Magnitude estimation of self-speed under different
visual cue conditions in virtual space
Kazuya Otake1 , Shogo Okamoto1,2 , Yasuhiro Akiyama1 and Yoji Yamada1
1. Nagoya University, Aichi, Japan
2. Tokyo Metropolitan University, Tokyo, Japan
Abstract—In recent years, the concept of the metaverse has
spread, and the demand for virtual reality (VR) technology
has increased. We focused on human perception in VR spaces,
particularly their own locomotive velocity. The amount of visual
information in the VR space was changed, and the subjective velocity perception was evaluated using the psychophysical methodof magnitude estimation. When walking in a bleak hallway, thevelocity was felt slower than when walking in a hallway withmany objects. However, the exponent of Stevens’ power law was
not signiﬁcantly changed by visual cues in the hallways.
Index Terms—Virtual reality, Speed perception, Locomotion
Fig. 1. VR space for this study. The left ﬁgure shows a bleak hallway, andthe right ﬁgure shows an object-ﬁlled hallway.

I. I NTRODUCTION
Virtual reality (VR) technology has been a keyword in
the information society, and will be increasingly useful as afundamental technology in the future. However, the humanperceptual properties in VR spaces are different from thosein actual spaces because the amount of information available
to humans is reduced in the latter. One example is theperception of one’s own locomotive speed. It is known thatone’s perceived speed is slower in a VR space because thereis less visual information available than in an actual space [1],[2]. This makes it difﬁcult to provide the user with a VR spacethat provides the experience that the creator of the VR space
originally intended.
Previous studies have mainly conducted matching tasks toinvestigate the perception of speed in a VR space [2], [3],[4]. For example, [3] reported that a speed of 12 km/h in a
VR space was underestimated by 31% compared to that in an
actual space. However, because human perception is generally
nonlinear, the human perception of speed may exhibit different
characteristics depending on the speed itself. We investigatedthe perception of locomotive speeds over a broader rangeof speed by using the psychophysical method of magnitude
estimation. We expected to acquire insights into the effectof background information on the perceived speed within aVR space, which has yet to be investigated. This study wasapproved by Institutional Review Board, Hino Campus, Tokyo
Metropolitan University (H21-034).
II. M ETHODS

B. Task
The magnitude estimation method was used to investigate
the perceived speed of locomotive movement. The reference
stimulus was a condition in which the avatar moves at 5.0 m/s
in a bleak hallway. As test stimuli, we used velocity stimuli
ranging from 2.0 to 14.0 m/s with the intervals of 1.5 m/s
in the bleak and the object-ﬁlled hallways. After experiencing the reference stimulus, participants watched a randomly
displayed test stimulus and answered how many times fasterthe test stimulus was than the reference stimulus. Individuals
conducted two trials under each of the two stimulus conditions.
They were able to watch the reference stimulus at any time.
The participants were seated such that the distance between
the display and their faces was 40 cm．

C. Participants

A. VR spaceTo investigate the human perception of speed in VR
spaces, virtual hallways were constructed using Unity (Unity
2020.3.12f1, Unity Technologies Co., Ltd., USA). Fig. 1

978-1-6654-1903-1/22/$31.00 2022 IEEE

shows the scenery viewed from a ﬁrst-person perspective. The
left ﬁgure shows a bleak hallway, and the right ﬁgure shows
an object-ﬁlled hallway. The length of the hallway was 150 m,
the width was 4.0 m, and the height was 3.0 m. The heightof the avatar providing the ﬁrst-person perspective was 1.6 m.
The distance between the centers of the neighboring windows
was 24 m.

Eighteen university students (in their 20s) participated inthe task after providing written informed consent. None of theparticipants were informed of the purpose of the experiment.

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TABLE I
R EGRESSION ANALYSIS USED TO COMPUTE THE COEFFICIENTS IN (2) FORTWO EXPERIMENT CONDITIONS . T HE COEFFICIENT, STANDARD ERRORS , t,AND p ARE ALL SHOWN .

Subjective velocity (m/s)

15(a) log kBleak
Object-ﬁlled

value
0.002
0.21s.e.
0.15
0.097

t0.0132.12p
0.99
0.04(b) aBleak
Object-ﬁlled

value
0.87
0.89

s.e.
0.078
0.05

t
11.04
17.91

p
1.3 × 10−12
1.4 × 10−18

1050D. Analysis
The subjective speeds reported in the experiment weremodeled using Stevens’ power law [5]:vs = kvra(1)

where vs is the subjectively perceived speed, vr is the speed
in the VR space, and k and a are constants. To compute thetwo constants using a linear regression analysis, the logarithmof (1) was used:
log vs = log k + a log vr .

