviations from the average of the control conditions, and these measurements were used as the dependent variable in a three-way repeated measures ANOVA. There was a significant main effect of location on the screen, F(1, 12) = 8.044, p = .015, η_p² = .401 (the main effect of location was not significant in the analysis before dropping cases). When the picture being judged is on the left side of the screen, the deviation is more in the anticlockwise direction (M = –1.014) than when the picture being judged is on the right side of the screen (M = 1.079). There were no other significant main effects (all p > .5). There were also no two-way interactions nor a three-way interaction (all p > .09). The lack of significant results as well as the pattern of results in Table 5 indicate that there was no LTI-like misperception when the stimulus to be judged was cued.

Table 5.

Experiment 3 Results Given as Left Side Misperception/Right Side Misperception (Average Parallel Judgement).

Right side sidewalk stimulus	Left side sidewalk stimulus
Right side sidewalk stimulus	Left \	Straight \|	Right /
Left \	\ \ –1.4°/0.8° (3.88)	\| \ –0.0°/0.0° (2.54)	/ \ –1.4°/2.4° (1.73)
Straight \|	\ \| –2.3°/0.7° (4.65)	\| \| 0.4°/0.4° (2.73)	/ \| –0.8°/–0.1° (2.23)
Right /	\ / –1.1°/2.8° (4.92)	\| / –0.6°/1.6° (4.69)	/ / –1.9°/0.1° (3.62)

Note. Negative values indicate an anti-clockwise difference score. For parallel judgments, 1 = perfectly parallel and 5 = not parallel.

Similar to Experiment 1, the parallel judgment data were analyzed using a two-way repeated measures ANOVA, with parallelism judgments as the dependent variable and which sidewalk pictures were in the left and right positions as the independent variables. Recall that the parallel judgments were performed after the main experiment, and no cues were used. There was a significant main effect of the sidewalk picture in the left position, F(1.259, 15.109) = 115.245, p < .001, η_p² = .906, and there was a significant main effect of the sidewalk picture in the right position, F(1.883, 22.594) = 67.847, p < .001, η_p² = .850. There was also a significant interaction between the sidewalk picture in the left position and the sidewalk picture in the right position, F(2.393, 28.716) = 5.597, p = .006, η_p² = .318. In general, the parallel judgments shown in Table 5 followed the same pattern of results as in Experiment 1 as shown in Table 2.

Discussion

The misperception of LTI-like stimuli was nearly eliminated when the participant knew which stimulus would be judged. Note that the participants are still perceiving the attended sidewalk as three-dimensional as indicated by the control condition adjustments not matching the actual stimulus orientation (see Supplemental Figure 2). However, unlike Experiment 1, the other stimulus present is not influencing perception of its orientation, presumably because participants simply did not attend to it nor process it. These results indicate that the misperception of orientation in LTI-like stimuli is not a low-level, inevitable result of the stimulus—as is the case for orientation repulsion (Blakemore et al., 1970) or direction repulsion (Hiris & Blake, 1996). Instead, sufficient attention must be given to both stimuli in order for the misperception to occur.

Experiment 4—More on Attention in the Leaning Tower Illusion

Experiment 3 showed that both stimuli need to be attended to or processed in order for LTI-like misperceptions to occur. In Experiment 4, we sought to show that requiring the participant to process both stimuli initially would minimize the effect of the cue to which stimulus would be judged. When two sidewalks were presented in Experiment 4, participants were required to make a judgment about how parallel the sidewalks appeared within the initial 3-second presentation of the stimuli. Therefore, even though a cue was presented regarding the orientation judgment as in Experiment 3, both stimuli needed to be processed during their presentation in order to make the judgment on how parallel the sidewalks appeared. Because both sidewalks were processed, we expected that the LTI-like misperception of orientation would be present again.

