Distance mis-estimations can be reduced with specific shadow locations

Abstract

Shadows in physical space are copious, yet the impact of specific shadow placement and their abundance is yet to be determined in virtual environments. This experiment aimed to identify whether a target’s shadow was used as a distance indicator in the presence of binocular distance cues. Six lighting conditions were created and presented in virtual reality for participants to perform a perceptual matching task. The task was repeated in a cluttered and sparse environment, where the number of cast shadows (and their placement) varied. Performance in this task was measured by the directional bias of distance estimates and variability of responses. No significant difference was found between the sparse and cluttered environments, however due to the large amount of variance, one explanation is that some participants utilised the clutter objects as anchors to aid them, while others found them distracting. Under-setting of distances was found in all conditions and environments, as predicted. Having an ambient light source produced the most variable and inaccurate estimates of distance, whereas lighting positioned above the target reduced the mis-estimation of distances perceived.

Full text

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Distance mis‑estimations can
be reduced with specic shadow
locations
Rebecca L. Hornsey
* & Paul B. Hibbard
Shadows in physical space are copious, yet the impact of specic shadow placement and their
abundance is yet to be determined in virtual environments. This experiment aimed to identify
whether a target’s shadow was used as a distance indicator in the presence of binocular distance
cues. Six lighting conditions were created and presented in virtual reality for participants to perform
a perceptual matching task. The task was repeated in a cluttered and sparse environment, where the
number of cast shadows (and their placement) varied. Performance in this task was measured by the
directional bias of distance estimates and variability of responses. No signicant dierence was found
between the sparse and cluttered environments, however due to the large amount of variance, one
explanation is that some participants utilised the clutter objects as anchors to aid them, while others
found them distracting. Under‑setting of distances was found in all conditions and environments,
as predicted. Having an ambient light source produced the most variable and inaccurate estimates
of distance, whereas lighting positioned above the target reduced the mis‑estimation of distances
perceived.
Keywords Distance perception, Virtual reality, Attention, Visual cues, Shadows
Many visual cues to distance are available in natural environments1, and the precision and accuracy with which
judgements can be made will depend on the particular combination of information available in a given context2.
For example, Surdick etal.3 found that in a stereoscopic display, perspective cues were more eective at producing
an accurate perception of distance than other depth cues, while the eectiveness of some lighting cues, such as
relative brightness, contributed very little. e eectiveness of many cues, especially parallax distance cues, also
tends to reduce rapidly with distance1,2.
Perception of distance in sparse environments tends to be poor, as predicted from geometrical considerations
of the limited visual cues that are available. For example, distance tends to be underestimated, with relatively high
uncertainty, when few visual cues are available4–9. We have previously tested whether adding specic environ-
mental cues (binocular cues, linear perspective, surface texture, and scene clutter) could enhance the accuracy
and precision of distance-dependent perceptual tasks using virtual reality10. Performance in this instance was
measured via the degree to which individual cues contributed to a reduction in the amount of bias and variability
in participant responses. It was found that adding visual information did indeed improve performance, such
that a full-cue context allowed for the highest levels of accuracy and precision. In this case, both binocular and
pictorial cues were important for obtaining accurate judgements. To further to these ndings, the current experi-
ment assessed the specic contributions made by clutter and cast shadows to the perception of relative distance,
to explore the importance of lighting cues in complex environments for the accurate perception of 3D space.
Shadows occur when an object or surface disrupts the visibility of another surface or object to a light source,
thus reducing the degree to which it is illuminated. e surface in shadow may belong to an object that is the
same as, or dierent from, the one that is responsible for the shadowing. Mamassian etal.11 provide denitions
for a number of distinct aspects of shadows and shading, including shading, attached shadows, and cast shadows.
Shading refers to the variation in the amount of light reected by surfaces, as a result of their orientation relative
to the light source. Shading may be distinguished from the shadowing eect under consideration in the presented
experiment, which is a result of the occluding of regions of surfaces from the light source. Attached shadows are
those that are formed on the same surface that is occluding the light source. In contrast, cast shadows are those
which are formed on a dierent surface from the one occluding the light source. It is cast shadows that are the
focus of the current experiment, and in particular shadows that are cast on a horizontal surface (such as a ground
plane or table top) by objects that are not attached to the surface.
