Factors influencing estimation of distances and traveled distances in real and virtual environments

Overall problem

Overall in action space (approximately 2-30m [link]), people underestimate distance in virtual environments relative to real world, where they are fairly accurate. The factors contributing to distance underestimation may include the display technology, field of view, stereopsis and parallax, the visual targets and settings, the fidelity of the visual virtual model, the range of distances examined, and the experimental methods.

Distance estimation in real environments

A lot of work has been done investigating distance estimation in real environments.

Gilinsky [link] created a formula to compute perceived distances using the method of equally apparent intervals. In this experiment, participants were asked to mark successive increments of equal perceived length, which were supposed to be one foot long. Because physical intervals needed to be larger and larger to match with the same perceived length as the increments went father and father from participants, there should be a strongly negative relation between perceived distances and physical distances. From the data of two participants, Gilinsky found that the desired function had a hyperbolic form d = D x A / (D + A), where d is the perceived distance, D is the physical distance, and A is the maximum limit of perceived distance for a given participant in a given condition. In this experiment A came out to be about 94 feet. This formula showed that perceived distances are always shorter than the physical distance, and hence people need some other cues to self-correct their distance perception.

Harway [link] conducted experiments to see the effect of eye-height and age in distance perception in real environments. The method used in his experiment was similar to Gilinsky's [link]: the task was to estimate successive one foot intervals using a foot-ruler, starting at the food of an immediately to the front of the subject. An experimenter moved a pointer along the ruler from the one end, and the subject had to tell the experimenter to stop when the pointer reached the other end. Then a marker was placed at the same location as the pointer, and the pointer would be moved along the same direction starting from the marker. The subject needed to tell the experimenter to stop when the pointer was moved as far from the marker as the length of the ruler (which is one foot). The next trial would start from the position where the pointer stopped. There were two conditions: in the first condition, participants made judgments with normal eye-height, then with adjusted eye-height (5 ft 6.5 inches); in the second condition, participants made judgments with adjusted eye-height, then with normal eye-height. The results showed that changing subjects' eye heights did not influence their distance judgments: there was no significant difference in their distance estimates in both conditions. There was a noticeable effect of age in the results: adults and 12-year-old children made distance estimates with significantly smaller error than children who were 10 years old or less. The author suggested that probably children less than 10 years old had not fully developed their cognitive system to perform the task accurately.

Loomis et al.[link] suggested that people can estimate the egocentric location of targets accurately, but this does not necessary mean that they can correctly estimate the distance between targets. They conducted three experiments to confirm their hypothesis. In the first experiment, participants could perform blindfolded walking accurately to previous seen targets (four, six, eight, 10 or 12 meters away), but they consistently estimated sagittal intervals to be much shorter than the equal frontal intervals (when being asked to put two objects in the sagittal plane so that the distance between them was equal to a given frontal interval, participants consistently made it to be 30 to 100 percent larger). In the second experiment, participants were asked to walk without vision to one target, and then kept walking without stopping to the next target so that the distance between two targets was equal to a previous seen frontal distance. The results showed that their performance was highly accurate, which suggested that even though their initial estimation of the sagittal distances is incorrect (as experiment 1 suggested), their estimation of the location of each target is correct. The third experiment showed that participants could correctly point continuously to a previously seen target while walking blindfolded. Because visually directed pointing is a form of triangulation, the results from the three experiments confirmed the idea that people can correctly estimate the location of the target, correctly update their current self-position based on integration of perceived self-velocity, and in the case of walking, they can correctly update the target location based on updated self-position, and in the case of pointing, correctly update the pointing direction based on updated target position.

Lappin et al.[link] found an interesting effect of surrounding environments in estimating distances in real environments when using a bisection protocol. In this study, the participant saw one experimenter as a target person at a distance away, then another experimenter started walking from the participant toward the target person, or from the target person toward the participant until they were told to stop at the mid-point between the participant and the target person. The distances were 15 and 30 meters. The experiment was carried out in three different conditions: in a lobby, in a hallway, and on a grassy lawn. The results showed that participants tended to overestimate the midpoint in all three conditions, but there was a significant difference in their estimates between lobby, hall conditions and lawn conditions. Participants significantly overestimated the mid-point in the lobby and hall conditions, but did not in the lawn condition. The variability of the data also showed the effect of the surrounding environment, with the variance in the hall condition was significantly higher than the other two conditions. Therefore the authors suggested that the environmental context influenced distance estimation in real environments.