In addition to the usual data validation procedures, one participant’s data were not considered for analysis because comments during the debriefing discussion made it clear that the participant did not understand the task. There were 12 participants after data validation procedures (see Table 1). The methods were the same as those given in the General Method with the following changes: Given that previous experiments showed no difference between control conditions, only the no perspective lines control condition was used. Also, a fourth practice session with eight trials was given. Here, participants practiced judging (on a 1–5 scale) how parallel the sidewalks were in the two pictures during the 3-second presentation time. In addition, the “0” key was used by the participant to indicate that a parallelism judgment was not applicable (when the comparison was a no perspective lines picture). In the main experiment, if a parallelism judgment was not made within 3 seconds, a “no response” was recorded and data from that trial were not used. The usual parallelism judgments (not made under a 3-second time pressure) were completed after the main experiment in the same way as previous experiments.

Results

Data were validated and analyzed the same way as the data in Experiment 1, except there was only one control condition. Therefore, the judgment of the appropriate sidewalk in the no perspective lines picture condition was subtracted from judgments of the same sidewalk picture when it was paired with other sidewalk pictures. Table 6 gives the exact values of the deviations from the control conditions, and these measurements were used as the dependent variable in a three-way repeated measures ANOVA.

Table 6.

Experiment 4 Results Given as Left Side Misperception/Right Side Misperception (Average Parallel Judgement; Average Parallel Judgment During Task).

Right side sidewalk stimulus	Left side sidewalk stimulus
Right side sidewalk stimulus	Left \	Straight \|	Right /
Left \	\ \ 1.4°/3.7° (3.14; 2.83)	\| \ –2.3°/5.8° (2.00; 2.03)	/ \ –5.8°/5.2° (1.36; 1.32)
Straight \|	\ \| –0.1°/–1.2° (4.09; 3.45)	\| \| –0.9°/1.6° (2.27; 1.97)	/ \| –5.1°/2.0° (2.00; 1.73)
Right /	\ / –4.4°/0.3° (4.86; 4.55)	\| / 0.1°/0.8° (4.14; 3.88)	/ / 0.5°/–2.3° (3.50; 2.99)

Note. Negative values indicate an anti-clockwise difference score. For parallel judgments, 1 = perfectly parallel and 5 = not parallel.

There was a significant main effect of location on the screen, F(1, 11) = 6.585, p = .026, η_p² = .374. When the picture being judged was in the left location, the deviation is more in the anti-clockwise direction (M = –1.845) than when the picture being judged was in the right location (M = 2.019). There were no other significant main effects or two-way interactions (all p > .08). There was a significant three-way interaction between location, the sidewalk picture in the left location, and the sidewalk picture in the right location, F(2.733, 30.065) = 7.756, p = .001, η_p² = .414. Note that in the analysis before dropping cases three additional tests were significant: the main effect of the left location stimulus, the interaction of left location stimulus and location judged, and right location stimulus and location judged. Table 6 shows that the LTI-like misperception had partially returned (compare upper right corner data to Tables 2 and 5).

As in Experiment 1, the parallel judgment data that were collected after the main experiment were analyzed using a two-way repeated measures ANOVA, with parallelism judgments as the dependent variable and which sidewalk pictures were in the left and right positions as the independent variables. There was a significant main effect of the sidewalk picture in the left position on the parallel judgment, F(1.977, 21.745) = 97.178, p < .001, η_p² = .898, and there was a main effect of the sidewalk picture in the right position on the parallel judgment, F(1.723, 18.950) = 100.491, p < .001, η_p² = .901. There was no significant interaction, F(1.566, 17.231) = 2.216, p = .245, η_p² = .114.

The parallel judgments collected during the main experiment and the parallel judgments collected after the main experiment were compared using a three-way repeated measures ANOVA, with the parallelism judgments as the dependent variable and the data type (during the main experiment or after the main experiment), sidewalk picture in the left location (left, straight, right), and sidewalk picture in the right location (left, straight, right) as the independent variables. There was a significant main effect of the data type, F(1, 11) = 19.522, p = .001, η_p² = .640. When the parallel judgments were made during the main experiment, the sidewalks were judged to be more parallel (M = 2.743) than when they were made after the main experiment (M = 3.056). Note that during the main experiment, the judgment of how parallel the sidewalks were had to be completed within 3 seconds. However, after the main experiment viewing time was unlimited, and this may have led to a difference in response or approach to the task, although it is not clear why time-pressured judgments would result in a bias to say stimuli were more parallel. Another difference between the two judgments is that after the main experiment, judgments come after extensive experience with the stimuli, which might result in better judgments. However, it is again unclear why those judgments should be overall “less parallel” than judgments made during the experiment.

