Perception-based high quality distributed virtual reality

Abstract

Virtual reality has great potential to enable remote collaborative work from anywhere in the world. Developing virtual reality into a platform suitable for natural interaction and immersive collaboration requires the experience to be reliably stable. For a networked collaborative environment, perceived smoothness of motion is limited by the tick rate, that is, the frequency at which information is distributed. As tick rate increases, motion will appear increasingly smooth; however, excessive tick rates may introduce additional load on a network without any perceptible benefit to a user. This paper details two visual psychophysics experiments (N1=16\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_1 = 16$$\end{document}, N2=11\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N_2 = 11$$\end{document}) carried out to evaluate participant sensitivity to tick rate in virtual reality. The influence of three variables, velocity, complexity, and digital medium were investigated. Both velocity and digital medium displayed a significant effect, whilst complexity did not show significance. A model was then built and validated from the results of these experiments. The model predicts for average walking speed within the desktop condition, that 90% of the population will perceive motion to be smooth at 56 Hz, whilst this 90% threshold lies at 113 Hz for the VR condition. This model can predict participant perception of tick rate under given conditions, enabling networks to intelligently optimise participant experience without adding unnecessary further load on the network.

Full text

Vol.:(0123456789)
1 3
Virtual Reality (2023) 27:2529–2539
https://doi.org/10.1007/s10055-023-00825-9
ORIGINAL ARTICLE
Perception‑based high quality distributed virtual reality
WilliamNaylor1 · KurtDebattista1· AlanChalmers1
Received: 7 February 2023 / Accepted: 18 June 2023 / Published online: 5 July 2023
© The Author(s) 2023
Abstract
Virtual reality has great potential to enable remote collaborative work from anywhere in the world. Developing virtual reality
into a platform suitable for natural interaction and immersive collaboration requires the experience to be reliably stable. For
a networked collaborative environment, perceived smoothness of motion is limited by the tick rate, that is, the frequency
at which information is distributed. As tick rate increases, motion will appear increasingly smooth; however, excessive tick
rates may introduce additional load on a network without any perceptible benefit to a user. This paper details two visual psy-
chophysics experiments (
N1
=
16
,
N2
=
11
) carried out to evaluate participant sensitivity to tick rate in virtual reality. The
influence of three variables, velocity, complexity, and digital medium were investigated. Both velocity and digital medium
displayed a significant effect, whilst complexity did not show significance. A model was then built and validated from the
results of these experiments. The model predicts for average walking speed within the desktop condition, that 90% of the
population will perceive motion to be smooth at 56Hz, whilst this 90% threshold lies at 113Hz for the VR condition. This
model can predict participant perception of tick rate under given conditions, enabling networks to intelligently optimise
participant experience without adding unnecessary further load on the network.
Keywords Virtual reality· Networks· Tick rate· Psychophysics
1 Introduction
Virtual reality (VR) has been proven to be an efficient tool
for remote collaboration and education, with experiments
exploring its applicability in manufacturing (Dixken etal.
2019; Herder etal. 2019), surgery (Weibel etal. 2020;
Chheang etal. 2019), fire safety training (Ha etal. 2016),
and school field trips (Zhao etal. 2020). These networked
virtual environments inspire immersive and natural face-
to-face interaction (Aseeri and Interrante 2021; Roth etal.
2016; Dzardanova etal. 2022); however, this is only attaina-
ble with a stable and efficient network (Elbamby etal. 2018).
Tick rate, the frequency at which information is distrib-
uted to all participants involved, is an essential component
within any network (Parthasarathy etal. 2020). If the tick
rate is too low the application will feel unresponsive and
jerky. On the other hand, if the tick rate is unnecessarily
high, it threatens to overload the network’s bandwidth, run-
ning the risk of overwhelming the system. This could result
in the unfortunate side-effect of introducing jitter or latency
spikes, which impairs participant experience and potentially
induces cybersickness when using VR (Stauffert etal. 2018).
Therefore, a balance needs to be struck that provides the
required fluidity for interaction without unnecessary data
transmission.