Daum and Hecht [link] investigated distance estimation in vista space (distances that are longer than 30m). Verbal report was used as the measurement protocol. Three experiments showed that people tend to underestimate distances in “near vista space” (less than 75m) and overestimated distances in “far vista space” (longer than 75m). The results also showed that eye height and the size of the target seem to be important in estimating distances in vista space. In another study, Canter and Tagg [link] had participants from seven different cities (Glasgow, Edinburgh, Heidelberg, London, Sydney, Tokyo and Nagoya) estimating, based on their memory/knowledge, the direct distances (as the crow flies) of several sets of two places in each city. The distances were from 1.28 miles to 13.61 miles. They found that all participant overestimated the distances, and there was a strong correlation between the actual distance and the amount of overestimation (i.e. the longer the actual distance, the larger the amount of overestimation).

Ooi and his colleagues attempt to explain some of the important factors in estimating distances in the real world. Some of the main conclusions are:

• Continuous ground is important [link]. In this study, participants were asked to estimate distances within 5m range. When there was a gap in the ground between participants and targets, they overestimated the distance. When the ground texture changed from where the participants stood to where the targets were (concrete to grass or vice versa), they underestimated the distances. This result suggested that texture gradient on the ground surface is an important depth cue for people to correctly estimate distances in the real world.
• Angle of declination from the horizon is important [link]. In this study, participants first wore a pair of base-up prisms (which shift rays such that the angle of declination to the target increases) and did some distance estimations with blindfolded walking and throwing protocols. Then the prisms were removed and participants completed the post-adaptation study with blindfolded walking protocol. The results showed that distances were significantly underestimated in adaption and overestimated in post-adaptation compared to the baseline condition. Because two types of protocols were used in adaptation, it ruled out the possibility that the effect in post-adaptation condition was solely due to an adaptation within the locomotion system. Therefore, the authors concluded that the eye level and the angle of declination are important in distance estimation in the real world.
• Near ground surface information and scanning from self to target are important in estimating distances, even when field of view (FOV) is restricted [link]. In the first experiment, participants wore a pair of goggles which restricted their FOV to the ground surrounding the target. They kept their head still while looking at the target, then closed their eyes and walked without vision to the target location. Distances were four, five, six and seven meters. There were three conditions with three different FOVs. The results showed that when the FOV was 38.6 degrees x 39.5 degrees, participants' estimates were very accurate (approximately 100%). Participants significantly underestimated distances when the FOV was reduced to 21.1 degrees x 21.2 degrees or 13.9 degrees x 13.5 degrees. Hence, the authors suggested that the the size of the visual ground surrounding targets was important in distance estimation, and that a large ground surface was essential to accurately estimate distances. To further assess the role of the size of ground surface surrounding the target, a second experiment was conducted involving a perceptual matching task. There was an L-shaped target with its awidth in the frontal plane and its height in sagittal plane. Its awidth was fixed in length (40.5cm) but its height could be adjusted. The participants' task was to adjust the length of the target's height so that its awidth and its height had the same length. The same three conditions as the first experiment were used. Again, the results showed that people accurately matched the target's height with the target's awidth when their FOV was 38.6 degrees x 39.5 degrees, but underestimated significantly in the other two conditions. Taken together, these two experiments suggested that the large ground surface surrounding the target was important in distance estimation in the real world. A third experiment aimed to investigate which part of the ground contained more essential information: the left-right ground surface or the near-far ground surface. There were two conditions. In the first condition, participants wore a pair of goggles whose vertical FOV was fixed to 50.9 degrees while the horizontal FOV could be adjusted (29.2, 21.5 or 14.3 degrees). In the second condition, the goggles has fixed horizontal FOV (57.7 degrees) and adjustable vertical FOV (39.9, 20.6, 21.1 and 13.6 degrees). Blindfolded walking protocol was used and the distances were from three to seven meters. The results showed that participant' performance did not change in the first condition in which the vertical FOV was fixed. In the second condition, participants significantly underestimated distances when the vertical FOV was smaller than 21 degrees. So it seemed that the near-far ground surface was an important factor. A forth experiment was to examine the importance of near ground and far ground. Participants estimated the distance by scanning the ground from self to target, or from horizon to target, then walked with their eyes closed to the target location. The results showed that participants' estimates were significantly better when they scanned from self to target, which confirmed that the near ground information was essential. The author also conducted a fifth experiment, in which participants did the same task in the same two conditions as the fourth experiment, but in the dark. The results showed that participants' performance was virtually the same in both conditions, which implied that when the ground information was not available, scanning did not help. Altogether, the author concluded that the near ground information and scanning from self to target were important in estimating distances in real environments.