There was also a significant effect of the sidewalk picture in the left position on parallel judgments, F(1.469, 16.157) = 100.255, p < .001, η_p² = .901, and a significant effect of the sidewalk picture in the right position, F(1.571, 17.285) = 147.576, p < .001, η_p² = .931. There were no significant interactions (all p > .2). In general, both sets of parallel judgments for Experiment 4 (Table 6) follow the same general pattern as for Experiment 3 (Table 5) and Experiment 1 (Table 2).

Discussion

When participants were required to judge how parallel the sidewalks appeared during the 3-second presentation time, LTI-like misperception of the sidewalk orientation re-emerged, even though the sidewalk that would be judged was cued. We believe the simplest explanation is that the processing of both stimuli, required for making a judgment of how parallel the sidewalks were, influenced the later orientation judgments. Note however that the LTI-like misperception of the orientation of the sidewalks was approximately half of the original misperception in Experiment 1, but distinctly more than the misperception in Experiment 3.

Considering response times to the task of making a parallel judgment during the initial display may indicate why there is only a partial misperception in the current experiment. Recall that the display of the images lasted for a total of 3 seconds. However, participants completed the judgment of how parallel the sidewalks were in just over half that time (M = 1.664 seconds, SD = 0.330; Median = 1.632 seconds). In the remaining trial time, the participant may have focused exclusively on the cued stimulus for the upcoming orientation judgment, reducing the influence of having just processed both displays.

Experiment 5—The Role of Simultaneity of Presentation in the Leaning Tower Illusion

Experiment 4 showed that requiring the participant to process both of the stimuli for at least a portion of the display time resulted in a partial misperception of the orientation of sidewalks. In Experiment 5, we sought to determine whether presenting the stimuli in alternation, so the stimuli were never present on the screen at the same time, would diminish the LTI-like misperception of orientation. Here, participants must monitor the orientation of each sidewalk (no cue was given to the identity of which sidewalk would be judged), but visually the sidewalks were never present at the same time. Here we would expect that LTI-like misperceptions of orientation would be eliminated or minimized when the stimuli were not present at the same time.

There were 16 participants after data validation procedures (see Table 1). The methods were the same as those given in the General Method with the following changes: The display and picture configurations were the same as described in the General Method, except the no picture control condition was not used and the pictures were not displayed on screen at the same time. One picture was shown for 0.75 seconds, then the other picture was shown for 0.75 seconds. This sequence repeated once for a total display time of 3 seconds (see Figure 8). A fourth practice session with four trials was added. For this fourth practice session, participants were told that the two pictures would never appear on the screen at the same time, and instead would alternate. However, the participant’s task was still to judge the orientation of a sidewalk in one of the pictures. Note that which picture (left or right location) was presented first in the alternation sequence varied randomly across trials. All trials in the main experiment were the same as the trials in the fourth practice session. In the parallel judgment task after the main experiment, displays alternated as they did in the main experiment (see Figure 8). Participants task was the same as the parallel judgment tasks in previous experiments, to indicate on a 1–5 scale (1 = perfectly parallel and 5 = not parallel) how parallel the sidewalks appeared to be.

Figure 8.

Main experiment trials for Experiment 5.

Results

Given that there was only one control condition, data were validated and analyzed as described in Experiment 4. Table 7 gives the exact values of the deviations from the control condition, and these measurements were used as the dependent variable in a three-way repeated measures ANOVA.

Table 7.

Experiment 5 Results Given as Left Side Misperception/Right Side Misperception (Average Parallel Judgement).