(2)

The t-tests were then applied to compare the differences inlog k and a between the two experiment conditions.
III. R ESULTS
The coefﬁcients obtained through the regression analysis of
the perceived speeds for the Stevens’ power law equation in(2) are shown in Table I. In addition to the coefﬁcients, thestandard errors, t-values, and p-values are listed. The valueof log k was 0.002 for the bleak hallway, which is not muchdifferent from 0, but was 0.21 for the object-ﬁlled hallway,
which is statistically different from 0. a were 0.87 and 0.89
for the bleak hallway and objects-ﬁlled hallway, respectively.
These values were statistically different from 0, but were notstatistically different from each other (t = 0.31, p = 0.38).
Fig. 2 shows the perceived speeds and the regression curvesin accord with Stevens’ power law. The regression curve forthe object-ﬁlled hallway (vs = 1.23vr0.89 ) was larger than thatfor the bleak hallway (vs = 1.00vr0.87 ).
IV. D ISCUSSION
Two suggestions were obtained from this experiment regarding the perception of walking speed in a VR space.
The ﬁrst is the perceived magnitude over a wide speed
range. The speed perceived when walking in the bleak hallway
with little visual information was smaller than that in an
object-ﬁlled hallway with relatively large visual cues. We
believe that this is due to the effect of the optical ﬂow of the
background caused by walking. The difference in perceived
speed between the two conditions was greater within theBleak space
Object-filled space
Stevens' power low for bleak space
Stevens' power low for object-filled space

0510

Actual velocity (m/s)

15Fig. 2. Means and standard errors of subjective velocities obtained using themagnitude estimation for two different virtual space conditions and Stevens’
power curves.

high speed range. In other words, the faster the speed, themore important the landscape information is to ﬁll in the gap
between the actual and perceived speeds in a VR space.
The second concern is the power exponent. In this study,
the exponent of Stevens’ power law ranged 0.87–0.89, and nodifference was found between the two conditions. In general,
when the exponent is greater than 1, humans are hypersensitive
to large physical stimuli, and when the exponent is less than1, we are hypersensitive to small physical stimuli. The speed
perception in a VR space is approximately linear within the
low-speed range and becomes slightly less sensitive in thehigh-speed range.
V. C ONCLUSION
In this study, we used the psychophysical method of amagnitude estimation to investigate the human perception ofspeed under different visual cue conditions in a VR space.
Unlike previous studies, this method allowed us to investigate
broadband speeds. The perceived speeds tended to be slower
when the amount of visual information was low. Regardlessof the visual cue conditions, a linear relationship between theactual speed and the perceived speed was maintained, withthe exponent of Stevens’ power law being 0.87–0.89. Theseﬁndings may help in designing VR spaces that are perceptuallyconsistent with the actual spaces.
R EFERENCES[1] O. Janeh, N. Katzakis, J. Tong, and F. Steinicke, “Inﬁnity walk in vr:
Effects of cognitive load on velocity during continuous long-distancewalking,” in ACM Symposium on Applied Perception, no. 9, 2019, pp.
1–9.
[2] N. C. Nilsson, S. Seraﬁn, and R. Nordahl, “Establishing the rangeof perceptually natural visual walking speeds for virtual walking-inplace locomotion,” IEEE Transactions on Visualization and Computer
Graphics, vol. 20, no. 4, pp. 569–578, 2014.

412

[3] M. Caramenti, C. L. Lafortuna, E. Mugellini, O. Abou Khaled, J.-P.
Bresciani, and A. Dubois, “Matching optical ﬂow to motor speed in virtualreality while running on a treadmill,” Plos One, vol. 13, no. 4, pp. 1–13,
2018.
[4] W. B. Thompson, S. H. Creem-Regehr, B. J. Mohler, and P. Willemsen,“Investigations on the interactions between vision and locomotion using atreadmill virtual environment,” in Human Vision and Electronic Imaging
X, vol. 5666, 2005, pp. 481–492.
[5] S. S. Stevens, “On the psychophysical law,” Psychological Review,
vol. 64, no. 3, pp. 153–181, 1957.

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