1. Introduction

The capacity of pictures to convey spatial aspects of real environments means that they can be used for planning navigation in environments before visiting them in person. Misapprehension of egocentric distances in pictured scenes (i.e., between the observer and objects pictured in the scenes) can lead to navigational errors, poor use of resources, and other negative consequences when used for this purpose. Understanding the factors that impact distance judgments in pictures thus has practical importance, in addition to the knowledge that pictures can provide about distance processing in humans more generally. Such knowledge can also improve computational vision models that aim to reconstruct 3D image properties from pictured scenes [1].

Viewers are seldom in exactly the right position relative to a photograph or picture of a scene to receive the kind of retinal stimulation that one would obtain if actually situated in the pictured environment [2–4]. Nevertheless, one can often get a compelling sense of objects in the scene appearing at different distances. The behavioral literature has often focused on issues such as the effect that viewing a picture at an angle has on shape perception [5–10]. Although relatively few studies have asked observers to judge the distance from themselves to objects in the depicted scenes, this literature has focused on issues such as the effect of camera focal length [11, 12], the effect of moving the observer closer or farther from the picture [13, 14], and the relative angular sizes of objects in the depicted scene [11, 15]. Increasing focal length is associated with not only decreased visible context but also perceptual flattening in the depth dimension [12, 16]. To some extent, changes in the size and shape of the pictured setting can mimic changes in camera focal length (e.g., smaller environments and long focal length pictures might both restrict the amount of visible context). The role of pictured environment size per se on judged distances is unclear, however, and this is the central focus of the experiments reported here.

Research on egocentric distance perception in real environments often focuses on the role of information specifying the distance to the target object itself, but there is general acknowledgement that non-target visual features can play a role in perceiving the distance of the target [17–21]. For example, for targets located beyond the effective range of primary distance cues, relative cues such as the texture gradient of the ground plane under the target can support judgments of the target distance if they are calibrated by egocentric distance information in the region close to the observer [22]. This is supported by evidence that disrupting the ground plane between the observer and the target systematically influences target distance judgments [17, 22, 23]. Beyond this, however, the role of other environmental features in egocentric distance judgments is poorly understood. Of particular relevance to the current work, there is some evidence that the size or shape of the environment can impact judgments of real-world egocentric distance [18, 20]. Quantifying this effect is both a conceptual and a methodological challenge, in that large changes in the size or shape of an environment—pictured or real—can potentially impact a host of known cues (e.g., the amount of visible ground plane texture, the availability of perspective cues, the proximity of nearby objects, the visibility of the boundaries of the environment, etc.).

In the following experiments, our approach was to study the impact of environment size and shape on distance judgments by creating computer-rendered indoor scenes of various sizes and shapes. We used crowdsourced data collection (Amazon’s Mechanical Turk, or MTurk) to collect distance judgments to traffic cone targets depicted in the scenes. Given that absolute accuracy in egocentric distance judgments within pictured scenes can vary dramatically with camera focal length [16, 24], in the experiments described below, we held focal length constant so as to focus on the role of environment size and shape. Although we will make note of the overall response accuracy when describing our results, our primary attention here is on how responses under one environmental setting compare to those in other settings, rather than how accurate they are compared to the depicted target distances. One way to characterize distance judgments is by considering both response sensitivity, or the degree to which responses increase as the depicted distance increases, and bias, or the central tendency across all responses. Response sensitivity may be thought of as the slope of the function relating the judged distance versus the depicted distance, with bias indicating the degree to which that function is shifted up or down along the vertical (response) axis. We will consider both of these aspects of performance in describing the results.

Given the known effects of image truncation and field of view in both pictured and real-world environments [12, 15, 25–28], we predicted that the size and shape manipulations would elicit systematic differences in distance judgments even when camera focal length was held constant. We found that narrow environments resulted in shorter distance judgments than wider settings. In subsequent experiments, we manipulated a variety of environmental features, including not only relatively nearby, local cues, but also more global changes in the farther reaches of the environments, in an attempt to constrain as much as possible the source of these context effects.

2. Experiment 1

Pictured scenes typically involve some truncation of the scene imposed by the image boundaries [28]. Increasing focal length increases this truncation, and indeed increases in both truncation and focal length are associated with decreases in distance judgments [12, 15, 28]. Similarly, limiting the field of view, even in real-world environments, can result in decreased distance judgments [25–27]. When judging distances, there may be a functional similarity between the effect of occluding parts of the environment with a visible wall (as in a small environment) and eliminating parts of the image entirely by reducing the field of view or truncating the image. If so, this predicts that smaller environments might be associated with smaller distance judgments, even when field of view is held constant. A central focus in Experiment 1 was to characterize the influence of the size and shape of the environment on distance judgments in pictured scenes, under conditions in which field of view and image truncation were held constant.

