Perceptual scale expansion: an efficient angular coding strategy for locomotor space

Perceiving distance in virtual reality: theoretical insights from contemporary technologies

Decades of research have shown that absolute egocentric distance is underestimated in virtual environments (VEs) when compared with the real world. This finding has implications on the use of VEs for applications that require an accurate sense of absolute scale. Fortunately, this underperception of scale can be attenuated by several factors, making perception more similar to (but still not the same as) that of the real world. Here, we examine these factors as two categories: (i) experience inherent to the observer, and (ii) characteristics inherent to the display technology. We analyse how these factors influence the sources of information for absolute distance perception with the goal of understanding how the scale of virtual spaces is calibrated. We identify six types of cues that change with these approaches, contributing both to a theoretical understanding of depth perception in VEs and a call for future research that can benefit from changing technologies. This article is part of the theme issue 'New approaches to 3D vision'.

EXPRESS: Perceptual scale expansion: A natural design for improving the precision of motor control

Space perception is systematically biased. Few theories of spatial bias address the possible functional advantages of mechanisms that produce spatial biases. The scale expansion hypothesis proposes that many spatial biases are due to the perceptual expansion of visual angles, which acts somewhat like a natural magnifying glass in vision. The present study examined the idea that visual expansion may improve motor precision (i.e., reduce motor variability) in movements when using closed-loop control but not when using open-loop control. Experiment 1 tested this idea in an online tracking task (closed-loop control), whereas Experiment 2 tested it in a fast-hitting task (open-loop control). The results were consistent with the hypothesis. To rule out the effect of the task difference (i.e., tracking vs. fast hitting), Experiment 3 examined the effect of visual expansion on the variability of motor performance in a line-reproduction task. The control type (closed-loop or open-loop) was manipulated by the form of visual feedback (online or offline). The results were again consistent with the present assumption. Taken together, the present data suggest that perceptual expansion in vision improves motor control precision when using closed-loop control (but not when using open-loop control), which supports the scale-expansion hypothesis. In addition, the present findings also improve our understanding of how visual error amplification affects motor control.

Postural and visual aftereffects to a slanted floor in lying and sitting positions

After lying on a slanted floor for a while with the eyes closed, we may perceive it to be less slanted than at the beginning. After viewing a slanted floor while lying on a flat base, we may perceive it to be more horizontal. We investigated these postural and visual adaptations and their interactions with participants lying and sitting on the floor. The participants were adapted to a floor that was posturally, visually, or jointly slanted, and were asked to estimate the test slants around the adapting slant. The estimates were described as a linear function of the test slant with a high goodness-of-fit over the adapting slant. This supported normalization, not satiation, view. Second, the slope of the function, i.e., sensitivity to slant, in the lying position was low in the postural and visual conditions but high in the joint condition, whereas the sensitivity in the sitting position was equally high in all conditions. This was explained by an increase in visual and non-visual cues to the gravitational vertical in the sitting position, and by an abnormal pattern of intracorporeal hydrostatic pressure in the lying position. Third, in both body positions, the angle at which the slant appeared horizontal, i.e., the subjective horizontal (SH), was larger in the postural condition than in the visual condition. Finally, when the postural and visual adaptations were joint, the SH in the lying position was somewhere between the postural- and visual-alone SHs, whereas the SH in the sitting position approximated the visual-alone SH.

Foreshortening increases apparent angles

The hypothesis that perspective foreshortening leads to errors in the visual perception of angles, was tested in four experiments. An oblique to a z-dimension line was presented (a) on the ground in Experiments 1 and 2, and (b) on a wall in Experiments 3 and 4. Observers judged the acute angle between the oblique and the z-line. Foreshortening increased with the oblique's distance along the z-line and, in Experiments 2 and 4, shorter distances from the eye to the ground or wall. As distance and eye-height vary, so does the target's slant to the line of sight. We argue the apparent angles between the lines increased with foreshortening because vision underestimates the fast rate of foreshortening with elevation compared with the slower rates in azimuth.

Blind-Walking Behavior in the Dark Affected by Previewing the Testing Space

Visual environments affect egocentric distance perceptions in full cue conditions. In this study, the effect of three spatial layouts was tested on the perceived location of a self-illuminated single target viewed in the dark. Blind-walking (BW) estimates of target distance were underestimated in all testing spaces, as expected, but foreshortened significantly more in the shortest of the three testing rooms. Additional experiments revealed that neither changes in the perceived angle of declination nor perceived eye height were responsible for this effect. The possibility that subjects made cognitive adjustments to BW behavior to reduce physical risk was assessed by remeasuring target locations in the three different locations with magnitude estimation and by comparing the BW results obtained from subjects who had no preview of the testing space with those who had. The results support the conclusion that the effect of spatial layout is likely due to cognitive adjustments to BW behavior. The results also indicate that the perceived angle of declination is always overestimated by at least a factor of 1.5. These results can be interpreted within the context of a theory of space perception called the angular expansion theory (AET).