Distance estimation in virtual environments

Messing and Durgin [link] tested the effect of live video of a real environment displayed in an monocular head-mounted display (HMD). Three conditions were used: HMD, restricted FOV (no HMD with one eye covered), and unrestricted FOV (no HMD with one eye covered). Distances were from two to seven meters. Estimates were made via blindfolded walking without feedback. The results showed that participants significantly underestimated distances in the HMD condition (77%) compared to the restricted FOV (96%) and the unrestricted FOV (96%). This suggested that mechanical characteristics of the HMD were the main factor contributing to the differences between the HMD and non-HMD conditions. As the authors noted in the paper, it is possible that the combination of very short accommodation of the HMD (one meter), the low resolution of the screen and the distortion of the optical system were responsible for the compression in distance estimation.

Plumert et al.[link] compared distance estimation between real and virtual environments displayed on a large-screen immersive display (LSID) system. The environment was a grassy lawn in front of a university building. Distances were from six to 36 meters and imagined walking was used to measure estimated distance. The results of the first two experiments showed that people tended to correctly estimate distances less than 18 meters and underestimate distances longer than 18 meters, but their estimates of distances were virtually identical for both real and virtual environment (this was true for adults and 12-year-old children, though 10-year-old children significantly underestimated distances in virtual environment). The last experiment compared imagined walking with blindfolded walking in the real environment. The authors found that there was no significant difference in people's estimates of distances between the two protocols. The results therefore suggested that distance estimation might be better in LSID setups compared to HMD setups, and that the non-encumbrance of the LSID system might help more than the lack of stereo and motion parallax in distance estimation tasks.

Bodenheimer et al.[link] investigated the role of environmental context in distance estimation in real and virtual environment using a bisection task. This work was a replica of [link] with virtual environments. There were three viewing conditions: 1) virtual via an HMD; 2) real world with restricted FOV; and 3) real world without restricted FOV. Two environments, a hallway and a grassy lawn in front of a building, were used to make six conditions. Distances were 15m and 30m (so the bisection distances were 7.5m and 15m). The procedure was the same as one used in [link], in which the participant saw a “target” person and then adjusted another person so that this person was at the midpoint between the participant and the target. The results showed that there was distance compression in virtual conditions but not in real conditions (both with and without restricted FOV). In contrast with [link], they did not find an effect of environment context: for each viewing condition, the performance of participants was the same for both environments. Thus, the authors suggested that the characteristics of the HMD such as restricted FOV and low resolution seemed to contribute to the underestimation of distances in virtual environments.

Interrante et al.[link] investigated the role of presence in distance estimation in virtual environments. The authors wanted to see if using a high fidelity model of the real world could reduce the amount of underestimation in virtual environments. The results from two experiments showed that with a blindfolded walking task, participants' estimates of distances from three to nine meters were not significantly different between real and virtual environments. The estimates in the virtual environment were slightly lower than those in the real world, but not significantly different. The authors suggested that presence and the feeling of being there are important factors in estimating distances in VEs; underestimation might not only come from the technology, but also from other factors, such as a lack of graphical realism, that contribute to a sense of presence and/or immersion.

Jones et al.[link] investigated distance estimation in augmented reality using an optical see-through HMD, and the effect of the HMD on distance estimation tasks. The experiment was carried out in a hallway, distances were from two to eight meters, and blindfolded walking was used as the measurement protocol. Four conditions were used: Real without HMD, Real with HMD, Virtual and Augmented Reality (AR). The results showed underestimation in the Virtual condition, but not in the AR condition or Real with HMD condition. This suggests that people can estimate distances correctly when viewing the virtual targets with the real environment. In this experiment, the characteristics of the HMD seem not to have a great effect.