In Experiment 1, we parametrically manipulated the size and shape of environments by varying the depth (6, 10, and 40 m) and width (1.5, 5, 10, and 40 m) of simple indoor scenes. With no firm theoretical or empirical guide for choosing specific values, these values were chosen to yield a range of values on each dimension, with some oversampling of smaller values within the respective ranges. Although the specific values were chosen more by eye than by theory, we suspected that the sensitivity of distance judgments to depth and width manipulations might be greater for smaller values than for larger values, as is often the case in egocentric distance judgments when environmental context is held constant [29]. Fig 1 shows examples of four of the twelve possible combinations of these room widths and depths (Fig 1). These manipulations affect a variety of individual cues (e.g., the area of the visible ground plane, the availability of linear perspective, the visibility of nearer or farther reaches of the environment, and the proximity and visual density of environmental features to the target object). Critically, however, these manipulations did not affect the angular declination of the targets across conditions, nor any image features directly between the camera perspective and the targets themselves. This study served as a starting point for investigations targeting more specific cues in subsequent experiments.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Experiment 1 stimuli examples.

Depicted target distance = 4.8 m. (a) 1.5 m width, 6 m depth. (b) 5 m width, 10 m depth. (c) 10 m width, 10 m depth. (d) 40 m width, 40 m depth.

https://doi.org/10.1371/journal.pone.0263497.g001

When using crowdsourced data collection, the characteristics of the participants’ testing environment and the device used for testing are unknown. In real-world settings, even in an experiment involving rendered scenes on a computer, the characteristics of the testing computers are known and the setting is generally more well-controlled across participants. To test the generalizability of our crowdsourced data to more well-controlled settings, in Experiment 1 we compared data collected from a population of MTurk workers against a group of college students taking part in the study on a single computer in a well-controlled laboratory space. These groups differed along a number of dimensions (e.g., age, testing environment, and device used for testing), and although we had no a priori reasons to expect any of these differences to have a systematic impact on the data, this contrast allowed us to characterize any group differences that arose.

2.2 Results

Statistics for this and all following experiments were conducted using the R statistical language with RStudio software [35]. All responses made in feet were converted to meters prior to analysis. Outlier criteria for this and all studies described in this paper were set prior to analysis to remove any trials outside 2.5 standard deviations (SD) from the mean for each combination of room condition and distance, calculated across subjects. This criterion was set based on the overall distribution of data in this first experiment. It was set to exclude obvious errors in the written judgments (e.g, “4030” feet when a participant’s responses under similar conditions were 40 or 30 feet) without trimming any real variability in the responses. Once set, the criterion was held constant throughout all the other experiment datasets and was applied prior to any subsequent analysis or evaluation. If, after this initial removal, there were any participants with less than one-third of the total trials remaining for any one room condition, that participant’s data were removed from the final dataset. For the MTurk participants, 391 trials were removed (3.12% of data) and for the GW participants, 188 trials were removed (3.2% of data). One additional participant from the MTurk group and two additional participants from the GW students were removed for having less than one-third of trials remaining in any one condition after the 2.5 SD removal, leaving 107 MTurk participants and 49 GW participants for analysis.

The data were analyzed using linear mixed models via maximum likelihood variance estimation with Satterthwaite’s method for degrees of freedom correction. The Distance factor was not fully crossed with the Depth factor, as the larger distances could not be presented in rooms with a shorter depth. We analyzed data from the three Depth conditions in separate analyses, in which Width, Distance, and Group were set as fixed factors and Subject as a random factor for a repeated measures design. The interactions between Width, Distance, and Group were also included in the model.

Fig 2 plots the indicated distance over the actual distance for all Depth conditions separately (Fig 2), while Tables 1 and 2 show the analysis output (Tables 1 and 2). The coefficient estimates and standard errors for all conditions are included in S5–S7 Files. Fig 3 depicts the average distance judgments across each Depth and Width condition (Fig 3). There were main effects of Group, Width, and Distance and significant Width x Distance interactions in all three Depth analyses. No other interactions were reliable in these analyses except the Distance x Group interaction. Pairwise comparisons between the Width conditions for each Depth condition are listed in Table 3. The Width effects indicate reliable differences in bias as a function of room width, while the Width x Distance interactions indicate that Width-related differences become more pronounced with increasing distance (i.e., differences in response sensitivity).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Indicated distance as a function of rendered distances in each depth condition of Experiment 1.