OPEN
Department of Psychology, University of Essex, Colchester, UK. *email: rlhornsey@outlook.com
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When an object is placed on a surface, its cast shadow will be directly adjacent to the object in the image, as
shown in Fig.1. In this case, the size of the shadow, relative to the height of the object, can be used to provide
information about the direction of the light source. For an object with a height (h
1
), and a shadow with a length
(f), the direction (
θ1
) of the light source is given by:
When an observer views an object above a table-top at eye-height, and the object is illuminated from a single
direction, the shadow will tend to be detached from the object, examples of this are presented in Figs.1 and 2.
When the light source is directly above the object, its shadow will be cast on the horizontal surface at the same
distance as the object. If the light source if further away than that the object, the shadow will be cast at a distance
that is nearer than the object itself. Conversely, if the light source is nearer than the object, or behind the observer,
the shadow will be cast at a distance that is further away than the object. e location of the shadow on the surface
provides information about the distance of the object relative to locations on the surface, albeit in a way that is
ambiguous due to its dependence on the direction of the light source. Geometrically, it can be seen that, when
the shadow is further away than the object, its distance from the object in the horizontal direction is given by:
where D is the distance, h
2
is the height of the object and
θ2
is the direction of the light source. us, if the direc-
tion of the light source can be estimated, the distance of the object along the surface, relative to the location of
its shadow, can be inferred.
Allen12 demonstrated that shadows can be used a source of information about the distance to objects, by
disambiguating the contributions of distance and vertical location to the height in the visual eld of objects. In
addition, another study by Allen13 showed that the direction of cast shadows contributes to distance judgements,
(1)
tan
θ1=
h1
f
(2)
D
=
h
2
tanθ2
Figure1. Examples of how the light source location can be more easily determined when there are multiple
shadows from additional objects within the scene. Dashed lines identifying the light occluded by objects on
the ground surface, where shadows and the objects are attached; solid line identifying the light occluded by the
oating object, where the cast shadow is not attached. e distance of the light source to each object, and their
relative heights, has an impact on the length of their cast shadows. Representation of Eqs.(1) and (2).
Figure2. Examples of the shadow conditions where the light source is locked to the target (a) Ambient; (b)
Static back; (c) Static in front; (d) Locked on top; (e) Locked back; (f) Locked in front.
e light location moves in sync with the adjustments made to the target object location. Light source in three
locations compared to observer, purple target object, pink reference line, black shadow on surface.
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and that shadows have also been found to improve distance judgements regardless of the direction of lighting14.
Cavanagh etal.15 showed that the lateral displacement of a shadow from a target object inuenced the perceived
depth between the two; therefore, for a given depth separation, the size and direction of this oset will be deter-
mined by the direction of lighting. e results obtained were consistent with both a model in which the visual
system assumes a single light source16, and a Bayesian model that weighted dierent lighting directions by their
relative likelihood in the natural environment.
Wanger etal.17 used two tasks to assess the contribution of shadows to the perception of 3D surface layout.
ey found that shadows improved observers’ ability to accurately align objects in three-dimensional space, and
to accurately match their size. Additionally, te Pas etal.18 conducted an odd-one-out experiment, in which par-
ticipants were presented with three stimuli with varying lighting and shadows. By collecting data of participant’s
eye xations, reaction time, and percentage of correct answers they showed that participants relied primarily on
shadows in identifying dierences in the direction and intensity of lighting.
Cast shadows can also have a strong inuence on the apparent 3D layout and motion in moving scenes19–22.
Kersten etal.19 showed that when presented with a ball moving linearly away from the observer in depth, and a
shadow which would correspond with a bouncing ball, an observer was more likely to use the shadow informa-
tion to perceive the ball as having non-linear movement. One of the conclusions of this study was that when
a shadow moves, observers assume that this is caused by the movement of the objects, rather than the light
source. at is, the locations of shadows are used to inform the estimation of the locations of objects under the
assumption of a xed light source.