This balance must also consider the high frame rates that
VR applications require in order to reduce cybersickness
(Kim etal. 2017; Hecht 2016; Brennesholtz 2018). Under
optimal circumstances, tick rate should be equal to the frame
rate to ensure an update every frame, however this would
put a great load upon the network. Therefore, through this
research, we may establish whether tick rate can be decou-
pled from frame rate, and thus operate at sub-frame rate
frequencies without affecting a participant’s experience.
This paper investigates this balance between network load
and satisfaction by evaluating human perception thresholds
for fluid tick rates. A visual psychophysics experiment was
conducted to establish perceptual thresholds for smoothness
* William Naylor
W.Naylor@warwick.ac.uk
Kurt Debattista
K.Debattista@warwick.ac.uk
Alan Chalmers
Alan.Chalmers@warwick.ac.uk
1 WMG, University ofWarwick, CoventryCV47AL, UK
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2530 Virtual Reality (2023) 27:2529–2539
1 3
of network tick rate in VR and comparatively to a computer
desktop visualisation. An initial exploratory experiment was
undertaken to determine the variables that have an effect on
perception. A secondary experiment was then conducted to
investigate all variables of significance as within-participant
variables and their effects to be fully evaluated. The objec-
tives were to establish the psychometric functions defin-
ing smoothness perception within VR and to use these to
develop a predictive model which could enable networked
collaborative VR systems to intelligently optimise a par-
ticipant’s experience. Through dynamically altering network
tick rate in accordance with conditions within a scene, the
system prevents expending excessive resources on imper-
ceptible benefits or cutting too much that would negatively
affect the experience. Figure1 depicts an example applica-
tion of such a system, in which the tick rate is adjusted rela-
tive to the connected client’s device and bandwidth, ensuring
quality remains within accepted thresholds of perceptibility.
2 Related work
Although there has been little previous work that investi-
gated the influence of tick rate on human perception, simi-
larities can be drawn between tick rate and frame rate evalu-
ations, which have been studied more often in the past. Tick
rate and frame rate both involve still images updating at a
fixed frequency, however tick rate enables single objects
within a virtual environment to update at sub-frame rate
frequencies whilst maintaining rendered performance for
the rest of the scene.
Claypool and Claypool (2009) investigated the impact
of frame rate and resolution on task performance in a desk-
top setting. They concluded that as frame rates increased
(5–15–30Hz) the precision of actions improved and one’s
ability to navigate around a space was also positively
affected. Improved resolution similarly improved precision
and navigational ability, but to a less significant degree.
Zielinski etal. (2015) came to similar conclusions for
task performance in VR. Participants were required to
undertake a target acquisition task at a low frame rate of
11Hz and at a higher frame rate of 55Hz. The results
showed that the performance improved with higher frame
Fig. 1 Framework Diagram depicting the creation and application of
the model. A series of psychophysics experiments were conducted to
develop a model that describes the influence of three variables upon
the psychometric function. The model enables the tick rate of a net-
work to be adjusted based upon the connected client and the condi-
tions within the virtual environment, without any detriment to the
experience of either client. The illustrated examples shows how serv-
ers can adjust the quality within desired thresholds based on the avail-
able bandwidth for available clients
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2531Virtual Reality (2023) 27:2529–2539
1 3
rates. Their study agrees with an earlier target acquisition
task experiment by Ware and Balakrishnan (1994). Per-
formance would likely continue to improve for frame rates
greater than 55Hz; however, the magnitude of improve-
ment is likely to diminish, as Denes etal. (2020). found
that the perceived improvement in the quality of anima-
tions stalled for frame rates above 100Hz in computer
desktop environment. No such experiment at these higher
frequencies has been conducted in VR, but potentially a
similar trend may occur where the increase in quality of
task performance also plateaus.
Contradicting results can be found in the study of stimu-
lus velocities. Sensitivity to motion has been reported to
increase for higher velocities (Denes etal. 2020; McDon-
nell etal. 2007) but also decrease for higher velocities
(Hulusić etal. 2011). Denes etal. found sensitivity to motion
increased for higher velocities, furthermore they found that
sensitivity to motion increased if the trajectory of the mov-
ing object was predictable. However, Hulusić etal. (2011)
concluded that higher velocities reduced sensitivity to
framerate. Hulusić etal. also established that multi-sensory
stimuli affected perception of frame rate. Individuals were
required to compare the smoothness of the movement and
when other sensory factors such as the sound of footsteps
were introduced, participants perceived the movement at
lower frame rates as more acceptable.