(a) 6 m depth. (b) 10 m depth. (c) 40 m depth. (d) 10 m depth with only 2–4.8 m targets. (e) 40 m depth with only 2–4.8 m targets. Error bars denote +/- 1 standard error of the mean.

https://doi.org/10.1371/journal.pone.0263497.g002

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Average distance judgment for each width and depth condition in Experiment 1.

The average distance judgment for each combination of Width and Depth, including the 10 and 40 m depths with only 2–4.8 m targets. The dotted lines indicate the actual average target distance for each room depth. Error bars denote +/- 1 standard error of the mean.

https://doi.org/10.1371/journal.pone.0263497.g003

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Output for the depth conditions of 6 and 10 m for Experiment 1.

https://doi.org/10.1371/journal.pone.0263497.t001

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Output for the depth condition of 40 m for Experiment 1.

https://doi.org/10.1371/journal.pone.0263497.t002

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. Pairwise comparisons for Width for the 6, 10, and 40 m depth conditions.

https://doi.org/10.1371/journal.pone.0263497.t003

To provide a means of comparing across Depth conditions, we performed one additional linear mixed model analysis using only the distances that were common across all Depth conditions (2, 2.2, 2.8, 3.2. 4.2, and 4.8 m). We will refer to this as the Depth Comparison analysis. In effect, this tested the impact on distance judgments of extending the environment beyond the targets. Width, Depth, Distance, and Group were set as fixed factors and Subject as a random factor. The interactions between Width, Depth, Distance, and Group were also included in the model. This analysis showed main effects of Group, Depth and Distance, but no main effect of Width (Table 4). The coefficient estimates and standard errors for all conditions are included in S8 File. There were significant interactions of Depth x Width, Depth x Distance, Width x Distance, Distance x Group, and Depth x Width x Distance. We will discuss these findings in greater detail below.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 4. Output for all depth conditions for targets up to 4.8 m for Experiment 1.

https://doi.org/10.1371/journal.pone.0263497.t004

2.2.1 Effect of group.

To begin, there was a main effect of experiment group in all four analyses, with the MTurk group generally having higher distance estimates than the GW group. Across all trials, the average distance estimate for the Mturk group was 5.64 m (undershooting by 32.84% on average), while the average distance estimate of the GW group was 4.30 m (undershooting by 44.31% on average). Although additional research is required to understand the cause of this effect, the source could be due in part to systematic differences in participant characteristics [36, 37], viewing distance and/or display size [13, 15], or experimental setting. Nevertheless, no interactions involving the Group factor reached significance in any of the analyses except for the Distance x Group interactions. Given that there were no significant interactions between the Group, Width, and Depth factors in these analyses, the groups appeared to differ in terms of the overall calibration of their responses but not in terms of how they responded to variations in room depth and width.

2.2.2 Effect of room depth.

In the Depth Comparison analysis (comparing distances below 5 m across manipulations of room depth), there was a main effect of Depth (p < 0.001), with distance judgments in the 6 m depth condition generally being larger (averaging 1.89 m) than those in the 10 m and 40 m depth conditions (averaging 1.86 and 1.81 m respectively), collapsing over the GW and MTurk groups. Pairwise comparisons (two-tailed, alpha = .05 with a Holm correction) indicated that estimations in the 6 m and 40 m depths and in the 10 m and 40 m depths differed significantly (p < 0.001 and p = 0.010 respectively), though there were no differences between the 6 m and 10 m depth conditions (p = 0.156). Thus, the effect of extending the open space beyond the target primarily becomes apparent when there are relatively large differences in environment depth. Extending the environment depth beyond the target does not affect egocentric distance cues to the target itself, and though some work has investigated the role of relative distance cues between the observer and a target object on the perceived distance of the target itself [17, 38–40], the role of relative cues beyond the target is poorly understood. When binocular disparity is present, the disparity between the target and a more distant object can increase distance judgments, at least under reduced cue conditions when these are the only visible objects [41]. The effect seen here—shorter distance judgments in environments with more visible space beyond the target—is a similar pattern to what has been found before in more natural real-world environments using somewhat different methods [18, 20]. Although more work is required to explain this effect, our work here suggests that the effect itself is fairly small in pictured environments involving relatively short target distances.