Dee etal.23 reviewed the literature on the visual eects of shadows. For simple cases with an object on a at
surface, when a light source does not move, then physical properties of the object such as its size, motion, and
shape can be inferred from the shadow.
Shadows have great potential for improving the perception of distance in augmented reality, by helping users
to accurately locate virtual objects within the physical environment. In virtual reality, Hu etal.24 showed that cast
shadows can be used to determine when an object is in contact with a tabletop, or to judge the distance between
the two. e presence of cast shadows can increase the accuracy of distance judgement in augmented reality25,26,
and this is aected by the degree of mismatch in the direction of lighting in the real and virtual environments25,27.
e current study had three goals. e rst was to determine whether the presence of cast shadows could
improve the accuracy of distance judgements for an object that was located above a horizontal surface. e second
was to determine how these distance judgements were aected by the position of the light source, which governs
the spatial location of the shadow relative to the target object. e third goal was to determine whether accuracy
could be further improved by the presence of visual clutter on the tabletop, which could be used to determine the
direction of the light source, and thus allow the shadow to serve as an unambiguous cue to distance.
e experiment consisted of two virtual environments which were tested separately, both using a perceptual
matching task in a VR headset. Participants were tasked with matching the distance of a oating target object
to that of a horizontal reference line on a tabletop. e location of the light source was varied between blocks.
In one lighting condition, only ambient lighting was present, so that no shadows were cast. In all other condi-
tions, one light source was present, and its location relative to the object was varied. is light source was either in
a xed location in the environment so that it did not move with the object, or it was locked to the object, so that
it moved and maintained a constant position relative to the object. In the xed light condition, the light source
was either at the near (observer’s) end of the table or the far end. For the conditions in which it was locked to the
object, the light was either nearer, directly above, or further away than the object. ese lighting conditions are
depicted in Fig.2. e experiment was repeated in a Sparse and a Cluttered environment.
e rst hypothesis relates to the overall performance in the Sparse and Cluttered environments: (1)
regardless of the inuence of shadows, the presence of additional visual cues in the Cluttered environment
compared to the Sparse environment is predicted to improve the accuracy of distance judgements10,28.
In the Sparse environment, shadows are predicted to have a number of eects. As shadows are expected
to contribute to distance estimation, the rst hypothesis here is that (2) performance will be worse overall in the
Ambient condition. In addition, (3) performance is expected to be more precise for the condition in which
the light source is directly above the target (Locked on top), when it is perfectly aligned with the reference
at the correct distance, than when the light source is in front or behind. is is because in this condition, the
observer is required to align two features (the shadow and reference line) that overlap, rather than alignment
with a spatial oset. Furthermore, (4) performance is hypothesised to be more accurate when the light source
is locked to the moving object than when it is static in the environment, since this creates a constant shape and
oset of the shadow. While the shadow provides a potentially useful cue to the location of the object, when the
light is not directly above the object there will be an oset between the reference line and the shadow when the
object and reference are perfectly aligned. Additionally, it is hypothesised (5) that observers may have a tendency
to align the shadow with the reference line. is would lead to an the object being positioned nearer when the
light is in front of the object than when it is behind it.
Finally, (6) it is hypothesised that conditions which improve the accuracy of settings will be more evident
in the Cluttered environment than in the Sparse, since this provides more reliable information about
the direction of the light source, from the sizes of the shadows cast by the surrounding objects on the table-top
(Eq.1). is should also reduce any systematic biases that are associated with the lighting direction. Note that
this predicted increase in the eects of shadows is in addition to the overall improvement in performance in the
cluttered environment relative the sparse environment.
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Methods
Participants
Total of 21 naive participants were recruited using the University’s online system as well as through word of
mouth. Participants received a £5 voucher for approximately 45 minutes of their time to complete the study.
e methods and protocols were approved by the Psychology Ethics Ocer and carried out in accordance
with the ethical guidelines at the University of Essex. All participants gave informed consent.