DoVale (2017) studied the just noticeable difference
(JND) for three different frame rates, determining the thresh-
old for a 24Hz frame rate to be between 26Hz and 28Hz.
JND thresholds for higher frame rates were significantly
larger than for the 24Hz condition, with the JND for 48Hz
at 62Hz, and 72Hz producing uncertainty in identification
at frame rates as high as 120Hz.
McDonnell etal. (2007) investigated the thresholds of
perceived smoothness for pose update rate in animations
on a two-dimensional monitor. Character type and scene
complexity had no influence on perceived smoothness, but
thresholds increased for higher linear velocities and inten-
sity of movement. When the number of individuals moving
increased, sensitivity decreased.
Latoschik etal. (2019) evaluated the performance of
a distributed VR environment based upon the number of
connected clients. Performance of the networks began to
diminish for groups larger than 25, and the server update
frequency fell from 120 to 6Hz for 125 clients. A follow-up
subjective experiment affirmed these results, with perceived
fluidity and synchrony significantly reducing for crowds
larger than 50, increasing dissatisfaction.
The only study dedicated specifically to tick rate was con-
ducted by Lee and Chang (2015), who evaluated the impact
of tick rate upon accuracy within an FPS game. They showed
that accuracy significantly increased for the higher tick rate
of 128Hz in comparison with 64Hz.
3 Methodology
The overarching motivation of this work is to improve net-
work efficiency within interactive environments, including
VR, without unnecessarily compromising on visual fidelity
or the immersive experience. We investigate human perception
to various visual conditions, in order to establish thresholds
for a given condition so that the bandwidth consumed can be
minimised without significant losses in perceived visual fidel-
ity. To help identify these thresholds a psychophysical experi-
ment was conducted.
Psychophysical experiments seek to identify a Psycho-
metric Function (PF) which describes the response from the
human visual system when presented with a stimulus (Treut-
wein 1999). As the stimulus intensity increases, the proportion
of trials evoking a positive response will increase in line with
the PF. For these experiments, the stimulus intensity will be
the tick rate, measured in Hertz (Hz). A logistic function was
chosen for the PF, as it can operate with log-transformed vari-
ables and the derivative is symmetric around the threshold.
This will simplify the construction of a predictive model later
on; however, with the data collected, other sigmoidal functions
could easily be fitted with the same methodology. Equation1
gives the generalised form of the PF(Strasburger 2001; Treut-
wein 1995)
The tick rate is denoted by x.
𝛼
corresponds to the threshold
of the PF, the point at which responses will be positive 50%
of the time.
𝛽
represents the slope of the PF, influencing
the gradient of the PF at the threshold.
𝛾
is the guess rate,
the lower bound of the PF as tick rate reaches its minimum.
Finally,
𝜆
represents the lapse rate, the result of responses
independent of the stimulus, such as misclicks or distraction
(Wichmann and Hill 2001).
The PF could hypothetically be affected by a large number
of variables, from the resolution and dynamic range of the dis-
play to the importance of the stimulus within the scene, and in
general, the four PF parameters can be described as a function
of variables
p1,…,pn
(Debattista etal. 2018)
Due to the nature of this experiment investigating tick rates,
𝛾
and
𝜆
can be constrained to reduce the complexity of
the problem. As the tick rate reduces to 0, the motion will
always appear jittery, so
𝛾
can be constrained to 0. Lapse rate
is usually fixed at a small nonzero value for psychophysi-
cal experiments (e.g. 0.01) and setting equal to zero may
introduce significant bias for threshold and slope (Swanson
and Birch 1992), so
𝜆
will be restricted to 0.01. With these
(1)
Ψ(
x∣𝛼𝛽𝛾𝜆)=𝛾+(1−𝛾−𝜆)
1
1+e
−𝛽(x−𝛼)
.
(2)
Ψ(x∣𝛼𝛽𝛾𝜆)∶𝛼(p
1
,…,p
n
),
𝛽
(p
1
,…,p
n
),𝛾(p
1
,…,p
n
),𝜆(p
1
,…,p
n
)
.
