The Role of Immersivity in Three-Dimensional Mental
Rotation
Maria Kozhevnikov, Jodie Royan, Olesya Blazhenkova, and Andrey
Gorbunov
George Mason University, USA
Recently, more realistic 3D displays have been designed as new, more ecologically valid alternatives to conventional 2D visual displays. However, research has
thus far provided inconsistent evidence regarding their effectiveness in promoting
learning and task performance. We are interested in the contribution of immersion
to 3D image transformations and compare subjects’ performance on mental rotation tasks in traditional 2D, 3D non-immersive (3DNI - anaglyphic glasses), and
3D-immersive (3DI - head mounted display with position tracking) environments.
Our findings suggest that 2D and 3DNI environments might encourage the use of
more “artificial” encoding strategies where the 3D images are encoded with respect to a scene-based frame of reference (i.e. computer screen). On the other
hand, 3D immersive environments can provide necessary feedback for an individual to use the same strategy and egocentric frame of reference that he/she would
use in a real-world situation. Overall, the results of this study suggest that immersion might be one of the most important aspects to be considered in the design of
learning and training environments.
Mental imagery and spatial transformations
In order to mentally explore and travel within our environment, we need to
represent three-dimensional (3D) visual-spatial images in our minds. Thus,
research concerning 3D image generation and manipulation has important
applications for the design of learning, training and testing environments.
Recently, more realistic non-immersive 3D displays have been designed as
new more ecologically valid alternatives to conventional 2D visual displays [1], [2], and [3]. Although these 3D environments are both more appealing to the user and richer in visual information, research has thus far
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provided inconsistent evidence regarding their effectiveness in promoting
learning and task performance [4], [5]. Thus, one goal of the current research was to investigate how performance in different types of 3D environments would differ from that in a traditional 2D environment.
Another goal of this research was to shed light on an ongoing debate regarding mental imagery and to examine whether imagery preserves the
same type of representation format for 2D environments as it does for 3D
environments. This debate, which began in the 1970s, was initiated between Kosslyn's depictive or analogous approach to mental imagery [6]
and Pylyshyn's [7] descriptionalist, anti-imagery standpoint. One of the
primary ideas of Kosslyn’s theory is that mental images are “quasipictorial” representations, in the sense that they preserve the spatial or
topological properties of the physical objects being represented. According
to Kosslyn’s theory, mental images are generated in the visual buffer (i.e.
retinotopically mapped areas V1 and V2 in the brain) and can be transformed, inspected, or manipulated, analogously to the physical manipulation of the objects they represent [8], [9].
Contrary to the preceding view, Pylyshyn and colleagues [7], [10], [11],
[12], and [13], claim that spatial images are “structural descriptions”,
which are simply complex linguistic representations, with basic semantic
parts representing object parts, properties and spatial relationships. Hinton,
another descriptionalist, agrees with the basic premise of Pylyshyn's theory, but goes one step further, stating, similarly to Marr’s geon theory [14],
that complex images are represented as a hierarchy of parts. For example,
an image of a human may be decomposed into six components, each corresponding to the head, torso, or one of the four limbs. At the second level of
decomposition, the arm can be further segmented into the upper arm, forearm, and hand. According to the structural description theory, and in contrast to the analogous view of imagery, spatial transformations of images
do not involve the mental rotation of images or their parts, but rather the
computation of changes to some of the parameters of their intrinsic and
projective relationships (i.e., relations that specify how the intrinsic frame
of reference of the object is related to the viewer) [15].
One of the main behavioral experiments which lends credence to the
analogue view of imagery was conducted by Shepard & Metzler [16]. In
their study, participants were presented with depictions of pairs of novel
3D objects presented on a 2D screen, one of which was at a different orientation relative to the other. The task was to decide if the objects were the
same or different. In each of these experiments, a positive, linear correlation was found between reaction time and the angle of displacement
between the two objects. This finding was interpreted as evidence that par-
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ticipants had mentally rotated one object into congruence with the other
object in 3D space, which has been taken as a strong support for depictive
nature of images. Moreover, the internal process of mental rotation was
found to approximate physical constraints associated with rotations of actual objects.