Walking with avatars: Gait-related visual information for following a virtual leader

Dynamic situations, such as interactive sports or walking on a busy street, impose high demands on a person's ability to interact with (others in) its environment (i.e., 'interact-ability'). The current study examined how distance regulation, a fundamental component of these interactions, is mediated by different sources of visual information. Participants were presented with a back and forwards moving virtual leader, which they had to follow by walking back and forwards themselves. We presented the leader in several appearances that differed in the presence of segmental (i.e., relative movements of body segments), cadence-related (i.e., sway and bounce), and global (i.e., optical expansion-compression) information. Results indicated that removing segmental motion information from the virtual leader significantly deteriorated both temporal synchronization and spatial accuracy of the follower to the leader, especially when the movement path of the leader was less regular/predictable. However, no difference was found between cadence-related and global motion information appearances. We argue that regulating distance with others effectively requires a versatile attunement to segmental and global motion information depending on the specific task demands. The results further support the notion that detection of especially segmental information allows for more timely 'anticipatory' tuning to another person's locomotor movements and intentions.

Pushing people to their tipping point: Phenomenal tipping point is predicted by phenomenal vertical and intuitive beliefs

Previous work has shown that people overestimate their own body tilt by a factor of about 1.5, the same factor by which people overestimate geographical and man-made slopes. In Experiment 1 we investigated whether people can accurately identify their own and others' tipping points (TPs) - the point at which they are tilted backward and would no longer be able to return to upright - as well as their own and others' center of mass (COM) - the relative position of which is used to determine actual TP. We found that people overestimate their own and others' TP when tilted backward, estimate their own and others' COM higher than actual, and that COM estimation is unrelated to TP. In Experiment 2, we investigated people's intuitive beliefs about the TP. We also investigated the relationship between phenomenal TP and perceived vertical. Whether verbally (conceptually) estimating the TP, drawing the TP, or demonstrating the position of the TP, people believe that the TP is close to 45°. In Experiment 3, we found that anchoring influences phenomenal TP and vertical. When accounting for starting position, the TP seems to be best predicted by an intuitive belief that it is close to 45°. In Experiment 4, we show that there is no difference in phenomenal TP and vertical when being tilted about the feet or waist/hips. We discuss the findings in terms of action-perception differences found in other domains and practical implications.

Pedal and haptic estimates of slant suggest a common underlying representation

It is well known that people verbally exaggerate the slant of visually perceived geographical, virtual, and man-made hills. More recently it has been shown that haptic and verbal estimates of slant result in similar exaggerations, supporting the proprioception calibration hypothesis-that similar biases exist in both verbal estimates of visually perceived slant and proprioceptively perceived hand orientation. This seems to point to a common underlying representation of slant. However, it is unclear if and how manual proprioceptive estimates might be relevant for perception of ground surface slant or how this might translate to pedal perception of surface orientation. In the current work we tested whether pedal perception is systematically connected to a representational system shared by haptic and visual perception. We did this by having people orient their foot to four different orientations of a ramp (Experiment 1) or to a staircase (Experiment 2) and compared these to estimates made using a free hand measure as well as to verbal estimates. Our results show that verbal, haptic, and pedal measures of visually perceived surface orientation all result in similar estimates of slant and do so across different slanted surfaces. This suggests that verbal and haptic proprioceptive estimates tap into a representational system of visually perceived surface orientation that is relevant for walking up various surface orientations.

Do Explicit Estimates of Angular Declination Become Ungrounded in the Presence of a Ground Plane?

In a series of seven experiments (total N = 220), it is shown that explicit angular declination judgments are influenced by the presence of a ground plane in the background. This is of theoretical importance because it bears on the interpretation of the relationship between angular declination and perceived distance on a ground plane. Explicit estimates of ground distance are consistent with a simple 1.5 gain in the underlying perceived angular declination function. The experiments show that, in general, functions of estimates of perceived angular declination have a slope of 1.5, but that an additional intercept can often be observed as a result of incorporating changes in ground distance into reports of changes in angular declination. By varying the background context, a variety of functions were observed that are consistent with this contamination hypothesis.

Rolling Motion Along an Incline: Visual Sensitivity to the Relation Between Acceleration and Slope

People easily intercept a ball rolling down an incline, despite its acceleration varies with the slope in a complex manner. Apparently, however, they are poor at detecting anomalies when asked to judge artificial animations of descending motion. Since the perceptual deficiencies have been reported in studies involving a limited visual context, here we tested the hypothesis that judgments of naturalness of rolling motion are consistent with physics when the visual scene incorporates sufficient cues about environmental reference and metric scale, roughly comparable to those present when intercepting a ball. Participants viewed a sphere rolling down an incline located in the median sagittal plane, presented in 3D wide-field virtual reality. In different experiments, either the slope of the plane or the sphere acceleration were changed in arbitrary combinations, resulting in a kinematics that was either consistent or inconsistent with physics. In Experiment 1 (slope adjustment), participants were asked to modify the slope angle until the resulting motion looked natural for a given ball acceleration. In Experiment 2 (acceleration adjustment), instead, they were asked to modify the acceleration until the motion on a given slope looked natural. No feedback about performance was provided. For both experiments, we found that participants were rather accurate at finding the match between slope angle and ball acceleration congruent with physics, but there was a systematic effect of the initial conditions: accuracy was higher when the participants started the exploration from the combination of slope and acceleration corresponding to the congruent conditions than when they started far away from the congruent conditions. In Experiment 3, participants modified the slope angle based on an adaptive staircase, but the target never coincided with the starting condition. Here we found a generally accurate performance, irrespective of the target slope. We suggest that, provided the visual scene includes sufficient cues about environmental reference and metric scale, joint processing of slope and acceleration may facilitate the detection of natural motion. Perception of rolling motion may rely on the kind of approximate, probabilistic simulations of Newtonian mechanics that have previously been called into play to explain complex inferences in rich visual scenes.