2.2.3 Effect of room width.

For the 10 and 40 m room depth conditions, robust and unexpected effects of room Width were found, such that responses tended to increase with increasing room width, averaged over Group (Figs 2 and 3). In the 10 m room depth condition, responses averaged 2.89, 3.27, 3.40 and 3.60 m in the 1.5, 5, 10 and 40 m room width conditions, respectively; in the 40 m room depth condition, responses averaged 6.60, 7.18, 7.72 and 8.45 m in the 1.5, 5, 10 and 40 m room width conditions, respectively. The pairwise comparisons shown in Table 3 indicate that these increases in distance judgments as a function of room width were generally significant between the different levels of Width. In the 6 m room depth condition, the pattern differs somewhat. Although there was again a main effect of Width, here the narrowest room was associated with larger judgments: responses averaged 2.00, 1.80, 1.87 and 1.88 m in the 1.5, 5, 10 and 40 m room width conditions, respectively. Importantly, however, for the 6 m depth condition, the images of the 10 and 40 m wide rooms were indistinguishable for each target distance, as the walls and doors to the left and right were out of the frame and not visible. One would thus not expect width-related response differences in these conditions. In the Depth Comparison analysis, there was no main effect of Width, with responses averaging 1.83, 1.87, 1.85 and 1.85 m in the 1.5, 5, 10 and 40 m width conditions, respectively. Note that these means are somewhat different than in the 6 m depth condition analysis, because they incorporate judgments of the shorter distances from the 10 and 40 m room depth conditions. Although there was a significant Depth x Width interaction, this is difficult to interpret due to the indistinguishable images in the 10 and 40 m width rooms for the 6 m depth condition.

3. Experiment 2

Experiment 1 showed that wider environments resulted in larger distance judgments, but the cue bases for the effect remain unknown. Of the many features that differ between wide and narrow pictured environments, one goal of Experiment 2 was to test the role of linear perspective in producing the width effect. The linear perspective information was less strong in the wide environment in Experiment 1 than in the narrow environment, as both the walls and doors in the wide environment were displaced to the far periphery. Experiment 2 included two conditions to test the effect of linear perspective: 1) In the Linear Perspective Lines condition (Fig 4A), dark lines were added on the floor and ceiling of the Wide room to mark the location where the walls would appear in the Narrow room. Like the Wide rooms, this condition provided full view of the ground plane, the far environment boundaries, and the visible horizon, but with enhanced linear perspective. 2) In the Freestanding Doors condition (Fig 4B), the walls in the Narrow condition were removed, but the doors and linear perspective lines were retained. The doors enhanced the linear perspective information still further and yielded a condition that was well-matched to the Narrow condition in Experiment 1 in terms of the overall availability of linear perspective. The primary difference was that the Freestanding Doors condition provided more visibility of the ground plane, far environment boundaries and visible horizon than Experiment 1’s Narrow condition. If linear perspective plays a substantial role in producing the room width effect, we predicted that distance judgments in these conditions would be smaller and more similar to those obtained in the Narrow room than the Wide room. By contrast, if general visibility of the ground plane, environment boundaries and visible horizon play a role, both the Linear Perspective Lines and Freestanding Doors conditions should yield the larger distance judgments associated with the Wide room condition, because all these conditions provide visibility of those features (albeit with somewhat less visibility in the Freestanding Doors condition due to occlusion by the doors).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Example stimuli from Experiment 2.

Depicted target distance = 4.8 m. (a) Linear Perspective Lines. (b) Freestanding Doors. (c) Near Ground Occluded. (d) Far Ground Occluded. (e) Narrow (1.5 m width). (f) Wide (40 m width).

https://doi.org/10.1371/journal.pone.0263497.g004

A second goal of Experiment 2 was to contrast the visibility of the relatively nearby ground plane versus visibility of the farther reaches of the environment. There is evidence that in both real-world and pictured environments, disruption or occlusion of the nearby ground plane can reduce distance judgments [17, 38, 40]. These studies have generally disrupted the ground plane directly between the observation point and the target; narrow hallways leave this space unobstructed, although the walls do occlude vision of the more lateral regions of the nearby ground plane and this occlusion could play a role in producing the width effect. Another view is that visibility of more global features in the farther regions of the scene could play a role in producing the width effect. Image features associated with the overall scene context have been shown to support judgments that group scenes into broad “mean depth” categories—e.g., whether the scene takes up kilometers of space or only a few meters of space [47, 48]. Global image features, for example, those associated with the farthest spatial boundaries or the openness of the space, could influence egocentric distance judgments by calibrating the available relative distance cues. To contrast the role of near versus far image features, Experiment 2 included two conditions that selectively occluded portions of the pictured scenes. In the Near Ground Occluded condition (Fig 4C), the nearby portion of the room resembled the Narrow condition from Experiment 1, occluding the lateral portions of the nearby ground plane, while the farther reaches of the space were left open except for a narrow corridor of freestanding doors. In the Far Ground Occluded condition (Fig 4D), there was a narrow hallway in the farther reaches of the environment, thus occluding the farther ground plane and leaving the nearby ground plane open except for several freestanding doors. If visibility of near versus far regions of the space plays a role in producing the room width effect, we predicted that this would be manifested in the contrast between these two conditions, such that larger distance judgments would indicate the condition that provides visibility of the crucial part of the scene, with smaller distance judgments indicating the condition that occludes the crucial part of the scene.