Willemsen et al.[link], [link] investigated the role of HMDs' mechanical characteristics in contributing to the underestimation of distances in VEs relative to the real world. In this study, participants either saw the virtual world through a real HMD, the real world through a mock HMD (a fake HMD with the same FOV, mass and moments of inertia as the real one) or the real world with unrestricted viewing. Using two different protocols for distance estimation (direct blindfolded walking or triangulated blindfolded walking), they found that the distances were significantly underestimated when participants wore the HMD or the mock HMD compared to the unrestricted viewing condition. And, there was no significant difference between the real HMD and the mock HMD. Hence, the result indicated that the mechanical properties of the HMD (weight, moments of inertia, limited FOV, etc.) account for some of the distance underestimation in virtual environments.

Grechkin et al.[link] investigated the role of presentation methods and measurement protocols in distance estimation in both virtual and real environment. The results of this study confirmed many findings of previous studies, and also pointed out some disagreements. In the first experiment, participants used an imagined-walking protocol to estimate distances from six to 18 meters in one of the five conditions: 1) Real without HMD, 2) Real with HMD see-through, 3) Virtual with HMD, 4) Virtual with LSID, and 5) Photograph-based with LSID. The experiment was conducted in a hallway and a precise model of the hallway was used for virtual conditions. The photo-based condition used photos of the hallway captured with correct eye heights and was rendered with correct eye locations. The results showed that people significantly underestimated distances in three conditions 3, 4, and 5 compared to conditions 1 and 2, and there was no significant difference between people's estimates in conditions 3, 4 and 5. The similarity in participants' performance of condition 4 and 5 implied that improvement in graphics quality by itself is not sufficient enough to improve people's estimates of distances in LSID systems. It is also worth noting that, when using the imagined walking protocol, there was no apparent effect of wearing the HMD. In the second experiment, participants used blindfolded walking protocol to estimate the same distances in one of the four conditions: 1) Real without HMD, 2) Real with HMD see-through, 3) Virtual with HMD, and 6) Augmented Reality with virtual targets overlaying the real hallway. The results showed that people significantly underestimated distances in the Real + HMD condition compared to the Real without HMD condition, and also significantly underestimated distances in the two virtual conditions (3 and 6) compared to the Real + HMD condition. There was no difference between the two virtual conditions. These suggested that the HMD had some effect on distance estimation when blindfolded walking was used as measurement protocol. The significant underestimation of distances in the AR condition disagreed with the finding of [link].

Research evaluating protocols for measuring distance judgments

Research studies have also used a number of different methods to measure participants' perception of distance, such as throwing, bisection, triangulated blindfolded walking, verbal report, timed imagined walking and direct blindfolded walking [link], [link], [link], [link], [link], [link], [link]. In throwing protocols, participants throw objects such as beanbags to indicate distances. More frequently used protocols are direct blindfolded walking and timed imagined walking. HMD-based studies often use the blindfolded walking protocol, in which participants physically walk towards previously seen targets with their eyes closed. Participants stop when they believe that the targets have been reached, and the distance they walked serves as a measure of the perceived distance. Throwing and direct blindfolded walking are usually suitable for use with HMD systems. The main difference between throwing and blindfolded walking is that throwing does not involve continuous updating about the space. Both protocols need vision to initiate the movement, but throwing requires no further interaction with the space. Timed imagined walking is typically employed in LSIDs, which requires participants to start a stopwatch when they imagine beginning to walk toward a target and to stop the stopwatch when they imagine reaching the target (without ever looking at the stopwatch).

Sahm et al.[link] tested distance judgments made via blindfolded throwing versus blindfolded walking in real and modeled hallways, with target distances of three to six meters. For blind throwing conditions, participants saw the target, then covered their eyes with a blindfold and threw a beanbag to the target. There was no feedback after each trial. Participants were given practice before testing, in which they threw the beanbag to the target with their eyes open. The practice was carried out in different location and the distances used for practice were also different (but in the same range) from those used for testing. The results showed that there were no significant differences between blindfolded throwing and blindfolded walking for indicating judged distances, and both protocols showed accurate performance in the real world (98%) but underestimation in the virtual environment (70%). Since throwing requires no spatial updating of the surrounding environment, it should reflect the initial estimate of the subject about the distance. Thus, both protocols seemed to be useful for expressing judgments of distance.