Right side sidewalk stimulus	Left side sidewalk stimulus
Right side sidewalk stimulus	Left \	Straight \|	Right /
Left \	\ \ 2.4°/1.3° (2.19)	\| \ –0.2°/2.3° (2.31)	/ \ –5.0°/0.9° (2.34)
Straight \|	\ \| 2.3°/0.4° (3.91)	\| \| –2.3°/1.2° (2.06)	/ \| –3.3°/1.3° (2.66)
Right /	\ / –1.5°/–3.0° (4.97)	\| / –0.7°/–4.7° (4.47)	/ / –0.5°/–2.3° (2.19)

Note. Negative values indicate an anti-clockwise difference score. For parallel judgments, 1 = perfectly parallel and 5 = not parallel.

There was a significant main effect of the stimulus in the right location, F(1.826, 27.386) = 8.807, p = .001, η_p² = .370. When the sidewalk picture in the right location was the right sidewalk, the deviation was more in the anti-clockwise direction (M = –2.121) than when it was the left sidewalk (M = 0.262, p = .012) or the straight sidewalk (M = 0.056, p = .006). There were no other significant main effects (all p > .1).

There was a significant interaction between location and the sidewalk picture in the left location, F(1.850, 27.751) = 5.560, p = .011, η_p² = .270, and between the location and the sidewalk picture in the right location, F(1.105, 16.577) = 10.944, p = .004, η_p² = .422. There was also a significant interaction between the sidewalk picture in the left location and the sidewalk picture in the right location, F(2.789, 41.831) = 4.371, p = .011, η_p² = .226.

There was a significant three-way interaction between screen location, the sidewalk picture in the left location, and the sidewalk picture in the right location, F(3.218, 48.264) = 3.309, p = .025, η_p² = .181. In the analysis before cases were dropped, the three-way interaction was not significant. Table 7 shows the data organized by what the left stimulus and right stimulus were. When the left stimulus was the right sidewalk, it was judged as rotated more anticlockwise (M = –2.913) than in the control condition. When the right stimulus was the left sidewalk, it was judged as rotated more clockwise (M = 1.471) than in the control condition. Table 7 shows that in general, any misperception is smaller than in Experiment 1, and in most cases limited primarily to the sidewalk in the left stimulus location.

Similar to Experiment 1, the parallel judgment data that were analyzed using a two-way repeated measures ANOVA, with parallelism judgments as the dependent variable and which sidewalk pictures were in the left and right positions as the independent variables. There was a significant main effect of the sidewalk picture in the left position on the parallel judgment, F(1.528, 22.923) = 53.320, p < .001, η_p² = .780, and there was a main effect of the sidewalk picture in the right position on the parallel judgment, F(1.791, 26.871) = 82.054, p < .001, η_p² = .845.

There was a significant interaction between the sidewalk picture in the left position and the sidewalk picture in the right position, F(1.816, 27.244) = 14.154, p < .001, η_p² = .485. Table 7 shows these results in the parentheses within the table. Note that a careful comparison to the parallel judgments from Experiment 1 (Table 2) shows that the pattern of results with alternating stimuli is distinctly different, with many more of the stimulus pairings appearing somewhat parallel, but no stimulus pairing appearing clearly parallel (no parallel judgments were less than 2 in Table 7). It may be the case that alternating the stimuli allowed the participants to more easily identify that the stimuli in the left–left, straight–straight, and right–right conditions were actually the same and adjusted their parallel judgments to reflect this perception. This also may explain the changes in the orientation judgments described above.

Discussion

Having the displays alternate so they are never present at the same time reduces the misperception of the orientation of the sidewalks. Alternating the displays also influences judgments of how parallel the sidewalks appear. This indicates that alternating displays disrupts the integration of the images of the sidewalks, perhaps introducing uncertainty about the orientation of the sidewalks resulting in more similar judgments of how parallel the sidewalks are over a variety of stimulus pairings. In turn, this may also influence the orientation judgments. Furthermore, our stimuli alternated with no blank period between them, so visual persistence (see, for example, Bowen et al., 1974; Farrell et al., 1990) may allow the stimuli to interact even though not technically present simultaneously. Varying the time each stimulus is present as well as introducing a blank period between stimuli may provide insights into the important factors in how the LTI-like misperception of orientation is modified by alternating the displays.