3.2 Results

218 trials fell outside 2.5 SD from the mean for each combination of room condition and target and were removed (3% of data). One participant was removed because fewer than one-third of the trials remained in one or more conditions after 2.5 SD outlier removal, leaving 97 participants in the final analysis. Fig 5A plots the indicated distance over the actual distance for each combination of room condition and target distance and Fig 5B shows the average distance judgment for each condition (Fig 5). The judgments undershot the physical (rendered) distances by only 4.79% on average, which was less than the 32.84% undershooting for the MTurk participants in Experiment 1. Experiment 1 utilized somewhat larger images–a feature known to reduce distance judgments in pictures [14], so this may play a role in explaining the calibration differences between experiments. Although we will comment on calibration differences across studies when appropriate, a full exploration of these differences is beyond the scope of the current paper.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Data from Experiment 2.

Error bars denote +/- 1 standard error of the mean. (a) Plot of the indicated distance over the actual distance for all conditions. (b) Average distance judgment for each room condition. The dotted line indicates the actual average target distance. Images on the x-axis depict the room width conditions from Fig 4.

https://doi.org/10.1371/journal.pone.0263497.g005

The data were analyzed using linear mixed models via maximum likelihood variance estimation with Satterthwaite’s method for degrees of freedom correction. Room and Distance were set as fixed factors with Subject as a random factor for a repeated measures design. The interactions between Room and Distance were also included in the model. The results indicated a main effect of Room (F[5,6705.0] = 9.15, p < 0.001, η_p² < 0.01), a main effect of Distance (F[11,6705.3] = 425.55, p < 0.001, η_p² = 0.41), and a significant Room x Distance interaction (F[55,6705.0] = 1.72, p < 0.001, η_p² = 0.01). Here, the main effect of Room indicates significant differences in the response bias for each room condition, and the Room x Distance interaction represents significant differences in response sensitivity, or the slopes of the functions relating estimated to actual target distance. Pairwise comparisons (at alpha = 0.05 with a Holm correction) showed significant differences in bias between the Wide room and all other rooms except Linear Perspective, which was also significantly different from all other rooms (Table 5). The coefficient estimates and standard errors for all conditions are included in S9 File.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 5. Pairwise comparisons and absolute mean differences for Experiment 2.

https://doi.org/10.1371/journal.pone.0263497.t005

4. Experiment 3

In Experiment 2, the Near- and Far Ground Occluded conditions, as well as the Freestanding Door condition, yielded a pattern of smaller distance judgments that is characteristic of the Narrow environments. The relative role of occluding near versus far regions of the environment, however, is difficult to determine from the results of Experiment 2, because both of these conditions contained doors, either freestanding in regions where the ground was otherwise visible, or embedded in walls. The freestanding doors by themselves were sufficient to produce the Narrow pattern in Experiment 2, so that study leaves unsolved the question of whether the width effect comes more from features specific to the doors, or whether occlusion of the environment (possibly restricted to near or far regions) drives the effect. We have already discussed reasons why occlusion could be a contributing factor. Doors, however, could play a distinct role by way of providing a richer cue environment: they enhance linear perspective and texture gradients, they provide reference objects in the vicinity of the target, and they are familiar-sized objects that could be used to provide a sense of scale. If the width effect disappears when the doors are removed, this would help constrain the search for cue bases of the width effect. Experiment 3 addressed this issue by removing the doors in all conditions. It included trials based on the Wide and Narrow conditions from Experiments 1 and 2, but without doors. Given that these experiments showed robust differences between the Wide and Narrow conditions, there is good reason to expect a similar effect here.

To further assess the role of occluding parts of the environment on the room width effect, Experiment 3 manipulated occlusion in four additional conditions: 1) a Near Ground Occluded condition that matched the condition from Experiment 2; 2) a close-range Far Ground Occluded condition that matched the condition from Experiment 2; 3) an intermediate Far Ground Occluded condition that occluded the mid-range of the environment and beyond; and 4) a farther Far Ground Occluded condition that occluded only the farthest range of the environment. One possible outcome is that when the doors are removed, responses are similar across all tested conditions. This would clearly implicate features associated with the doors in producing the width effect and would rule out explanations associated with occluding different parts of the environment. Another possibility is that, in the absence of doors, the Narrow pattern of responses is elicited when only the nearby environment or only the far environment is occluded. This kind of outcome would be informative about which region plays a role in the width effect.