Swan et al.[link] found that blindfolded walking was better than verbal report for making judgments. This study examined distances from three to seven meters, with two measurement protocols (blindfolded walking and verbal report) and four conditions (Real, Real + HMD, Real + Virtual + HMD and Virtual + HMD). An optical see-through HMD was used, without head tracking (the HMD was mounted on a frame that could only change its height to match participants' eye height). Participants first viewed the target object on the ground, and then either 1) walked blindfolded toward the target and stopped when they thought they had reached it, or 2) gave verbal report of how far the target was (in the unit of their choice). The results showed that the blindfolded walking protocol had less underestimation than the verbal report protocol. The verbal report protocol, in fact, had such high variability that it did not seem to be useful as a measurement protocol.

Some of the results in [link], [link] found no significant difference between blindfolded walking and imagined walking in both real and virtual environments. Grechkin et al.[link] compared blindfolded walking with imagined walking protocols in three setups: Real, Real + HMD and Virtual + HMD. In all conditions, participants saw targets (again, six to 18 meters away) in a hallway, and made distance judgments via walking blindfolded or using a timer to indicate how far it took to walk to the targets. The differences between conditions were that in Real, participants saw real targets and a real hallway; in Real + HMD participants saw real targets and a real hallway while wearing a optical see-through HMD; and in Virtual + HMD, participants saw virtual targets and a virtual hallway displayed by an HMD. The results showed that for each condition, there was no significant difference in participants' performance between the two measurement protocols. However, the imagined walking protocol yielded slightly more underestimation (i.e. lower distance estimates) than the blindfolded walking protocol in all three conditions. These two papers suggest that people's responses for distance estimates are similar in both virtual and real environment whether using blindfolded walking or imagined walking.

Klein et al.[link] found no significant difference between imagined walking, triangulated walking and verbal report as protocols in estimating distances in real world (distances were from two to 15 meters). They also found no significant difference between imagined walking and verbal report when using LSID and Wall display setups, but triangulated walking was significantly different from the other two protocols with the same virtual display setup.

Campos et al.[link] found that blindfolded walking and imagined walking are significantly different when a pointing task was used. In this study, participants viewed the target, then they continuously pointed to the target while walking blindfolded along a straight line (5-6m) passing the target, or imagining that they walked a long that line. The author found that participants could point to the target fairly accurately when walking blindfolded, but significantly worse when imagining walking.

Traveled distance estimation in Real Environments

Sadalla et al.[link] evaluated the role of information retrieval in estimating traveled distances. In this study participants walked in a route consisting of two nine-meter segments perpendicular with each other, one segment contained seven intersections and the other contained eight intersections. In the first task, after the initial walk, participants walked an additional 2.2m segment and then were given a sheet of paper with a three-centimeter line representing the 2.2m walk. Participants estimated the distance of their initial walk by drawing another line proportional to the three-centimeter line. Their second task was either recalling the names of fifteen intersections, or recognizing the names of fifteen intersection from a set of thirty names. The first walk was carried out in a lab, and the second walk was carried in the hall outside of the lab. Participants wore a special headpiece so that when they looked down, they could only see the one-meter area in front of their feet. Participants were also instructed to keep their gaze down to this one-meter area so that they did not see the whole traveled route instantaneously. The authors found that when the route consisted of fifteen easy-to-remember names, participants gave significantly larger traveled distance estimates compared to when the route consisted of fifteen hard-to-remember names. They also found that for the recognition task, participants performed equally for both conditions, but for the recall task, participants with easy-to-remember names were able to recall many more names than participants from the other condition. The recognition task is about storing route information while the recall task is about retrieving route information. The difference in performance of the recall task paralleled the difference of traveled distance estimation, but the recognition task did not. Thus, the authors suggested that the process of retrieving route information might influence traveled distance estimation. To further verify this hypothesis, a second experiment was designed in which participants were put in two conditions. In the first condition, participants were given five categories of fifteen intersection names (three names for each categories), while the other group did not receive this information. The design and procedure was the same as the first experiment. If the hypothesis is correct, we would expect that participants in the first condition would give larger estimates than those in the second condition because the given five categories would facilitate the recall task but not the recognition task. The results of the second experiment clearly showed that it was indeed the case, that participants in the first condition gave much larger estimates than participants in the second condition. Taken altogether, the authors suggested that retrieving route information influences the estimation of route length.