Does perceived angular declination contribute to perceived optical slant on level ground?

When one looks at a spot on level ground, the local optical slant (i.e., surface orientation relative to the line of sight) is geometrically equivalent to the angular declination (i.e., sagittal visual direction relative to horizontal). In theory, angular declination provides an unbiased proximal source of information for estimating optical slant on level ground. Two experiments were conducted to investigate whether human visual systems take advantage of this information. An aspect ratio task was used as an implicit measure for assessing perceived optical slant. Participants gave verbal estimates of the perceived aspect ratio of an L-shaped arrangement, formed by three balls on level ground or on slanted surfaces (hills). Gaze direction was held horizontal when viewing the stimuli on hills. Experiment 1 examined two optical slants (22° to 35°) at relatively short viewing distances (3.1 to 11.5 m), while Experiment 2 tested a shallow optical slant (6°) at relatively long viewing distances (5.7 to 17.2 m). No significant difference in perceived aspect ratio was found between the level-ground and the hill conditions in either experiment. These findings suggest that angular declination does not contribute to perceived optical slant on level ground. It seems that the perception of optical slant and of gaze declination are independent, and this may be because the two variables are normally used jointly to determine a higher order perceptual variable-geographical slant.

Differential Angular Expansion in Perceived Direction in Azimuth and Elevation Are Yoked to the Presence of a Perceived Ground Plane

It has been proposed that perceived angular direction relative to straight-ahead is exaggerated in perception, and that this exaggeration is greater in elevation (or declination) than in azimuth. Prior research has suggested that exaggerations in elevation may be tied to the presence of a visual ground plane, but there have been mixed results across studies using different methods of dissociation. In the present study, virtual environments were used to dissociate visual from gravitational upright while human participants (N = 128) made explicit angular direction judgments relative to straight ahead. Across these experimental manipulations, observers were positioned either upright (Experiments 1A and 1B) or sideways (Experiment 2), so as to additionally dissociate bodily orientation from gravitational orientation. In conditions in which a virtual environment was perceived as containing a level ground plane, large-scale exaggerations consistent with the visually-specified orientation of the ground plane were observed. In the absence of the perception of a level ground plane, angular exaggerations were relatively small. The ground plane serves as an important reference frame for angular expansion in the perceived visual direction.

Counterpoint

Claims about alterations in perception based on manipulations of the energetics hypothesis (and other influences) are often framed as interesting specifically because they affect our perceptual experience. Many control experiments conducted on such perceptual effects suggest, however, that they are the result of attribution effects and other kinds of judgmental biases influencing the reporting process rather than perception itself. Schnall (2017, this issue), appealing to Heider's work on attribution, argues that it is fruitless to try to distinguish between perception and attribution. This makes the energetics hypothesis less interesting.

Walking through a virtual environment improves perceived size within and beyond the walked space

Distances tend to be underperceived in virtual environments (VEs) by up to 50%, whereas distances tend to be perceived accurately in the real world. Previous work has shown that allowing participants to interact with the VE while receiving continual visual feedback can reduce this underperception. Judgments of virtual object size have been used to measure whether this improvement is due to the rescaling of perceived space, but there is disagreement within the literature as to whether judgments of object size benefit from interaction with feedback. This study contributes to that discussion by employing a more natural measure of object size. We also examined whether any improvement in virtual distance perception was limited to the space used for interaction (1-5 m) or extended beyond (7-11 m). The results indicated that object size judgments do benefit from interaction with the VE, and that this benefit extends to distances beyond the explored space.

A large-scale horizontal-vertical illusion produced with small objects separated in depth

We conducted two experiments (total N = 81) to investigate the basis for the large-scale horizontal-vertical illusion (HVI), which is typically measured as 15%-20% and has previously been linked to the presence of a ground plane. In a preliminary experiment, vertical rods of similar angular extents that were either large (4.5-7.5 m) and far, or small (0.9-1.5 m) and near, were matched to horizontal extents in a virtual environment by adjustment of horizontal gaps or rods. Large/far objects showed a larger HVI (∼13%) than did small objects (∼7%), as has been shown before, but the horizontal gap normally used to measure the large-scale HVI was not the source of the larger bias. In the second experiment, we found that simply separating the comparison rod in depth from the vertical rod (thus forcing an evaluation of size at a distance) was sufficient to produce a large HVI (17%), even with small rods. The results are interpreted in light of evidence that the large-scale HVI is dependent on ground plane orientation and may be related to differential angular expansion in the visual coding of elevation and azimuth. (PsycINFO Database Record

Palm board and verbal estimates of slant reflect the same perceptual representation