Another aspect of mental rotation processing that has attracted much
less attention, and which seems to be at odds with the analogue view of
imagery, is the finding that subjects mentally rotate objects in depth as fast
as (and in some cases even faster than) in the picture plane [16], [17], [18],
[19], and [20]. If subjects were in fact mentally rotating 2D retina-based
visual representations, the depth rotation would take longer than rotation in
the picture-plane, since rotation in depth would have to carry out foreshortening and hidden line removal operations not required during picture
plane rotation. Interestingly, Shepard & Metzler were the first to discover
such a surprising phenomenon. They interpreted similar slopes for rotation
in depth and in picture plane as indicative of latency being a function of
the angle of rotation in three dimensions, not two, as in a retinal projection.
To investigate this finding further, Parsons [19] conducted an extensive
experimental study examining the rates of imagined rotation, not only
around the three principal axes of the observer’s reference frame, but also
around diagonal axes lying within one of the principal planes (frontal,
midsaggital, or horizontal) and around “skew” axes not lying in any of the
principal planes. Consistently with Shepard & Metzler’s findings, Parsons
reported that the rate of rotation around the vertical axis perpendicular to
the line of sight (Y-axis) was several times faster than that for the line-ofsight axis (X axis), suggesting that subjects rely largely on the “gravitational vertical” or “environmental” frame of reference. In addition, Parsons
reported that the rotation rates for other axes (including rotation in depth
around horizontal Z axis were as fast as or even faster than for the line-of
sight-axis. Parsons concluded that this equal ease of rotation was contradictory to the analogous view on imagery but it was consistent with the
hypothesis that spatial and shape information might be internally represented in three dimensions, and that observers, instead of rotating viewercenter 2D retinal images, might largely rely on representations containing
“structural” information about spatial relations between the components of
the object and their orientations with respect to the scene or environment
in which the object lies (See the Figure 1 for the illustration of rotations
around X, Y, and Z axes).
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Fig. 1. Rotations around the three principle axes of rotation, X, Y, and Z.
One of the limitations of the previous experimental studies is that they
have been conducted using traditional laboratory environments. In most of
these environments, stimuli are presented on a 2D computer screen or another flat surface (e.g., a table-top in Hinton & Parsons’ experiment, see
[21]), which defines a fixed local frame of reference. The limited and fixed
field of view defined by the four sides of a 2D computer screen (or tabletop) may encourage the use of a more structural (propositional) encoding,
during which the parts of the 3D image are encoded in relation to the sides
of the computer screen or another salient object in the environment. In the
above case, as Hinton & Parsons suggested, encoding in relation to the
scene-based frame of reference would have a computational advantage: if
the orientation of the objects were defined and computed relatively to the
scene, an observer could move his/her body or head around without having
to update all the representations of objects’ orientations with every change
of his/her perspective. In laboratory environments, subjects usually view
the experimental stimuli exocentrically, “outside” of the scene in which the
object lies. In real environments, however, an observer in many cases constitutes a part of the scene; being “immersed” in it and viewing it “egocentrically”. Furthermore, in real world environments, objects might not be
always embedded into a permanent and fixed local framework, and the
perceived scene is constantly changing depending on the viewer’s position
while he/she is navigating and exploring the environment. In this case, the
advantage of structurally encoding image parts in relation to the permanent
scene-based frame of reference would be lost. Also, since the viewer becomes a part of the environment him/herself, the use of an egocentric (retina-based) encoding, in which an image is encoded as a 2D representation
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on the retina and subsequently rotated mentally in a way analogous to
physical rotation, might become more effective.
The goal of the current study was to investigate 3D mental rotation
processes in three different environments: 3D Immersive (3DI) Virtual
Environment, 3D Non-Immersive (3DNI) Virtual Environment and 2D
conventional non-immersive visual display. These environments differ in
terms of richness and manner of delivery of visual perceptual information,
and our hypothesis is that they might encourage generation of 3D spatial
images of different format, and that they could lead to different types of
3D transformation processes. A key difference between 2D/3DNI versus
3DI environments is that modern 3D immersive environments involve a
head-mounted display (HMD) used in conjunction with a computer and
head tracker. These 3DI environments are interactive in the sense that
when the person turns his/her head, the image adjusts accordingly. This
dramatically widens the "effective" visual field-of-view, giving the participant a sense of true immersion, which might encourage the participants to
rely more on the egocentric spatial system which is used in many realworld navigational and locomotive tasks (see [22] for a review). Given
that 2D and 3DNI displays do not provide the same level of non-visual
cues for 3D image generation that would be experienced in a real-world
environment, we suggest that only the 3DI environment will provide the
necessary visual and non-visual cues to encode and manipulate 3D spatial
images in a format that preserves perspective properties of objects in accordance with the depictive theory of imagery. In contrast, non-immersive
environments might encourage encoding of abstract “structural” information about 3D spatial images in line with descriptive view of imagery.