Regarding the 3 levels of occlusion of the farther portions of the environment, one might predict a graded response, such that as progressively more of the far environment is occluded, responses increasingly resemble the Narrow pattern. Although perhaps less diagnostic from the perspective of specifying what visual features are responsible for the width effect, such a result would confirm that the presence of doors is not required to elicit the Narrow pattern and that the effect is driven by some feature that varies in conjunction with occlusion of the farther environment. Another possible outcome is that the Narrow pattern is elicited in all three Far Occlusion conditions. This would be striking, given the very salient differences in the appearance of these settings and the visual similarity between the farthest Far Occlusion condition and the Wide condition images. Such a result would focus attention on aspects that these three conditions hold in common with the Narrow room images. We will return to this question in the Experiment 3 discussion.

4.1. Method

4.1.1 Participants.

Participants consisted of 101 Master MTurk Workers. Participants here were paid $2.50 in exchange for their participation. This experiment was conducted at a time when other studies were in progress in the laboratory, and the current study was posted at the compensation rate for those slightly longer experiments. The difference in compensation compared to the other studies in this article is likely to be of little consequence, however.

4.1.2 Stimuli and design.

All stimuli were rendered with a room depth of 40 m and the same 12 target distances as Experiment 2. Images were 500 x 375 pixels. In contrast to the previous two experiments, no doors were included in any of the stimulus scenes. Six conditions were used in Experiment 3, as depicted in Fig 6: 1) Narrow (1.5 m width) (Fig 6A); 2) Near Ground Occluded, with narrow walls separated laterally by 1.5 m and extending 2.0 m into the room from the camera position (Fig 6B); 3) Far Ground Occluded-Close, with walls beginning 5 meters into the room and extending laterally, leaving a 1.5 m hallway beyond (Fig 6C); 4) Far Ground Occluded-Mid, with walls beginning 11 meters into the room and extending laterally, leaving a 1.5 m hallway beyond (Fig 6D); 5) Far Ground Occluded-Far, with walls beginning 23 meters into the room and extending laterally, leaving a 1.5 m hallway beyond (Fig 6E); and 6) Wide (40 m width) (Fig 6F). The Narrow, Near Ground Occluded, Far Ground Occluded-Close, and Wide conditions were the same as in Experiment 2, except with no doors. All stimulus conditions and target distances were randomized within participants for a total of 72 trials.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 6. Example stimuli from Experiment 3.

Depicted target distance = 4.8 m. (a) Narrow. (b) Near Ground Occluded. (c) Far Ground Occluded–Close. (d) Far Ground Occluded–Mid. (e) Far Ground Occluded–Far. (f) Wide.

https://doi.org/10.1371/journal.pone.0263497.g006

4.1.3 Procedure.

The study was executed as described in Experiment 1.

4.2 Results

Prior to outlier removal, two participants were removed from the dataset because they gave the same number for every trial. Of the remaining 99 participants, 209 trials fell outside 2.5 SD from the mean for each combination of room condition and target and were removed (2.93% of data). One additional participant was removed for having less than one-third of the trials remaining in one or more condition after the 2.5 SD removal, leaving 98 participants in the final analysis.

Fig 7A plots the indicated distance over the actual distance for each combination of room condition and distance and Fig 7B shows the average distance judgment for each condition (Fig 7). In this study, the judgments undershot the physical (rendered) distances by 13.28% on average. The data were analyzed using linear mixed models via maximum likelihood variance estimation, with Satterthwaite’s method for degrees of freedom correction. Room and Distance were set as fixed factors and Subject as a random factor for a repeated measures design. The interactions between Room and Distance were also included in the model. The results indicated a significant main effect of Room (F[5,6796.6] = 13.28, p < 0.001, η_p² = 0.01), a significant main effect of Distance (F[11,6796.7] = 499.33, p < 0.001, η_p² = 0.45), and a significant Room x Distance interaction (F[55,6796.5] = 2.94, p < 0.001, η_p² = 0.02), mirroring the results from Experiment 2. Pairwise comparisons (at alpha = 0.05 with a Holm correction) showed significant differences in response bias between Wide and all other room conditions. No other comparisons were significantly different (Table 6). The coefficient estimates and standard errors for all conditions are included in S10 File.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 7. Data from Experiment 3.

Error bars denote +/- 1 standard error of the mean. (a) Plot of the indicated distance over the actual distance for all conditions. (b) Average distance judgment for each room condition. The dotted line indicates the actual average target distance. Images on the x-axis depict the room width conditions from Fig 6.

https://doi.org/10.1371/journal.pone.0263497.g007

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 6. Pairwise comparisons and absolute mean differences for Experiment 3.

https://doi.org/10.1371/journal.pone.0263497.t006

5. Experiment 4

Experiment 3 suggested that the presence of objects (walls) in the vicinity of the target locations plays a strong role in eliciting the shorter distance judgments characteristic of Narrow settings. That study manipulated the location of walls near the targets in the three Far Occlusion conditions and found that all three conditions yielded judgments that resembled the Narrow response pattern. The Far Occlusion conditions, however, not only placed objects (walls) in the vicinity of the target locations, but also occluded parts of the farther environment, including the far ground plane and large portions of the farthest wall of the rooms. One aim of Experiment 4 was to test the unique role of objects near the farther target locations under conditions of minimal ground plane occlusion.