People verbally overestimate the orientation of slanted surfaces, but accurately estimate or underestimate slanted surfaces using a palm board. We demonstrate a fundamental issue that explains why the two different values typically given for palm board and verbal/visual matching estimates express similar perceptual representations of slanted surfaces. The fundamental problem in studies measuring palm board and verbal estimates is that the "measure"-either (1) reproducing a verbally given angle or the orientation of a slanted surface with an unseen hand or (2) verbally or visually estimating a visually perceived surface-has always been confounded with the "surface"-either using (1) a palm board or (2) a hill or ramp. Although reproduction has exclusively been used with palm boards in these studies, at the same time verbal estimation or visual matching has exclusively been used with hills/ramps. In three experiments, we showed that verbally estimating palm board orientations produces overestimates by a factor of 1.5, whereas reproducing the orientation of the surface of a ramp to verbally given angles produces gains of ~0.6. These values are similar to those seen for verbal overestimates of slanted surfaces, and to palm board gains for near surfaces and the relative palm-board-to-verbal gains for outdoor hills, respectively. Eliminating this confound eliminated the difference previously seen across surfaces. We discuss how and why different measures should produce different results if we overestimate slant in general and perceptually represent slant in the same way, both haptically and visually.

Do Individual Differences and Aging Effects in the Estimation of Geographical Slant Reflect Cognitive or Perceptual Effects?

Several individual differences including age have been suggested to affect the perception of slant. A cross-sectional study of outdoor hill estimation (N = 106) was analyzed using individual difference measures of age, experiential knowledge, fitness, personality traits, and sex. Of particular note, it was found that for participants who reported any experiential knowledge about slant, estimates decreased (i.e., became more accurate) as conscientiousness increased, suggesting that more conscientious individuals were more deliberate about taking their experiential knowledge (rather than perception) into account. Effects of fitness were limited to those without experiential knowledge, suggesting that they, too, may be cognitive rather than perceptual. The observed effects of age, which tended to produce lower, more accurate estimates of hill slant, provide more evidence that older adults do not see hills as steeper. The main effect of age was to lower slant estimates; such effects may be due to implicit experiential knowledge acquired over a lifetime. The results indicate the impact of cognitive, rather than perceptual factors on individual differences in slant estimation.

Manual anchoring biases in slant estimation affect matches even for near surfaces

People verbally overestimate hill slant by ~15°-25°, whereas manual estimates (e.g., palm board measures) are thought to be more accurate. The relative accuracy of palm boards has contributed to the widely cited theoretical claim that they tap into an accurate, but unconscious, motor representation of locomotor space. Recently, it was shown that a bias that stems from anchoring the hand at horizontal prior to the estimate can quantitatively account for the difference between manual and verbal estimates of hill slant. The present work extends this observation to manual estimates of near-surface slant, to test whether the bias derives from manual or visual uncertainty. As with far surfaces, strong manual anchoring effects were obtained for a large range of near-surface slants, including 45°. Moreover, correlations between participants' manual and verbal estimates further support the conclusion that both measures are based on the same visual representation.

Perceived azimuth direction is exaggerated: Converging evidence from explicit and implicit measures

Recent observations suggest that perceived visual direction in the sagittal plane (angular direction in elevation, both upward and downward from eye level) is exaggerated. Foley, Ribeiro-Filho, and Da Silva's (2004) study of perceived size of exocentric ground extent implies that perceived angular direction in azimuth may also be exaggerated. In the present study, we directly examined whether perceived azimuth direction is overestimated. In Experiment 1, numeric estimates of azimuth direction (-48° to 48° relative to straight ahead) were obtained. The results showed a linear exaggeration in perceived azimuth direction with a gain of about 1.26. In Experiment 2, a perceptual extent-matching task served as an implicit measure of perceived azimuth direction. Participants matched an egocentric distance in one direction to a frontal extent in nearly the opposite direction. The angular biases implied by the matching data well replicated Foley et al.'s finding and were also fairly consistent with the azimuth bias function found in Experiment 1, although a slight overall shift was observed between the results of the two experiments. Experiment 3, in which half the observers were tilted sideways while making frontal/depth extent comparisons, suggested that the discrepancy between the results of Experiment 1 and 2 can partially be explained by a retinal horizontal vertical illusion affecting distance estimation tasks. Overall the present study provides converging evidence to suggest that the perception of azimuth direction is overestimated.

Distance perception in an open water environment: Analysis of individual differences

We investigated whether distance estimation accuracy over open water is influenced by the viewing direction of the observer. Twenty-two healthy students (9 male, 13 female) made 10 distance estimates ranging between 50 and 950 m actual distance in 2 viewing conditions: (1) from shore to boat and (2) from boat to shore. There were no consistent differences in estimation accuracy between viewing directions. The group data revealed a general tendency to underestimate actual distances (74%), but there was considerable interindividual variance (mean error of 74% ± 27%, range = 31% to 145%). A multilevel regression model of estimate accuracy suggests there were three subgroups of participants. One subgroup (N = 4, 18%) were consistent underestimaters, regardless of distance, whereas another subgroup (N = 5, 23%) consistently overestimated. However, the majority (N = 13, 59%) tended to underestimate at shorter distances (less than 400 m) and then overestimate at longer distances. These findings have important implications in survival situations in open water where an individual may need to judge an estimated distance against their perceived swimming capacity in order to self-rescue.