Sadalla et al.[link] investigated how the number of turns affects people's estimation of traveled distance. In the first experiment, participants first walked a 200-foot path, then walked a 100-foot path. After the walk, participants were presented with a sheet of paper that had a line on it. There were two points, X and Y, representing the length of the second walk. Starting with X as one endpoint, their task was to mark on the line the second endpoint so that the distance represented the length of the first walk proportionally to the length of the second walk. There were two different routes for the first walk: they had the same length but the one had seven right turns and the other had only two right turns. The route for the second walk was a straight line. The results from the first experiment showed that participants' estimates of the route with seven turns were significantly longer than those of the route with two turns. In the second experiment, participants first walked a 185-foot path, and then were supposed to reproduce that distance on a path with a different number of turns. There were two conditions. In the first condition participants' first walking path had seven turns, and their second walking path had two turns. In the second condition, their first path had two turns and their second path had seven turns. The results showed that participants' second walk was significantly longer when they experienced the seven-turn path first than when they experienced the two-turn path first. Taken together, the results from these two experiments suggested that the number of turns is an important factor in traveled distance estimation.

Sadalla et al.[link] investigated the effect of number of intersections along the route in estimating the route length. Two experiments were conducted, the first one in a laboratory and the second one outdoors in a city. In the first experiment, participants first walked a 28-foot path, then walked a five-foot path and were given a sheet of paper that contained a five-centimeter line. The line was to represent the five-foot path and their task was to draw another line to indicate the length of the first walk proportionally to the second walk. There were three types of first path: one with one intersection, one with four intersections and one with seven intersections. Each participant experienced all three types of path and gave estimates of traveled distance after each walk. The results clearly showed that participants' estimates of traveled distance increased as the number of intersections increased, and there was a significant difference between participants' estimates of each type, which indicated that the number of intersections influenced people's estimates of traveled distances. One noticeable thing was that the actual time it took for participants to finish the first walk was the same for all three types; thus, travel time did not seem to be an important cue in this task. The second experiment was a replica of the first experiment in a real city. Participants estimated the length of two roads by drawing onto a sheet of paper a line proportional to another line which represented the distance between two known intersections. The two roads had equal length (1.7 miles) but different number of intersections (one had six while the other had two). The result of the second experiment again showed that people gave larger estimates for the one with six intersections than the one with two intersections. The authors also noted that in fact the road with six intersections took longer time to walk than the one with two intersection because of the traffic lights, but since the time was not an important factor as shown in Experiment 1, it should not become an important factor in the second experiment. Therefore the author suggested that the number of intersections is an important factor in traveled distance estimation.

Lee [link] investigated the effect of direction to the city on people's estimates of walking distances. In this study, participants estimated the length of 11 pairs of familiar-to-them walking paths ranging from 0.17 miles to 0.85 miles. Each pair contained one outward-from- the-city path and one inward path. Participants indicated their estimates by marking on a ruler having increments of 0.25 miles up to 2 miles. The results showed that estimates for outward distances were significantly longer than estimates for inward distances. The authors suggested that the observation could be explained by “valence” hypothesis, which said that the more favorable the route, the shorter it appeared to be. So the destination of the route seems to be an important influence in estimating traveled distance.

Crompton [link] found that estimates of distances up to two miles in a crowded street in Manchester were correlated with the length of time that participants had known the street. They had first year, second year and third year students estimate the walking distance from a fixed location to twenty different places along the road, and found that on average one mile was estimated as 1.24 miles by first year students, 1.33 miles by second year students, and 1.45 miles by third year students. The explanation for this phenomenon could be that the continuous accumulation of detail and richness of the route makes it become longer and longer in people's mind. This implies that the route content is an important factor in traveled distance estimation because the more details the route has, the longer it seems to be.