General Discussion

When presenting multiple pictures with sidewalk-based perspective cues, there is a consistent pattern of misperception of the orientation of those sidewalks. In many cases, the far (top) portion of the sidewalks are perceived as rotated away from each other in orientation. In a few other cases, the far (top portion) of the sidewalk are rotated in the same direction, but the magnitude of the rotations are such that the sidewalk orientations overall appear more different than they actually are (see Tables 2, 6, and 7 representing the conditions where the LTI-like effect is present or partially present). The pattern is somewhat present in Table 3 as well, but now the “far” portion of the sidewalk is at the bottom because the stimuli have been inverted. The consistency of the effect across experiments suggest that the method of measuring the perceived orientation of the sidewalks is reliable. Finding the expected differences (based on Osa et al., 2011) in the control condition results for sidewalks in three-dimensional space (Experiments 1) and for lines in two-dimensional space (Experiment 2) suggest that the method of measuring the perceived orientation of the sidewalks is valid. Recall that actually parallel lines were perceived as most parallel in Experiment 2, but sidewalks that converged in the distance were judged most parallel in Experiment 1. This difference in judgments of how parallel the stimuli were further supports the interpretation that the misperception in control conditions was due to three-dimensional versus two-dimensional interpretations of the stimuli.

Judgments of how parallel the sidewalks (or lines) were proved useful in verifying conditions where the LTI effect occurred. For example, when actually parallel sidewalks were judged to be parallel (see the middle cell of Tables 3 and 7), their orientations were not misperceived (or the misperception was minimized). However, when sidewalks that were not parallel were judged to be parallel (see the upper right cell of Tables 2 and 6), their orientations were misperceived.

The results presented here are also somewhat surprising given that they show that the traditional LTI with the same image presented side-by-side represents only a moderately sized misperception of orientation that can occur when presenting multiple pictures containing perspective lines. Specifically, when the sidewalks most clearly recede in the distance towards a common point (recede to right in the left location and recede to left in the right location), the misperception of orientation is greater than in a traditional LTI displays (compare the upper right corners of Tables 2, 3, 6, and 7 with the data in the upper left, middle, and lower right of each table). As discussed earlier, the LTI effect is easier to appreciate given that the observer knows that the two images are actually the same, but appear different. In the condition represented in the upper right portion of the tables, the observer may be misperceiving the orientation of the sidewalks by nearly twice the amount as in the traditional LTI effect, but there is no way for the observer to be aware of this misperception in a phenomenological sense.

Parovel and Costall (2018) showed that once the images are too far apart in a LTI display, the images are perceived as two separate images and no LTI occurs. In Experiments 3 through 5, we showed other factors can influence LTI effects. When attention can be focused solely on one of the images (because of a cue that indicates which image will be judged), the LTI effect is eliminated (Experiment 3, Table 5). This shows that the LTI effect is not an inevitable result of the presence of the other image; attentive processing of that image is necessary for the LTI. Even with the image to be judged cued, the LTI effect can be partially reintroduced by requiring the observer to make a judgment of how parallel the sidewalks are during the initial presentation of the images (Experiment 4, Table 6). Requiring processing of both stimuli for at least a portion of the observation period is sufficient to create the LTI effect. Alternating presentation of the images also reduced the LTI effect (Experiment 5). Taken together, there are several factors that influence the strength of the LTI effect based on how much the stimuli are visually integrated: attention (Experiments 3 and 4), alternating presentation of stimuli (Experiment 5), and distance between images when presented to the observer (Parovel & Costall, 2018).