Materials and apparatus
An Oculus Ri headset and associated controllers were used, with two environments created in Unreal Engine
4.2. Figure3 shows the virtual Sparse environment presented to participants: a room containing just a long
table (1 m width by 4 m length) and the target object (an 10 by 10 by 5 cm cuboid presented at eye-height). e
architecture of the room, target, and reference line were created using the Engine’s Starter Content. e Clut-
tered environment incorporated objects added on to the tabletop, shown in Fig.4. ese were scans obtained
from Unreal Engine Marketplace29,30 or real objects scanned by the experimenters. A total of 21 objects were
positioned randomly across the full length of the table surface.
e target object had a point light locked to the participant-facing side, with an intensity of one lumen and
attenuation radius of 10 cm. is light was programmed to not cast any shadows during the experiment, and
ensured that the luminance of the target object itself did not dier across the lighting conditions of the experi-
ment, which did however aect the presence, location and shape of the cast shadows.
Figure3. View from above: the Sparse environment, where the target object is oating above the tabletop,
the reference line is visible on the tabletop, and the cast shadow is also visible.
Figure4. View from above: the Cluttered virtual environment, where additional objects are positioned
randomly on the tabletop, casting their own shadows.
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Shadow conditions
Both experiments contained the following six shadow-lighting conditions, depicted in Fig.2:
• Ambient: no point light source, no cast shadows.
• Static back: a light source locked to the edge of the table furthest from the participant (position in
environment: X = 36.7, Y = 0, Z = 175 cm; rotation: X = 360 °, Y =
−65
°, Z = 180 °). e size and shape of the
shadow changed as a function of the distance between the target and the light source, which was positioned
between the target and the far edge of the table.
• Static in front: a stationary light source, positioned at the edge of the table closest to the participant
(position in environment: X = 37, Y = 0, Z = 175 cm; rotation: X = 0 °, Y =
−65
°, Z = 0 °). e size and shape
of the shadow varied as a function of the distance between the target and light source, which was positioned
between the target and participant.
• Locked on top: a light source attached to the target object (position from target: X = 0, Y = 0, Z = 120;
rotation pointing directly down onto target). e cast shadow was directly below the target.
• Locked back: a light source attached to the target object (relative transformation position from Locked
on top: X =
−60
, Y = 0, Z = 0 cm; rotation: X = 0 °, Y = 50 °, Z = 0 degrees °). e cast shadow moved with
the target object and was positioned between the target and the far edge of the table.
• Locked in front: a light source attached to the target object (relative transformation position from
Locked on top: X = 60, Y = 0, Z = 0 cm; rotation: X = 0 °, Y =
−50
°, Z = 0 °). e cast shadow moved
with the target object and was positioned between the participant and target
In Fig.2b,c the light is static in the environment, whereas in (d), (e), and (f) the light source is attached to the
target object and moves along with the distance adjustments to the target. ere was no point light present in
(a). e light sources were obtained from Unreal Engine’s Starter Content.
e conditions were presented in separate blocks, each having 20 trials. In the Cluttered environment,
the objects on the virtual table cast their own shadows from the light sources; these were not manipulated in
any way. e light sources were not visible objects themselves, rather the emitted light was visible only on the
objects within the environment.
Task and procedure
e goal was for each participant to match the distance of the target object (a oating box) to that of a reference
line on the table surface. Participants were told to read instructions and these were also described to them by the
experimenter; there was an opportunity to ask questions before starting. e order of the environments was coun-
terbalanced, alternate participants were allocated to start in either the Cluttered or Sparse environment. In
all conditions the task was to move the target object so that it aligned in distance with the reference line on table.