Large perceptual distortions of locomotor action space occur in ground-based coordinates: Angular expansion and the large-scale horizontal-vertical illusion

What is the natural reference frame for seeing large-scale spatial scenes in locomotor action space? Prior studies indicate an asymmetric angular expansion in perceived direction in large-scale environments: Angular elevation relative to the horizon is perceptually exaggerated by a factor of 1.5, whereas azimuthal direction is exaggerated by a factor of about 1.25. Here participants made angular and spatial judgments when upright or on their sides to dissociate egocentric from allocentric reference frames. In Experiment 1, it was found that body orientation did not affect the magnitude of the up-down exaggeration of direction, suggesting that the relevant orientation reference frame for this directional bias is allocentric rather than egocentric. In Experiment 2, the comparison of large-scale horizontal and vertical extents was somewhat affected by viewer orientation, but only to the extent necessitated by the classic (5%) horizontal-vertical illusion (HVI) that is known to be retinotopic. Large-scale vertical extents continued to appear much larger than horizontal ground extents when observers lay sideways. When the visual world was reoriented in Experiment 3, the bias remained tied to the ground-based allocentric reference frame. The allocentric HVI is quantitatively consistent with differential angular exaggerations previously measured for elevation and azimuth in locomotor space. (PsycINFO Database Record

Gaze direction and the extraction of egocentric distance

The angular declination of a target with respect to eye level is known to be an important cue to egocentric distance when objects are viewed or can be assumed to be resting on the ground. When targets are fixated, angular declination and the direction of the gaze with respect to eye level have the same objective value. However, any situation that limits the time available to shift gaze could leave to-be-localized objects outside the fovea, and, in these cases, the objective values would differ. Nevertheless, angular declination and gaze declination are often conflated, and the role for retinal eccentricity in egocentric distance judgments is unknown. We report two experiments demonstrating that gaze declination is sufficient to support judgments of distance, even when extraretinal signals are all that are provided by the stimulus and task environment. Additional experiments showed no accuracy costs for extrafoveally viewed targets and no systematic impact of foveal or peripheral biases, although a drop in precision was observed for the most retinally eccentric targets. The results demonstrate the remarkable utility of target direction, relative to eye level, for judging distance (signaled by angular declination and/or gaze declination) and are consonant with the idea that detection of the target is sufficient to capitalize on the angular declination of floor-level targets (regardless of the direction of gaze).

Visual space perception at different levels of depth description

The main purpose of this study was to determine the effect of the depth description levels required in experimental tasks on visual space perception. Six observers assessed the locations of 11 posts by determining a distance ranking order, comparing the distances between posts with a reference unit, and estimating the absolute distances between the posts. The experiments were performed in an open outdoor field under normal daylight conditions with posts at distances ranging from 2 to 12 m. To directly assess and compare the observers' perceptual performance in all three phases of the experiment, the raw data were transformed to common measurement levels. A pairwise comparison analysis provided nonmetric information regarding the observers' relative distance judgments, and a multidimensional-scaling procedure provided metric information regarding the relationship between a perceived spatial layout and the layout of the actual scene. The common finding in all of the analyses was that the precision and consistency of the observers' ordinal distance judgments were greater than those of their ratio distance judgments, which were, in turn, greater than the precision and consistency of their absolute-magnitude distance judgments. Our findings raise questions regarding the ecological validity of standard experimental tasks.

Direct manipulation of perceived angular declination affects perceived size and distance: a replication and extension of Wallach and O'Leary (1982)

In two experiments involving a total of 83 participants, the effect of vertical angular optical compression on the perceived distance and size of a target on the ground was investigated. Replicating an earlier report (Wallach & O’Leary, 1982), reducing the apparent angular declination below the horizon produced apparent object width increases (by 33 %), consistent with the perception of a greater ground distance to the object. A throwing task confirmed that perceived distance was indeed altered by about 33 %. The results are discussed in relation to cue recruitment and to recent evidence of systematic bias in the perception of angular declination.

Using a generalized linear mixed model approach to explore the role of age, motor proficiency, and cognitive styles in children's reach estimation accuracy

The purpose was to use a multi-level statistical technique to analyze how children's age, motor proficiency, and cognitive styles interact to affect accuracy on reach estimation tasks via Motor Imagery and Visual Imagery. Results from the Generalized Linear Mixed Model analysis (GLMM) indicated that only the 7-year-old age group had significant random intercepts for both tasks. Motor proficiency predicted accuracy in reach tasks, and cognitive styles (object scale) predicted accuracy in the motor imagery task. GLMM analysis is suitable to explore age and other parameters of development. In this case, it allowed an assessment of motor proficiency interacting with age to shape how children represent, plan, and act on the environment.

Navigating in a three-dimensional world

The study of spatial cognition has provided considerable insight into how animals (including humans) navigate on the horizontal plane. However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation. The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments. We suggest that three-dimensional spaces are represented in a quasi-planar fashion, with space in the plane of locomotion being computed separately and represented differently from space in the orthogonal axis - a representational structure we have termed "bicoded." We argue that the mammalian spatial representation in surface-travelling animals comprises a mosaic of these locally planar fragments, rather than a fully integrated volumetric map. More generally, this may be true even for species that can move freely in all three dimensions, such as birds and fish. We outline the evidence supporting this view, together with the adaptive advantages of such a scheme.