Method
Participants
Sixteen undergraduate students (8 males and 8 females, average age =
21.5) from George Mason University participated in the study. They received either course credit or monetary compensation.
Materials
Each participant completed the Mental Rotation (MR) task, which was a
computerized adaptation of Shepard & Metzler’s version of the task, in
three different environments: 3DI, 3DNI, and 2D. There were 72 randomly
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ordered trials. For each trial, participants viewed two spatial figures, one of
which was rotated relative to the position of the other. Subjects were to
imagine rotating one figure to determine whether or not it was identical to
the other figure and to indicate their decision by pressing the left (same) or
right (different) button on a remote control device. Participants were
asked to respond as quickly and as accurately as possible. The next trial
began immediately, following the button press. Twelve rotation angles
were used: 20, 30, 40, 60, 80, 100, 120, 140, 150, 160, and 180 degrees. In
addition, the figures were rotated around 3 spatial coordinate system axes
including the picture (X), vertical (Y), and depth (Z) (see Figure 2). Each
test included: 12 trial groups for the 12 rotation angles, 3 trial pairs for the
3 axes, and each pair had 1 trial with matching figures and 1 trial with different figures; thus, there were 72 (12 x 3 x 2) trials in total. Vizard Virtual Reality Toolkit v. 3.0 [23] was used to create the scenes and capture
dependent variables (latency and accuracy).
Fig. 2. Example of a MR test trial, used in the current study.
In the 3DI virtual environment, scenes are presented to the participant
through a stereo head-mounted display (HMD) with a visual field of 150
degrees (see Figure 3a). The participants viewed an environment room
containing only Shepard & Metzler’s shapes presented in front of them.
The position tracking system [24] permits full 3D optical tracking of up to
4 wireless targets over large ranges (more than 10 x 10 meters) with submillimeter precision. In conjunction with a gyroscopic orientation sensor,
it supports the real-time picture-to-position simulation in virtual reality
when any movement of subject’s head immediately causes a corresponding
change of the picture he/she sees in the head-mounted display. In the 3DNI
environment, scenes are presented to the participant on a computer screen.
Stereoscopic depth is provided by means of anaglyphic glasses (see Figure
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3b). In the 2D environment, scenes are presented for monocular vision on
a standard computer screen (see Figure 3c).
Fig. 3. Three different viewing environments: a) 3DI, which includes HMD with
position tracking, b) 3DNI with anaglyphic glasses to present a stereo picture of
three-dimensional spatial forms, and c) 2D monocular viewing environment.
Design and Procedure
Each participant performed the MR task in all 3 environments. Environment order was counterbalanced across participants. Before beginning the
MR trials, participants listened to verbal instructions while viewing example trials (one match and one nonmatch trial) in each environment. Eight
practice trials were given to ensure participants’ comprehension of the instructions and use of rotation strategies. If a response to a practice trial
was incorrect, the participants were asked to explain how they solved the
task in order to ensure the use of a rotation strategy (i.e. rather than verbal
or analytical strategy). In 3DI, to familiarize the participants with immersive virtual reality, there was also an exploratory phase, in which the participants were given general instructions about virtual reality and the use of
remote control device, and they had the possibility to explore the virtual
room and Shepard & Metzler’s shapes from different perspectives (but
they were not allowed to move around during the practice and test phases.
After the experiment, participants were debriefed and received either their
credit or monetary compensation.
Results
Descriptive statistics for performance in the three environments are given
in Table 1. All simple main effects were examined using the Bonferroni
correction procedure. Four subjects that did not demonstrate rates of rotation indicative of the classic positive linear relationship between RT and
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angular deviations (c.f. [16], [19]) were not included in the analysis, so
that the final analysis was performed on 12 subjects.
First, we examined accuracy (the proportion of correct responses) and
latency (seconds) as a function of axis of rotation (X, Y, and Z) and of test
environment (3DI, 3DNI, and 2D). Data were analyzed using a 3 (axis) X
3 (environment) repeated measures ANOVA with General Linear Model
(GLM).