Once inside the VR headset participants adjusted the height of a chair to ensure targets appeared at eye-height,
and sat in an indicated area for the duration of the experiment. ey were instructed to not move from this
position during the experiment. A horizontal reference line appeared on the surface of the table in front of the
observer at a random distance between 40 and 365 cm. e target object was positioned at eye-height and, using
the controller’s A and B face-buttons, participants could move the target along the X axis (forwards/backwards
in egocentric distance) to a position where it looked as though it was directly above the reference line. Once the
distance was decided upon, the participant pressed the controller’s trigger which saved the trial and moved onto
the next one. e next trial automatically began by randomising the distance of the reference line and target
box. No indication was given to participants about when the condition was to change, and no feedback on the
accuracy of their settings was provided.
e lighting condition was altered across blocks of trials. e metrics recorded were the nal position par-
ticipants set the target object to be at in each trial and the position of the reference line, so that the oset for
each trial could be calculated.
Results
Formatting data
e raw data output from the experiments were in a comma separated value format; each session had an inde-
pendent .csv le named by the experiment name, time, and date of the session. Each row represented an indi-
vidual trial with columns for the condition number, the distance of the reference line (in cm), and the set distance
of the target (in cm). A numerical key was used to identify the conditions.
e signed and unsigned error for each trial was calculated by subtracting the distance of the reference stimu-
lus from the set distance of the target stimulus. For the signed errors, a positive value indicated that the object
was positioned further away than the references, and a negative value indicated that it was positioned closer
than the reference. Unsigned errors reect the overall error in settings, incorporating both systematic biases
and random variability. Signed errors reect any systematic biases in the settings, since random variability will
tend to cancel out across repeated trials.
e following exclusion criteria were decided upon before the experiment: any participants who did not nish
the entire experiment, and any participant who withdrew their data aer a two-week window from completion.
Additionally, removal of trials where the set distances were further or closer than the ends of the table were to
be excluded, but no data were set beyond these limits (see Section“Evaluation of the methodology”). No data
were excluded based on these criteria.
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Analysis strategy
A Pearson’s correlation was conducted, separately for the two environments, on the distance of the reference
line and set target positions in each trial to identify the general relationship between participant estimates and
correct settings.
A linear mixed eects model was used to analyse the data with the following equation, where the distance set,
by participants (P) in each trial, is predicted by the distance of the reference line (D) and the lighting condition
(L, numbered from 1 to 6):
Two-way (environment-by-condition) repeated measures ANOVAs were used to identify how these factors
inuenced the unsigned and signed distance-setting errors. ese were followed up with one-way repeated
measures ANOVAs to assess how settings were aected by the shadow condition in each environment, Tukey’s
HSD to which pairs of conditions diered.
Analyses
ere was a consistent under-setting of distances, in that regardless of the lighting or sparsity of the context,
participants set the target to be not as far away as it should have been, which can be seen in Figs.5 and 6. A
correlation was conducted on the distance of the reference line and set target positions, to determine the overall
relationship between the estimates and correct settings. In the Sparse environment, there was a strong posi-
tive relationship between the two (r = 0.935, p<0.001); the same positive trend was found in the Cluttered
environment (r = 0.933, p<0.001).
e data for each environment were analysed separately: Table1 presents the slope and intercept information
for the lighting conditions from both environments. Accurate performance would produce a slope value of one
and an intercept of zero. In both environments the intercept was largest in the Static back lighting condition,
and closest to zero in the Locked in front condition. All slopes were below one, indicating under-setting
of distances. e closest to accurate slope estimate was produced by the Locked on top condition in the
Sparse environment, and Locked back in the Cluttered environment.
Unsigned error
Unsigned errors, which reect the overall accuracy of the settings, are plotted as a function of environment and
condition in Fig.7. A two-way repeated measures ANOVA showed a signicant eect of condition (F (5, 100) =
12.187, p< 0.001) but no eect of environment nor interaction . Overall performance, and the eects of shadows,
were thus no more dierent in the Cluttered environment (hypotheses 1 and 6).
e eects of shadows were analysed separately for the sparse and cluttered environments. Unsigned errors
were signicantly inuenced by the lighting conditions in both the sparse (F (5, 100) = 9.11, p< 0.001) and clut-
tered (F (5, 100) = 7.47, p< 0.001). e only conditions with consistently smaller unsigned errors was the lit from
above condition, which were signicantly smaller than in all other conditions (all p< 0.02).
ese results show that performance was most accurate when the light was directly above the target, and the
shadow directly aligned with the reference when the object is at the correct location (hypothesis 3). However,
there was no evidence that unsigned errors were reduced in any of the other shadow conditions (hypothesis 2).