Why women see differently from the way men see? A review of sex differences in cognition and sports

The differences of learning and memory between males and females have been well documented and confirmed by both human and animal studies. The sex differences in cognition started from early stage of neuronal development and last through entire life span. The major biological basis of the gender-dependent cognitive activity includes two major components: sex hormone and sex-related characteristics, such as sex-determining region of the Y chromosome (SRY) protein. However, the knowledge of how much biology of sex contributes to normal cognitive function and elite athletes in various sports are still pretty limited. In this review, we will be focusing on sex differences in spatial learning and memory - especially the role of male- and female-type cognitive behaviors in sports.

Slope estimation and viewing distance of the observer

The overestimation of geographical slant is one of the most sizable visual illusions. However, in some cases estimates of close-by slopes within the range of the observer's personal space have been found to be rather accurate. We propose that the seemingly diverse findings can be reconciled when taking the viewing distance of the observer into account. The latter involves the distance of the observer from the slope (personal space, action space, and vista space) and also the eye-point relative to the slope. We separated these factors and compared outdoor judgments to those collected with a three-dimensional (3D) model of natural terrain, which was within arm's reach of the observer. Slope was overestimated in the outdoors at viewing distances between 2 m and 138 m. The 3D model reproduced the errors in monocular viewing; however, performance was accurate with stereoscopic viewing. We conclude that accurate slant perception breaks down as soon as the situation exits personal space, be it physically or be it by closing one eye.

Anchoring in action: manual estimates of slant are powerfully biased toward initial hand orientation and are correlated with verbal report

People verbally overestimate hill slant by approximately 15° to 25°, whereas manual estimates (e.g., palm board measures) are thought to be more accurate. The relative accuracy of palm boards has contributed to the widely cited theoretical claim that they tap into an accurate, but unconscious, motor representation of locomotor space. In the current work, 4 replications (total N = 204) carried out by 2 different laboratories tested an alternative anchoring hypothesis that manual action measures give low estimates because they are always initiated from horizontal. The results of all 4 replications indicate that the bias from response anchoring can entirely account for the difference between manual and verbal estimates. Moreover, consistent correlations between manual and verbal estimates given by the same observers support the conclusion that both measures are based on the same visual representation. Concepts from the study of judgment under uncertainty apply even to action measures in information rich environments.

Angular declination and the dynamic perception of egocentric distance

The extraction of the distance between an object and an observer is fast when angular declination is informative, as it is with targets placed on the ground. To what extent does angular declination drive performance when viewing time is limited? Participants judged target distances in a real-world environment with viewing durations ranging from 36-220 ms. An important role for angular declination was supported by experiments showing that the cue provides information about egocentric distance even on the very first glimpse, and that it supports a sensitive response to distance in the absence of other useful cues. Performance was better at 220-ms viewing durations than for briefer glimpses, suggesting that the perception of distance is dynamic even within the time frame of a typical eye fixation. Critically, performance in limited viewing trials was better when preceded by a 15-s preview of the room without a designated target. The results indicate that the perception of distance is powerfully shaped by memory from prior visual experience with the scene. A theoretical framework for the dynamic perception of distance is presented.

Gaze behavior and the perception of egocentric distance

The ground plane is thought to be an important reference for localizing objects, particularly when angular declination is informative, as it is for objects seen resting at floor level. A potential role for eye movements has been implicated by the idea that information about the nearby ground is required to localize objects more distant, and by the fact that the time course for the extraction of distance extends beyond the duration of a typical eye fixation. To test this potential role, eye movements were monitored when participants previewed targets. Distance estimates were provided by walking without vision to the remembered target location (blind walking) or by verbal report. We found that a strategy of holding the gaze steady on the object was as frequent as one where the region between the observer and object was fixated. There was no performance advantage associated with making eye movements in an observational study (Experiment 1) or when an eye-movement strategy was manipulated experimentally (Experiment 2). Observers were extracting useful information covertly, however. In Experiments 3 through 5, obscuring the nearby ground plane had a modest impact on performance; obscuring the walls and ceiling was more detrimental. The results suggest that these alternate surfaces provide useful information when judging the distance to objects within indoor environments. Critically, they constrain the role for the nearby ground plane in theories of egocentric distance perception.

Angular scale expansion theory and the misperception of egocentric distance in locomotor space

Perception is crucial for the control of action, but perception need not be scaled accurately to produce accurate actions. This paper reviews evidence for an elegant new theory of locomotor space perception that is based on the dense coding of angular declination so that action control may be guided by richer feedback. The theory accounts for why so much direct-estimation data suggests that egocentric distance is underestimated despite the fact that action measures have been interpreted as indicating accurate perception. Actions are calibrated to the perceived scale of space and thus action measures are typically unable to distinguish systematic (e.g., linearly scaled) misperception from accurate perception. Whereas subjective reports of the scaling of linear extent are difficult to evaluate in absolute terms, study of the scaling of perceived angles (which exist in a known scale, delimited by vertical and horizontal) provides new evidence regarding the perceptual scaling of locomotor space.