Parovel and Costall (2018) also show that increasing the peripheral position (obliqueness) increases the LTI effect. Our results show a more a complicated interpretation of obliqueness may be necessary. Across experiments that resulted in at least a partial LTI effect (see Tables 2, 3, 6, and 7), the condition in the upper right of the tables (sidewalks receding towards each other) resulted in the largest misperception of orientation, with the orientations appearing more parallel than they actually are. These are in fact stimuli (receding left and receding right) that have the largest obliqueness. However, presenting two sidewalks receding to the left or two sidewalks receding to the right also have equally large obliqueness. In this case though, the misperception of orientation is much smaller, with the orientations appearing less parallel (somewhat diverging) than they actually are. Finally, presenting sidewalks that recede straight (no obliqueness) results in the second largest misperception of orientation, with the orientations again appearing less parallel (somewhat diverging) than they actually are. Therefore, when keeping other factors constant (e.g., distance between the presented images), obliqueness does not appear to be the only explanation of the magnitude of the LTI effect. The resulting overall perception of how parallel the sidewalks are may influence the perception of the orientation (in the current studies). One notable difference of our data is that they were collected in the context of more possible combinations of stimulus conditions (rather than just always presenting the same images side-by-side). This may have resulted in more uncertainty about the “correct” orientation of any of the pictures presented, although it remains unclear why this particular pattern of results was obtained.

It is worth noting too that for the receding straight—receding straight and the receding right—receding left conditions, each orientation is misperceived so the far end appears repelled away from the other orientation. However, in receding right—receding right or receding left—receding left conditions the orientations are misperceived such that each is either more clockwise (receding right—receding right) or anti-clockwise (receding left—receding left) than actual. Despite this, the magnitude of the misperception is such that the orientations are still perceived to be more different than they actually are. These results, where orientations of replicated oblique sidewalks are misperceived in the same way are difficult to account for in terms of a new point of observation (Parovel & Costall, 2018) which would predict shifts in the opposite direction as seen in our receding straight—receding straight condition. An explanation based on convergence vectors (Hiris, 2019) does not explain the result either, as it makes the same general predictions as a shift in the observation point.

Participants could potentially use three spaces when making judgments of the orientation of perspective lines: the two-dimensional plane of the picture on the computer screen, the three-dimensional space that created the picture, and/or the three-dimensional space perceived in the picture by the observer. Our data do not definitively address which of these spaces the participants were using in making their judgments. However, Experiments 1 and 2 indicate that in pictures with perspective lines, the two-dimensional plane of the picture on the computer screen was not being used. Regardless of which space was being used, presenting a second picture with perspective lines clearly influenced the judgments. These data do not necessarily imply that participants had access to the retinal image, that is, proximal perception (for a discussion of such issues, see Todorović, 2002). Future research could address what space was being used by participants when making judgments and how this might explain LTI-like illusions.

The data reported here have clear orientation anisotropies (Jenkins, 1985; Saarinen & Levi, 1995), where the receding straight conditions always has the lowest standard error of the mean of any of the conditions (see Figure 5 and Supplemental Figures 1 and 2). Despite this, orientation anisotropies cannot easily explain the overall pattern of results given that oblique orientations are sometimes more misperceived (receding right—receding left) than receding straight—receding straight and sometimes less misperceived (receding right—receding right or receding left—receding left).

We have shown that the LTI effect applies to perspective stimuli in general, not just to the same image placed side-by-side (see also, Hiris, 2019). We have also shown that it is possible to quantify the magnitude of the illusion in various combinations of images with perspective stimuli after taking into account the influence of three-dimensional space on orientation judgments in general (see Osa et al., 2011). These data can be used to rule out some explanations of how people integrate perspective across multiple pictures (e.g., a new observation point, convergence vectors) and could be used to inform models of perspective space (Erkelens, 2017). It may also be fruitful to investigate the relationship of the current findings to individual differences in perception of how parallel objects appear (Hiris, 2019) and the individual differences in the distance required for images to be no longer visually integrated (Parovel & Costall, 2018).

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Eric Hiris

Supplemental Material

Supplemental material for this article is available online.

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