(3)
DistanceSetting ∼D+L+D∗L+(1+D|P)
Figure5. Scatter plot of the relationship between the distance of the reference line and the set target distance in
each trial. Black line represents accurate performance with an intercept of zero and a slope of one.
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Figure6. Scatter plot of the mean signed errors in the position of the set target in each condition and
environment. Errors from the Sparse environment in green and Cluttered environment in purple.
Table 1. Regression Analyses of the distance perceived in each lighting condition in the two environments
showing estimates, standard errors (SE) and 95% condence limits (CLs), using Eq.(3). Accurate performance
would have an intercept of zero and a slope of one. e p value indicates whether the row is signicantly
dierent from the values of the Ambient condition.
Condition Intercept estimate SE TIntercept CLs p
Ambient Sparse 6.199 3.698 1.676 [−1.052 13.449]
Cluttered 5.822 4.112 1.416 [−2.241 13.855]
Locked in front Sparse −0.485 3.162 −2.114 [−6.685 5.715] 0.035
Cluttered −0.986 3.387 −2.010 [−7.629 5.656] 0.045
Locked on top Sparse 2.987 3.115 −1.031 [−3.121 9.095] 0.303
Cluttered 3.865 3.364 −0.586 [−2.732 10.452] 0.561
Locked back Sparse 10.129 3.132 −1.031 [3.988 16.270] 0.210
Cluttered 3.120 3.298 −0.819 [−3.347 9.587] 0.413
Static in front Sparse 7.238 3.123 0.333 [1.114 13.362] 0.739
Cluttered 5.536 3.308 −0.086 [−0.950 12.022] 0.931
Static back Sparse 16.005 3.106 3.157 [9.914 22.096] 0.002
Cluttered 9.749 3.271 1.201 [3.3349 16.163] 0.230
Slope Estimate SE T Slope CLs p
Ambient Sparse 0.891 0.020 44.311 [0.852 0.931]
Cluttered 0.885 0.017 52.008 [0.852 0.919]
Locked in front Sparse 0.925 0.0152 2.250 [0.895 0.955] 0.025
Cluttered 0.930 0.016 2.783 [0.898 0.961] 0.007
Locked on top Sparse 0.952 0.015 4.048 [0.923 0.982] <0.001
Cluttered 0.943 0.016 3.551 [0.911 0.974] <0.001
Locked back Sparse 0.922 0.015 2.044 [0.892 0.951] 0.001
Cluttered 0.959 0.016 4.616 [0.928 0.990] <0.001
Static in front Sparse 0.887 0.015 − 0.266 [0.857 0.917] 0.026
Cluttered 0.885 0.016 − 0.045 [0.854 0.916] 0.964
Static back Sparse 0.888 0.015 − 0.222 [0.858 0.917] 0.824
Cluttered 0.928 0.016 2.704 [0.897 0.959] 0.007
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Signed errors
Signed errors, which reect systematic biases in the settings, are plotted as a function of environment and condi-
tion in Fig.7. A two-way repeated measures ANOVA showed a signicant eect of condition (F (5, 100) = 19.815,
p< 0.001) but no eect of environment nor interaction . Overall bias, and the eects of shadows, were thus no
dierent in the Cluttered environment (hypotheses 1 and 6).
e eects of shadows were analysed separately for the two environments. Signed errors were signicantly
inuenced by the lighting conditions in both the Sparse (F (5, 100) = 10.6, p< 0.001) and Cluttered (F (5,
100) = 12.7, p< 0.001).
It was predicted that, if observers had a tendency to align the shadow with the reference, then settings should
be closer when objects were lit from in front than behind (hypothesis 5). is was found for both environments,
and for both the static lights and those that were locked to the target objects (all p< 0.05).