Depth compression based on mis-scaling of binocular disparity may contribute to angular expansion in perceived optical slant

Three studies, involving a total of 145 observers examined quantitative theories of the overestimation of perceived optical slant. The first two studies investigated the depth/width anisotropies on positive and negative slant in both pitch and yaw at 2 and 8 m using calibrated immersive virtual environments. Observers made judgments of the relative lengths of extents that were frontal with those that were in depth. The physical aspect ratio that was perceived as 1:1 was determined for each slant. The observed anisotropies can be modeled by assuming overestimation in perceived slant. Three one-parameter slant perception models (angular expansion, affine depth compression caused by mis-scaling of binocular disparity, and intrinsic bias) were compared. The angular expansion and the affine depth compression models provided significantly better fits to the aspect ratio data than the intrinsic bias model did. The affine model required depth compression at the 2 m distance; however, that was much more than the depth compression measured directly in the third study using the same apparatus. The present results suggest that depth compression based on mis-scaling of binocular disparity may contribute to slant overestimation, especially as viewing distance increases, but also suggest that a functional rather than mechanistic account may be more appropriate for explaining biases in perceived slant in near space.

Perceptual experience as a bridge between the retina and a bicoded cognitive map

The bicoded cognitive maps described by Jeffery et al. are compared to metric perceptual representations. Systematic biases in perceptual experience of egocentric distance, height, and surface orientation may reflect information processing choices to retain information critical for immediate action (Durgin et al. 2010a). Different information processing goals (route planning vs. immediate action) require different metric information.

What do hands know about hills? Interpreting Taylor-Covill and Eves (2013) in context

Hills appear much steeper than they are. Although near surface slant is also exaggerated, near surfaces appear much shallower than equivalently slanted hills. Taylor-Covill and Eves (2013) propose a new type of palm orientation measuring device that provides outputs that accurately reflect the physical slants of stairs and hills from 19 to 30° and also seems to accurately reflect the slants of near surfaces (25-30°). They question the validity of the observations of Durgin, Hajnal, Li, Tonge & Stigliani (2010), who observed that palm boards grossly underestimated near surfaces. Here I review our recent work on the visual and haptic perception of near surface orientation in order to place Taylor-Covill and Eves' arguments in context. I note in particular that free hand measures of real surfaces in near space show excellent calibration, but free hand measures show gross exaggeration for hills. This leads to the question of the grounds for preferring a mechanical device to a freely wielded hand. In addition I report an investigative replication of the crucial observations that led to our concerns about the value of palm boards as measures of perception and note the specific methodological details that we have accounted for in our procedures. Finally, I propose some testable hypotheses regarding how better-than-expected haptic matches to hills may arise.

Aging and the perception of egocentric distance

The present study examined whether there is an age-related difference in judging egocentric distances. In 4 experiments, both younger and older observers judged the physical distance of an object on a ground plane and reported their judgments by verbal report and by blind rope pulling. Overall, we found that (a) younger observers in general underestimated egocentric distance and showed foreshortening; (b) older observers judged more egocentric distance than younger observers and did not show foreshortening; and (c) this age-related difference was not due to an age-related difference in scaling or output calibration (Experiment 2), the use of eye height information (Experiment 3), or the use of texture gradient information (Experiment 4). These results may be accounted for by differences in perceived slant of the ground surface or a greater reliance on pictorial cues with increased age.

Humans have precise knowledge of familiar geographical slants

Whereas maps primarily represent the 2-dimensional layout of the environment, people are also aware of the 3-dimensional layout of their environment. An experiment conducted on a small college campus tested whether the remembered slants of familiar paths were precisely represented. Three measures of slant (verbal, manual, and pictorial) were collected in 2 different between-subject conditions (perception and memory) for 5 familiar paths on the campus of Swarthmore College, ranging in slant from 0.5° to 8.6°. Estimates from memory and from perception did not differ for any of the measures. Moreover, estimates from all measures, though different in mean value, were correlated within participant, suggesting a common underlying representation was consulted in all cases.

The visual system's intrinsic bias and knowledge of size mediate perceived size and location in the dark

Dimly lit targets in the dark are perceived as located about an implicit slanted surface that delineates the visual system's intrinsic bias (Ooi, Wu, & He, 2001). If the intrinsic bias reflects the internal model of visual space-as proposed here-its influence should extend beyond target localization. Our first 2 experiments demonstrated that the intrinsic bias also influences perceived target size. We employed a size-matching task and an action task to measure the perceived size of a dimly lit target at various locations in the dark. Then using the size distance invariance hypothesis along with the accurately perceived target angular declination, we converted the perceived sizes to locations. We found that the derived locations from the size judgment tasks can be fitted by slanted curves that resemble the intrinsic bias profile from judged target locations. Our third experiment revealed that armed with the explicit knowledge of target size, an observer perceives target locations in the dark following an intrinsic bias-like profile that is shifted slightly farther from the observer than the profile obtained without knowledge of target size (i.e., slightly more veridical). Altogether, we showed that the intrinsic bias serves as an internal model, or memory, of ground surface layouts when the visual system cannot rely on external depth information. This memory/model can also be weakly influenced by top-down knowledge.

Sugar and space? Not the case: Effects of low blood glucose on slant estimation are mediated by beliefs

There is a current debate concerning whether people's physiological or behavioral potential alters their perception of slanted surfaces. One way to directly test this is to physiologically change people's potential by lowering their blood sugar and comparing their estimates of slant to those with normal blood sugar. In the first investigation of this (Schnall, Zadra, & Proffitt, 2010), it was shown that people with low blood sugar gave higher estimates of slanted surfaces than people with normal blood sugar. The question that arises is whether these higher estimates are due to lower blood sugar, per se, or experimental demand created by other aspects of the experiment. Here evidence was collected from 120 observers showing that directly manipulating physiological potential, while controlling for experimental demand effects, does not alter the perception of slant. Indeed, when experimental demand went against behavioral potential, it produced judgmental biases opposite to those predicted by behavioral potential in the low blood sugar condition. It is suggested that low blood sugar only affects slant judgments by making participants more susceptible to judgmental biases.