Table 1 Descriptive statistics for 3 versions of the MR test
Test
3D-immersive
3D-non-immersive
2D
Mean accuracy (SD)
0.87(0.09)
0.86(0.10)
0.90(0.07)
Mean RT (s) (SD)
5.42(1.46)
5.47(1.64)
5.33(1.02)
For accuracy, the patterns of subjects’ response were similar for all test
environments (see Figure 4a). There was a significant main effect of axis
[F(2,22) = 19.83, p < .001] where Y axis rotations were more accurate than
X and Z axes rotations (p’s < .01). The effect of environment was marginally significant [F(2,28) = 2.9, p = .040] and as pairwise comparison
showed, the accuracy in 3DNI environment was slightly less than in 2D (p
= 0.08). The effect of interaction was not significant (p = .27). Overall, the
accuracy level was high for all the environments and all the axes, ranging
from 0.84 to 0.97 proportion correct. Given the high rate of accuracy, that
for some rotations was reaching ceiling performance, we focused our remaining analyses on response times.
For latency (see Figure 4b), there was a significant effect of axis [F(2,
22) = 15.40, p < .001] where Y axis rotations were significantly faster than
X and Z (p’s < .05). There was no effect of environment (F<1, p = .89),
However, there was a significant interaction between axis and test environment [F(4,44) = 6.45, p < .001].
Examination of simple main effects revealed that, consistently with previous studies [16], [19] in 3DNI and 2D, X latencies were greater than
those for Y (p=.009 and .005) and Z latencies were greater than Y latencies
(p = .047 and .029), however, X and Z latencies were similar (p = 1.00 and
0.79). Interestingly, the pattern was completely different in 3DI: Z latencies were greater than those for either X (p = .001) or Y (p = .01) latencies,
while X and Y latencies were identical (p = 1.00). Thus, our central finding is that in 3DI, the RT of rotation differed between the X and Z axes (Z
was slower) and that Y rotations were faster than Z but not faster than X
rotations. This differs from previous findings for equivalent X and Z rotations and for faster Y rotations than both X and Z rotations [16], [19]. In
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contrast, reaction time patterns for 3DNI and 2D environments were similar to those found in previous MR studies (i.e. Y rotations are faster than X
and Z rotations, while X and Z rotations are conducted as similar speeds).
Fig. 4. a) Proportion correct as a function of axis of rotation and viewing environment. b) Latency as a function of axis of rotation and viewing environment. b)
Error bars represent standard error means. Note that the Y-axis does not begin at
the origin.
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Given that axis of rotation interacted with test environment for latency,
our next step was to investigate whether another variable, rate of rotation
around three principles axes (X, Y, and Z), also interacted with test environment. To examine rates of rotation around different axes in different
environments, we calculated and compared the mean regression slopes
based on average individual subject regressions in a 3 Axes X 3 Environments repeated measures GLM. The mean regression slopes for each environment and axis of rotation along with SD are presented in Table 2.
Table 2 Mean regression slopes (sec/deg) and SD
Environment
3D-immersive
3D-non-immersive
2D
Axis of rotation
X
0.028(0.003)
0.003(0.004)
0.003(0.003)
Y
0.001(0.003)
0.001 (0.001)
0.001(0.002)
Z
0.042(0.005)
0.030 (0.003)
0.037 (0.002)
Figures 5a, 5b, and 5c represent latency as a function of angle of rotation around X, Y, and Z axes for 3DI, 3DNI and 2D environments respectively using a range of angles from 20 to 160). Repeated measures
analysis revealed that there was a significant effect of axis [F(2,22) = 51.34,
p < .001] and a significant interaction between environment and axis of
rotation [F(4,44) = 3.38, p < .05].
Next, we investigated the contrasts between axes of rotation for each
environment. For 3DI, the rate of rotation around axis Z was significantly
slower than around axis X (p < 0.05) and axis Y (p < 0.01). There was
also a significant difference between the rate of rotation around X and Y (p
= 0.01) so that the rate of rotation around Y was almost twice as fast as
around X. In contrast, in both 3DNI and 2D, there was no significant difference between the rate of rotation around X and Z (p = 1.00 and p = .44
respectively). The rate of rotation around Y was the fastest (all p’s < .01).
Across environments, as pairwise comparisons showed, there were no
significant differences in the rate of rotation around Y axis (all p’s > 0.5).
The rate of rotation around axis X in 3DI was significantly faster than that
in 2D (p < 0.05), while there was no significant difference in rate of rotation around X between 2D and 3DNI environment (p = 0.76). For Z rotation rates, the rate of rotation in 3DI was the slowest, significantly slower
than the rate of rotation around 3DNI and 2D (ps < 0.05).