Residual errors
Using the data from Table1, the residual errors for each participant in each environment and condition were
calculated. ese were calculated by performing a regression of set distance on reference distance for each
participant and each condition, then calculating the average absolute dierence between each setting and the
values predicted by the regression. is separates out the between-trial variation in settings from the systematic
error captured by the regression. e mean unsigned residuals were then used in two way repeated measures
ANOVA. A signicant eect of condition was found (F (5, 100) = 3.654, p = 0.004), but no eect for environment
nor interaction. e distribution of these data are shown in Fig.7. Residual errors were lowest when the light
source was locked to the top of the object.
Discussion
is experiment aimed to identify which cast-shadow conditions produced the most accurate responses in a
perceptual matching task, and whether the addition of scene anchors enhanced the inuence of cast shadows.
Six lighting conditions were created and presented in virtual reality. e task was repeated in Cluttered and
Sparse environments. A thin box was used as a target so that the most visible face was at and therefore did
not have shading as an added visual cue. e presence of scene clutter did not improve the accuracy of settings,
and did not aect the inuence of shadows on these settings. A light source directly above the target, projecting
a shadow at the same distance as the object onto the table-top, produced the most accurate settings. When the
light source was in front of or behind the target, there was a tendency for observers to align the shadow with
the reference line.
Interpreting the ndings
ere was a strong correlation between the reference stimulus location and set target location, showing that
participants understood the task and completed it appropriately. ere was an overall tendency however, for
participants to set the target stimulus at a shorter distance than the reference line Fig.7. is indicates an over-
estimation of target distance relative to the reference line, which may reect a partial misinterpretation of its
greater height-in-the-eld as a cue to distance1,2. is eect has been found for similar contexts in augmented
reality31.
No dierences in accuracy or precision were identied between the environments. However, a dierence was
found between the lighting conditions. e overall error in responses for each condition can be seen in Fig.6,
where the Locked on top lighting clearly produces the most precise distance estimates. is is supported
by the unsigned errors made, Fig.7, which were lowest in this condition.
Figure7. Box and whisker plots showing the distribution of errors from the six lighting conditions. e average
unsigned and signed error for the Sparse environment in green; Cluttered environment in purple.
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Evaluation of the methodology
Initially, an exclusion criterion was to remove any trials with set distances outside the range of the table length,
as this would not be possible should the experiment have been completed correctly. However this exclusion
criterion was not used, because in the hypothesised event that the shadow was visible and being aligned with
the reference at either end on the table, but the target was subsequently located beyond, this would have led to
the removal of trials in which the participant was following a coherent strategy.
Lighting conditions experienced in daily life tend to include ambient light from overcast weather diusing the
light source, and directional lighting, for example from the sun or from ceiling lights32. e lighting conditions
used here were created to replicate these, with overtly visible cast shadow eects (with the notable exception of
the Ambient lighting condition). Additionally, some less common light instances were created, although all
were physically plausible.
We hypothesised that performance would be more most accurate when the position of the light source was
locked to the target objects, so as to produce a constant oset in the location of the shadow. While light sources
that are a xed location produce more complex shadow eects, these are also more likely to be encountered in
everyday life, and that participants may be more familiar with this dynamic shadow cues. We might also predict
that the additional shadows present in the cluttered condition might be most useful when the light source was
moving with the target object, by providing information about the movement of the light source.
Retinal size is a reliable cue when either the dimensions of a stimulus or the distance is known by the
observer33,34. Here, the participants were not familiarised with either the dimensions of the target, or the testing
area within the virtual environment. e participants were not primed as to whether the size of the target would
be consistent or changing throughout the experiment. However, if they assumed the target was of a constant size,
then its retinal size provides a reliable cue to changes in distance, which are likely to contribute to the reliable
distance estimation shown in Fig.5.
e reference stimulus was presented at a randomly chosen distance on each trial, unlike many other dis-
tance-matching studies where the target appears at a limited few distances35–37. is avoided the possibility of
participants remembering the relative size of the target at each set distance, and then try to replicate the size,
rather than complete the trial as required38.
e two environments were created so that a comparison of whether scene clutter aids in the perception of
distances. e specic objects used in the Cluttered environment were chosen as they are typical everyday
objects that varied in size and shape so that the shadows produced would also be varied. e positioning for
these objects was random, a structured approach to the positioning of the clutter may inuence the perception
of the scene.