In Experiment 4, we included doors in all conditions, as these are objects that do not occlude large portions of the environment, particularly when they appear in the farther regions. We contrasted a condition in which the doors appeared only in the foreground (Near Doors) against a condition in which there were freestanding doors only in the farther regions of the space (Far Doors). For comparison, a full Freestanding Doors condition included freestanding doors along the full length of the space.

A fourth condition in Experiment 4 used the wide room, but with all ground plane texture removed (No Ground Texture). If various degrees of occlusion of the ground plane texture was responsible for the decreased distance judgments (whether due to the presence of doors or walls), removing the ground texture entirely should yield decreased judgments even in the wide-room environment. Two other conditions included the standard Narrow and Wide rooms with doors, yielding 6 total conditions.

5.1. Method

5.1.1 Participants.

Participants consisted of 101 Master MTurk Workers. Participants here were paid $1.75.

5.1.2 Stimuli and design.

All stimuli were rendered with a room depth of 40 m and the same 12 target distances from Experiments 2 and 3. Images were 500 x 375 pixels. Three conditions manipulated the location of the doors and consequently tested the visible objects and boundaries in proximity to the target: 1) Near Doors (Fig 8A); this condition included two doors in the immediate foreground separated laterally by 1.5 m. These doors were embedded in walls in the same locations as the walls in the Near Ground Occluded conditions of Experiments 2 and 3, although here, only a thin sliver of the walls themselves was visible outside of the doors. In these locations, the doors did occlude some of the nearby ground plane but provided a salient connection to the doors in the Freestanding Door and Far Door conditions. 2) Freestanding Doors along the boundary of a narrow hallway extending the full depth of the room (Fig 8B); and 3) Far Doors, which included freestanding doors along the boundary of a narrow hallway just near the far targets (Fig 8C). A No Ground Texture (Fig 8D) condition was also included, which removed visible ground texture from the Wide room condition. The Wide (40 m wide room) and Narrow (1.5 m wide) rooms from the previous experiments were also included. All stimuli conditions and target distances were randomized within participants for a total of 72 trials.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 8. Example stimuli from Experiment 4.

Depicted target distance = 4.8 m. (a) Near Doors. (b) Freestanding Doors. (c) Far Doors. (d) No Ground Texture. Not pictured: Narrow and Wide conditions, which were the same stimuli as in Experiment 2.

https://doi.org/10.1371/journal.pone.0263497.g008

5.1.3 Procedure.

This study was conducted as described in the previous experiments.

5.2 Results

192 trials fell outside 2.5 SD from the mean for each combination of room condition and target and were removed (2.64% of data). No participants were removed for having less than one-third of the trials remaining in any one condition, and all 101 participants were included in the final analysis. Fig 9A plots the indicated distance over the actual distance for each combination of room condition and distance and Fig 9B shows the average distance judgment for each condition (Fig 9). Contrary to the previous studies, the judgments overshot the physical (rendered) distances, but only by 0.27% on average.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 9. Data from Experiment 4.

Error bars denote +/- 1 standard error of the mean. (a) Plot of the indicated distance over the actual distance for all conditions. (b) Average distance judgment for each room condition. The dotted line indicates the actual average target distance. Images on the x-axis depict the room width conditions from Fig 8.

https://doi.org/10.1371/journal.pone.0263497.g009

As in the previous two experiments, the data were analyzed using linear mixed models via maximum likelihood variance estimation, with Satterthwaite’s method for degrees of freedom correction. Room and Distance were set as fixed factors and Subject as a random factor for a repeated measures design. The interactions between Room and Distance were also included in the model. Replicating the results of Experiments 2 and 3, the results indicated a main effect of Room (F[5,6979.0] = 20.51, p < 0.001, η_p² = 0.01), a main effect of Distance (F[11,6979.3] = 584.10, p < 0.001, η_p² = 0.48), and a significant Room x Distance interaction (F[55,6979.1] = 3.35, p < 0.001, η_p² = 0.03). Pairwise comparisons (at alpha = 0.05 with a Holm correction) are listed in Table 7 (Table 7). The coefficient estimates and standard errors for all conditions are included in S11 File.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 7. Pairwise comparisons and absolute mean differences for Experiment 4.

https://doi.org/10.1371/journal.pone.0263497.t007

6. General discussion

Across 4 experiments involving 452 participants judging targets at distances up to 37 m, we have shown that as deep indoor spaces become wider, targets are judged as farther away. Average judgments for the farthest targets in a 40 m wide room were between 16–33% larger than for the same target distances seen in a 1.5 m hallway. The room width effect holds even when cues to the egocentric distance of the target are held constant, highlighting the importance of more peripheral contextual information. Further, obscuring the fine-grained ground plane texture is not primarily responsible for this effect.