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Fig. 5. a) Latency as a function of axis of rotation and angle in 3DI environment.
b) Latency as a function of axis of rotation and angle in 3DNI environment.
c) Latency as a function of axis of rotation and angle in 2D environment.
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Discussion
Overall, the results for the 2D and 3DNI environments were consistent
with previous studies, suggesting that objects’ components in these environments were encoded in a descriptive way. The fact that in 2D and
3DNI environments the rate of rotation was significantly faster around Y
than around any other axis, while at the same time the rates of rotation
around X and Z were identical, suggests that the objects’ components were
encoded in terms of “vertical” and “horizontal” relations with regard to
their own internal structure, as well as to the sides of the computer screen.
In this case, rotations in the picture plane would not be easier since it perturbs the encoding of the relative positions of the object’s components. For
example, if one component of the object is above another in an upright image of an object, it will be beside the other when the object is rotated 90
degrees, and a vertical component in an upright object will be horizontal
after a 90 degree rotation. In contrast, rotation in horizontal depth would
not be as difficult as one would expect, since rotating object’s components
around Z axis would not alter the orientation of the “sides” of the object
with respect to the “left” and “right” sides of the computer screen, in
which the object lies (see also [19] for similar discussion).
In contrast, the behavioral pattern of results for 3DI was unique and
suggested the use of a depictive format of mental imagery and the use of
egocentric, retinocentric frame of reference. Overall, the rate of rotation
around axis Z was slower in the 3DI environment, compared to 2D and
3DNI, suggesting that subjects were in fact rotating in depth 2D retinabased object representations, experiencing difficulties with foreshortening
and occlusion. At the same time, the rate of rotation around the Z axis was
significantly slower than the rate of rotation in the picture plane (around X
axis), which is expected for rotation in a plane where no object components are occluded. Overall, the rate of rotation around axis X was the
fastest in 3DI environment in comparison with 2D and 3DNI.
The above findings suggest that in 3DI, RT is a function of the angle of
rotation not in three dimensions, as in the case of 2D and 3DNI environments, but in retinal projection. Given that the primary difference between
3DI and the other environments is the perceptual immersion as well as the
addition of vestibular feedback (i.e., the image is updated while the head is
turning), it appears that depth information per se, which is provided in a
3DNI environment, is insufficient to encourage the use of imagery analogous processes. Furthermore, 2D and 3DNI displays seem to encourage the
use of more “artificial” encoding strategies, in which the 3D image is encoded with respect to an environmental frame of reference, in this case, the
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computer screen. On the other hand, immersive environments can provide
the necessary feedback for an individual to use a similar strategy and
frame of reference as he/she would use in a real-world situation.
Overall, the results of this study indicate that people use a combination
of menta; images encoded in a depictive format in relation to scene-based
frames of reference while performing spatial transformations of the objects
embedded in a permanent scene, viewed by them from the “outside.” This
strategy is exchanged for a combination of retina-centered frames of references when performing mental rotation of the objects in the scene in which
the viewer himself/herself is immersed. These findings have implications
for future studies on spatial transformations of mental images and the design of testing environments. They show that the results of the previous
experiments on mental rotation, performed in laboratory conditions using a
traditional 2D computer screen, might be limited and do not reflect the
mental rotation patterns as if they were measured in a natural, threedimensional environment.
In addition to its theoretical implications, this research could be of a
considerable interest from an applied perspective; specifically for the design of learning environment. Although 3D environments might be more
attractive to the user, the results of the current research show that 1) there
will probably be no significant differences between 2D and 3DNI environments for spatial task performance, whereas a 3DI environment can
provide a unique and possibly more realistic learning environment; and 2)
3DI environment is beneficial for those tasks that benefit from encoding
from an egocentric frame of reference (e.g., navigation, wayfinding, etc).
In addition, the findings of this research have important implications for
training, and explain the results of the studies that show no transfer from
training in 2D environments to immersive VR. For instance, Pausch, Proffitt & Williams [25] reported that immersive prior practice with conventional 2D displays in visual search tasks impaired performance in immersive VR. The researchers suggested that using desktop graphics to train
users for real world search tasks may not be efficient. The current study
explains this finding by pointing out that the encoding of spatial relations
and cognitive strategies applied to perform visual/spatial transformations
in these two types of environments are different.
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