Clutter objects and an abundance of shadows on the tabletop may have been distracting for some participants,
which may have contributed to the non-signicant dierence between the two environments. Aer discussions
with some of the participants it became apparent that a subset of the participants valued the objects in the Clut-
tered environment dierently than other participants. In particular, individuals with attention decit hyperac-
tivity disorder may nd the additional objects in the Cluttered environment too distracting. us, increasing
the availability of extra visual cues may not always lead to the anticipated improvements in performance39.
Practical implications
Sugano etal.27 showed that shadows are an important depth cue in AR, but that lighting needs to be consistent
with physical lighting due to the see-through nature of the device. Gao etal.25 used an AR device to test the
impact of shadows on distance perception. It was predicted that distance would be under-estimated, that virtual
shadows would enhance accuracy in the perceptual matching task, and that misalignment between physical
and virtual lights would however impair these estimates. Our results also showed a misestimation of distances
and that lighting conditions also had a signicant impact on these judgements. Our results are thus consistent
with those of Gao etal.25, in that we found an improvement in performance, shown in the reduction in signed,
unsigned and residual errors when objects were lit from above. is is consistent with other studies that have
that the presence of these ‘drop’ shadows support the most accurate perception of distance in AR40. In our VR
study we did not consider the possibility of an inconsistency in the shadows created for dierent objects. is
is an important practical implication for AR, in which some shadows will be created by natural light sources
in the real world, and others by virtual light sources. is misalignment can negatively aect the accuracy of
distance judgements25.
e lit from above condition in this experiment, where the light was attached to and moving with the object, is
a special case in that it creates a situation in which the shadow is cast on the horizontal plane at the same distance
as the object. Moreover, the fact that it moves with the object may mark it out as an additional light source, thus
potentially reducing any eects of conict between this and other light sources in the virtual scene. As such, this
condition is likely to also improve accuracy in augmented reality applications.
Conclusions
Adding clutter to an environment, where there are more shadows cast and more points of reference, does not
enhance the accuracy of distance estimates within the scene compared to an identical environment minus the
clutter. Clutter objects are therefore not used as points of reference, or at least there are some subsets of partici-
pants who do not nd them useful for improving performance.
Consistent with previous literature, there was an under-setting of distances throughout the experiment. From
the lighting techniques tested, both the precision and accuracy were highest in the Locked on top lighting
condition. is condition provides the observer with a simple strategy of aligning the shadow with the refer-
ence line in order to complete the task accurately. Dierences in biases between the cases where the light was in
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front of or behind the object suggest that observers did in fact have tendency towards aligning the shadow and
reference line, even in cases where lighting was not from directly above.
Some of the lighting conditions presented in this experiment can be considered to be ‘unnatural’ in typical
viewing of physical space, as there are few instances where a light source is attached to an object with some sort
of oset. e two static lighting conditions are more representative of typical viewing. However, implementa-
tions of unnatural lighting can be seen in specic applications of VR and cinematography. It is in these instances
where the perception of distance can be enhanced through the use of the conditions presented in this experiment.
Data availability
e datasets generated and analysed during the current study are available in the University of Essex Research
Data Repository, http:// resea rchda ta. essex. ac. uk/ 143/
Received: 1 November 2023; Accepted: 3 April 2024
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Acknowledgements
is was funded by the Economic and Social Research Council.
Author contributions
Conceptualization (RH, PH); Data Curation (RH); Formal Analysis (RH, PH); Investigation (RH); Methodology
(RH, PH); Soware (RH); Supervision (PH); Visualisation (RH); Writing (RH, PH); Review & Editing (RH, PH)
Competing interests
e authors declare no competing interests.
Additional information
Correspondence and requests for materials should be addressed to R.L.H.
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