At a broad level, the presence of occlusion in the scene seems to be driving the width effect. Occlusion within the nearby environment elicits the Narrow pattern, even when the farther reaches of the environment remain visible; likewise, occlusion within the far environment elicits the Narrow pattern, even when the nearby regions remain visible. Consistent with this view, the Freestanding Doors conditions involved substantial occlusion by the nearby doors, even though portions of the nearby and farther reaches remained visible, and accordingly yielded the Narrow response pattern. In sum, we have attempted to separately assess several environmental features associated with occlusion, and to this point, shorter distance judgments seem to be elicited when relatively large regions of the environment are rendered less visible by objects.

Egocentric distance information available from the nearby ground plane can be used as a reference for scaling relative distance cues in real-world environments [17, 40, 49–51]. When viewing pictures, this role is likely diminished, not only because the nearby ground plane is truncated by the border of the picture itself, but also because many of the egocentric distance cues available when viewing a picture provide a signal that the image is flat. Earlier, we suggested that observers might rely on more global scene information to scale relative distance cues, e.g., information that specifies the overall depth of the environment [47]. This predicts that manipulation of features even in the farther regions of space (outside the nearby ground plane) can influence egocentric judgments, and this is exactly what we have found. In particular, our work has shown that the presence of walls in the farther reaches of the environment centered in the image is associated with shorter distance judgments. Importantly, this global image feature mechanism need not be mutually exclusive with the nearby ground plane reference mechanism [50]. Indeed, we assume that when egocentric distance cues are abundant and highly reliable (e. g., in real environments, within 6 m of the observer and with binocular vision), the visual system likely relies heavily on these cues to scale the relative distance cues.

The visual information underlying extraction of mean depth in pictured scenes remains poorly understood, but a variety of global image features no doubt plays a role (e.g., features associated with openness and ruggedness) [52, 53]. Indeed, so many environmental features covary with the size and shape of the setting that Sedgwick and Gillam [54] have suggested that perception of the spatial aspects of pictured scenes may transcend a modular, cue-based understanding (See also Gibson [49]).

Although we did not attempt to measure this directly, it is possible that the perceived slant of the ground plane varied in correlation with the distance judgments, such that when distances were systematically judged to be smaller, the ground plane slant was perceived to be tilted upwards toward the far end of the scene. This could be an alternate explanation of the width effects, if changes in the perceived ground slant were the causative mechanism rather than direct changes in mean depth. It is not obvious how some of our manipulations that influenced distance judgments may have impacted perceived ground slant (e.g., isolated doors in the intermediate-to-far distances). Nevertheless, if the perceived spatial layout were globally rescaled toward smaller distances, resulting in a smaller mean depth, the ground plane should appear tilted, assuming that the perceived eye height and angular directions remained otherwise constant [50]. Thus, mean depth and perceived ground slant are likely to be linked, but future research is required to determine if there is a direction of causality in this linkage.

Distance judgments made in real-world indoor settings are sometimes larger than those of the same physical distances in outdoor settings [18, 19, 55, 56]. Although it is plausible that the constellation of egocentric and exocentric distance cues available in indoor environments is generally enriched relative to outdoor settings, the cue bases of this result are not known, so it is not clear whether environment size or shape play a role. Our results with pictured scenes indicate that narrower settings are associated with smaller distance judgments than wider environments. There are many differences between viewing pictures of scenes and directly viewing the scenes while being immersed in them, as authors have frequently noted [2, 4, 11, 28, 57–60]. More research is required to determine the extent to which the current results involving pictured stimuli might generalize to real-world contexts. Manipulating the width of large, real environments presents considerable logistical challenges. Virtual environments would provide a convenient means of exploring these issues, as virtual environments afford fine-grained control over the size, shape and contents of the setting and allow the observer to be more fully immersed in the scene. Nevertheless, our results indicate a robust effect of environment width on egocentric distance judgments in pictured settings. Given the wide variety of electronic devices available and the prevalence of pictured scenes in electronic content, this result has broad applicability for understanding how humans process spatial relationships in pictures.

Supporting information