Systematic biases in human heading estimation

Heading estimation is vital to everyday navigation and locomotion. Despite extensive behavioral and physiological research on both visual and vestibular heading estimation over more than two decades, the accuracy of heading estimation has not yet been systematically evaluated. Therefore human visual and vestibular heading estimation was assessed in the horizontal plane using a motion platform and stereo visual display. Heading angle was overestimated during forward movements and underestimated during backward movements in response to both visual and vestibular stimuli, indicating an overall multimodal bias toward lateral directions. Lateral biases are consistent with the overrepresentation of lateral preferred directions observed in neural populations that carry visual and vestibular heading information, including MSTd and otolith afferent populations. Due to this overrepresentation, population vector decoding yields patterns of bias remarkably similar to those observed behaviorally. Lateral biases are inconsistent with standard bayesian accounts which predict that estimates should be biased toward the most common straight forward heading direction. Nevertheless, lateral biases may be functionally relevant. They effectively constitute a perceptual scale expansion around straight ahead which could allow for more precise estimation and provide a high gain feedback signal to facilitate maintenance of straight-forward heading during everyday navigation and locomotion.

On the anisotropy of perceived ground extents and the interpretation of walked distance as a measure of perception

Two experiments are reported concerning the perception of ground extent to discover whether prior reports of anisotropy between frontal extents and extents in depth were consistent across different measures (visual matching and pantomime walking) and test environments (outdoor environments and virtual environments). In Experiment 1 it was found that depth extents of up to 7 m are indeed perceptually compressed relative to frontal extents in an outdoor environment, and that perceptual matching provided more precise estimates than did pantomime walking. In Experiment 2, similar anisotropies were found using similar tasks in a similar (but virtual) environment. In both experiments pantomime walking measures seemed to additionally compress the range of responses. Experiment 3 supported the hypothesis that range compression in walking measures of perceived distance might be due to proactive interference (memory contamination). It is concluded that walking measures are calibrated for perceived egocentric distance, but that pantomime walking measures may suffer range compression. Depth extents along the ground are perceptually compressed relative to frontal ground extents in a manner consistent with the angular scale expansion hypothesis.

A comparison of two theories of perceived distance on the ground plane: The angular expansion hypothesis and the intrinsic bias hypothesis

Two theories of distance perception-ie, the angular expansion hypothesis (Durgin and Li, 2011 Attention, Perception, & Psychophysics 73 1856-1870) and the intrinsic bias hypothesis (Ooi et al, 2006 Perception 35 605-624)-are compared. Both theories attribute exocentric distance foreshortening to an exaggeration in perceived slant, but their fundamental geometrical assumptions are very different. The intrinsic bias hypothesis assumes a constant bias in perceived geographical slant of the ground plane and predicts both perceived egocentric and exocentric distances are increasingly compressed. In contrast, the angular expansion hypothesis assumes exaggerations in perceived gaze angle and perceived optical slant. Because the bias functions of the two angular variables are different, it allows the angular expansion hypothesis to distinguish two types of distance foreshortening-the linear compression in perceived egocentric distance and the nonlinear compression in perceived exocentric distance. While the intrinsic bias is proposed only for explaining distance biases, the angular expansion hypothesis provides accounts for a broader range of spatial biases.

The social psychology of perception experiments: hills, backpacks, glucose, and the problem of generalizability

Experiments take place in a physical environment but also a social environment. Generalizability from experimental manipulations to more typical contexts may be limited by violations of ecological validity with respect to either the physical or the social environment. A replication and extension of a recent study (a blood glucose manipulation) was conducted to investigate the effects of experimental demand (a social artifact) on participant behaviors judging the geographical slant of a large-scale outdoor hill. Three different assessments of experimental demand indicate that even when the physical environment is naturalistic, and the goal of the main experimental manipulation was primarily concealed, artificial aspects of the social environment (such as an explicit requirement to wear a heavy backpack while estimating the slant of a hill) may still be primarily responsible for altered judgments of hill orientation.

Expert performance by athletes in the verbal estimation of spatial extents does not alter their perceptual metric of space

Athletes often give more accurate estimates of egocentric distance along the ground than do non-athletes. To explore whether cognitive calibration was accompanied by perceptual change, athletes and non-athletes made verbal height and distance estimates and also did a perceptual matching task between perceived egocentric distances and frontal vertical extents. Both groups were well calibrated for height estimation for poles viewed frontally, but athletes were much better calibrated at estimating longer egocentric distances (which are systematically underestimated by non-athletes). Athletes were more likely to have learned specific units of ground distance from relevant sports contexts. Both groups reported using human height as a metric for vertical extent. For non-athletes, verbal underestimation of ground distance corresponded to predictions based on perceptual matches between egocentric distances and vertical extents in conjunction with human-height-based verbal estimates of vertical extents. For athletes, the verbal scaling of egocentric distances of 10 m or more was more accurate and was not predicted by their egocentric distance matches to vertical extents.