Crompton and Brown [link] investigated the estimation of traveled distance in environments of different scale. In this experiment, participants either walked in Manchester or in Portmeirion - an antique Italian town where all the buildings are about seven-eighths of normal buildings. After traveling the distance of approximately 0.31 miles, their task was to mark on a ruler the distance they just traveled (the ruler had increments of 0.1 miles up to 1.5 miles). The results showed that people who walked in Manchester overestimated the distance by about 50% (their average estimate was 0.5 miles), but people who walked in Portmeirion overestimated by almost 200% (their average estimate was 0.91 miles). The author suggested that the differences in the scale of the environment is likely the reason for the significant difference of people's estimates in the two environments, and that traveled distance in small-scaled environments seems to be much larger than traveled distance in normal environments.

Berthoz et al.[link] examined whether people could reproduce traveled distances by using vestibular cues and body senses only. In this experiment, participants sat on a motor robot with their heads restrained and with headphones on to block all audio cues. In the encoding phase, participants were passively transported forward by the robot. When the robot came to a complete stop, the testing phase began and participants used a joystick to control the robot to go forward the same distance as they just traveled. Participants did not have vision during either travel period. There were five distances (2, 4, 6, 8 and 10m) appearing in random order. There was a training period before the encoding phase in which participants practiced controlling the speed of the robot by a joystick while sitting on it with eyes open. In the first experiment, the velocity of the robot in the encoding phase was accelerated from zero to top speed (range from 0.6 to 1 m/s), then was decelerated to zero with the same absolute acceleration. In the testing phase, participants controlled the speed of the robot and could get to maximum speed of 1.4 m/s. The results showed that participants estimates of traveled distance were fairly accurate (86%) despite the fact that they did not have any auditory or visual cues. To rule out the possibility that participants may use travel time as the main cue to estimate traveled distance, the second experiment was conducted. In the second experiment, the velocity of the robot in the encoding phase was accelerated and decelerated in a way that for all five distances the travel time was approximately the same (16 seconds). Participants from the first experiment participated in the second experiment again, without doing any retraining. The results showed that their performance was still as accurate (89%) as the first experiment, which suggested that travel time was not an important cue in this task. Altogether, the authors suggested that people could reproduce traveled distances by using vestibular and somesthetic cues without using any auditory and visual cues.

Glasauer et al.[link] investigated the role of travel time in a reproduction task. In this study, participants first walked a predefined distance (encoding phase), then reproduced the traveled distance (reproduction phase) in three conditions: 1) Control condition in which no mental task was required (Control); 2) Mental task during encoding phase (MTE); 3) Mental task during reproduction phase (MTR). The mental task was counting down by sevens from a three-digit number given to participants at the beginning of the phase. In the first experiment, participants walked on a treadmill. The distances were from 3.5 to 14 meters. The treadmill's speed during encoding phase was either 0.7 or 1.4 m/s. The treadmill's speed during reproduction phase was controlled by participants. In the second experiment, participants walked blindfolded in a large open space (100m x 17m). The distances were from 6.5 to 49 meters. The results from both experiments showed that participants' reproduction of traveled distances was fairly accurate in the control condition, but underestimated in the MTE condition and overestimated in the MTR condition. By a series of analysis and computational model testing, the author suggested that participants reproduced only the duration of traveled distance, which was computed in the encoding phase with the assumption that the speed was constant in both phases. Thus, the authors suggested that travel time was an important factor in reproducing traveled distances. In a more recent study [link], the authors also found that travel time was an important factor in a reproduction task when the route content information was limited (blindfolded walking task in a long underground corridor which had no noticeable texture regularities).

Traveled distance estimation in virtual environments

Kearns et al.[link] investigated the role of optic flow and body senses in homing tasks in virtual environment. They used a triangle-completion task where participants went to the first target with eyes open, then turned to see and went to the second target also with eyes open, then closed their eyes, turned and attempted to return to the starting position. There were six types of triangles used in this study. These triangles all had the same length first leg (4.25m), but varied in the second leg's length (2.25m or 4.25m) and the angle between the two legs (60, 90 or 120 degrees). In experiments 1 and 2, joysticks was used to move in the virtual environment. The results of the first two experiments indicated that optic flow was an important cue for translation and rotation, and the optic flow information from the floor texture was more important than the optic flow information from the wall texture. In the third experiment walking was used to move through the virtual environment, and the result showed that people can perform the task with information from optic flow when necessary, but normally rely on the information from body senses whenever it is available.

Redlick et al.[link] wanted to see if optic-flow only can be used to estimate traveled distances. The virtual environment was a virtual corridor with time-varying textured wall and untextured floor and ceiling, and was displayed via an HMD without stereo. For each trial, a target appeared at one of four distances (4, 8, 16 or 32m). When the participant was ready, they pressed a button to make the target disappear and the optic flow begin. They pressed the button again when they thought that they were at the location of the previously seen target. The optic flow moved with either constant speed (0.4 - 3.2 m/s) or constant acceleration (0.025 - 1.6m/s2). The results showed that when the optic flow moved with constant speed or with acceleration less than 0.1m/s2, participants stopped the motion before they reached the targets, which meant they overestimated their traveled distances (e.g. they traveled only 20m, but they estimated that they had traveled 32m). But when the optic flow moved with acceleration larger than 0.1m/s2, their estimates of traveled distances were fairly accurate. The authors therefore suggested that humans can use optic flow to estimate traveled distances. However, the errors in estimating traveled distances with constant motion speed or low acceleration implied that people could accurately judge traveled distance only when the appropriate motion information was provided.

Popp et al.[link] investigated traveled distance perception in large-scale urban areas. The authors wanted to test whether there is a difference between real walking in real environment and moving by computer mouse in a virtual environment, and if whether the richness of surrounding environments is important or not. The reality was the campus of university, and the virtual world was a model of the campus projected onto a large curved display system with 180 degree horizontal FOV. To manipulate the richness of surrounding environments, they chose two routes on the campus such that one of them had a lot of trees and bushes on both sides while the other route did not. These two routes were modeled in the virtual condition. The task was to walk/move 0.31 miles in real/virtual environment (learning phase), then reproduce the distance they had just moved in the same environment but on a route with different surrounding richness (testing phase). The results showed that the reproduction distances in test phase were significantly larger than the distances in learning phase for both real and virtual environments, and there was no difference in the reproduction distances in test phase for both environments. However, there was no effect of the richness of surrounding environments, there was no difference between estimates in testing phase whether participants went from rich- to low-surrounding or from low- to rich-surroundings. This would suggest that for reproduction tasks, differences between real walking and moving with computer mouse do not seem to be important factors; and the surrounding environments of the route do not seem to have a strong effect either.

Frenz and Lappe [link] tested if people could use optic flow to build up an internal representation of traveled distances, and then estimate them accurately. In this study, the virtual environment was displayed on a large screen, participants sat on a chair adjusted so that they all had the same eyeheight (1.6m), and there was no stereo or motion parallax. The scene was a ground with texture. In the first experiment, participants viewed the moving scene, then the motion stopped, and participants estimated the traveled distance by adjusting a line on the virtual ground so that the distance from that line to another fixed line (1.84m away from participants) was equal to the traveled distance. There were three conditions: textured ground plane, dot plane 1 (consisting of 3000 white light points), and dot plane 2 (consisting 150 white light points). The three different textures provided three different levels of optic flow. The authors observed that the dot plane 2 texture seemed to provide too little depth information to be useful and thus decided to provide texture movement during estimation phase as well. There was a control condition in which the textured ground plane was used and (like in the dot plane 2 condition) the scene moved during estimation. The results from the first experiment showed that people significantly underestimated traveled distances in all conditions: 49% with textured ground plane, 33% for dot plane 1, 24% for dot plane 2, and 28% for control condition. There was a strong correlation between the traveled distance and the estimate of traveled distance, which indicated that people could estimate traveled distances from optic flow only. There also was a significant difference between people's estimates between the three conditions (basically, more flow yields worse performance) which implied that changing the optic flow information would affect people in perceiving and estimating traveled distances.

The goal of the second experiment was to explain the difference between this first experiment's results and Redlick's results [link], since underestimation was found in this study but overestimation was found in [link]. With the same apparatus as experiment 1, the authors reproduced Redlick's study and found that people overestimated traveled distances as well, which suggested that people tend to underestimate short distances (as in the first experiment) but overestimate long distances (as in the second experiment and [link]), and that the display type (HMD versus l