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2532 Virtual Reality (2023) 27:2529–2539
1 3
constraints, Eq.(2) can be simplified to a function depending
only upon
𝛼
and
𝛽
,
If all variables are known, this PF could be calculated
at run-time to dynamically alter the tick rate depend-
ing upon the conditions within the scene. In order to
reduce the complexity of this equation, this paper will
explore three key variables which potentially influ-
ence the visual experience. The three variables explored
are
p1=
medium,
p2=
velocity, and
p3=
complexity.
Once restricted to these three variables,
𝛼
and
𝛽
can be
described as a function
𝛼(medium,velocity,complexity)
and
𝛽(medium,velocity,complexity)
.
3.1 Motivation forchoice ofvariables
Human perception was investigated in relation to three
variables.
The first variable was the digital platform itself. Par-
ticipants were shown the same stimulus in both VR and
on a computer desktop to establish potential differences in
perception between the two digital mediums. This variable
will hereafter be referred to as medium. This is a neces-
sary variable to evaluate whether the increased immersion
(Skarbez etal. 2018; Slater 2018) experienced in the VR
platform will change the sensitivity to tick rate (Shu etal.
2019; Cao etal. 2021).
The second variable is the visual complexity of the
stimulus, referred to here as complexity. Complexity of
objects significantly affects bandwidth requirements, as
more data would be required to update the object on each
tick. Therefore, understanding the influence of complexity
due to increased optical flow (Horn and Schunck 1981)
upon human perception is essential to maximising network
efficiency without visual detriment.
The third variable we considered is the velocity of the
stimulus, denoted throughout as velocity. Previous psycho-
physical experiments have evaluated velocity on a com-
puter desktop and have found it to have a significant effect;
however, the exact influence of velocity has been incon-
sistent. Hulusić etal. (2011) found perceived smoothness
increased as velocities increased, whereas McDonnell
etal. (2007) and Denes etal. (2020) found lower velocity
stimuli were perceived as smoother. Therefore it is worth-
while to explore velocity in VR for it was likely to also
display an effect.
These three variables lead to three hypotheses:
H1 Perception thresholds will be higher in VR.
(3)
Ψ(
x∣𝛼𝛽)=(1−0.01)
1
1+e
−𝛽(x−𝛼)∶𝛼(p1,…,pn),𝛽(p1,…,pn)
.
H2 Complex objects will require higher tick rates than sim-
ple objects.
H3 Stimulus velocity will affect participant sensitivity.
3.2 Overview ofexperiments
The predictive models are developed over the course of two
experiments. The first experiment explores the influence
of all three variables, medium, velocity, and complexity, to
establish the effect each may have upon a PF. The second
experiment refines this evaluation to explore only the varia-
bles that displayed significance in the first experiment. From
the results of the second experiment, predictive models are
developed and validated. Finally, the results and observa-
tions from these experiments are discussed and suggestions
for future development are provided.
4 Experiment 1: broad evaluation
Throughout both experiments, a 1 Alternative Forced Choice
(1AFC) psychophysical methodology was employed (King-
dom and Prins 2016). This method enabled a full PF to be
developed for every participant for each combination of
conditions. Therefore, the perception of smooth motion for
individuals under each of the three variables at a range of
tick rates could be explored, as participant sensitivity influ-
ences the shape of the PF.
4.1 Design
The first experiment followed a 2
×
2
×
2 factorial design,
with complexity and medium as within-participant vari-
ables, and velocity as a between-participant variable. Veloc-
ity was operated as a between-participant variable to halve
the number of trials required for each participant, to reduce
the potential error and drift in results from fatigue. For each
combination of conditions, the corresponding PF was inves-
tigated through three concurrent Weighted Up/Down adap-
tive procedures targeting the 25%, 50%, and 75% thresholds
(Kaernbach 1991). The 50% threshold was targeted through
a step size ratio
Δ−∕Δ+=1∕1
procedure, whilst the 25% and
75% were targeted through
Δ−∕Δ+=3∕1
and 1/3, respec-
tively. Three thresholds were required to estimate the full
shape of the PF, as a single Up/Down method cannot be used
to estimate the slope. Each Up/Down procedure was run for
40 trials, with the first 15 trials excluded from the analysis to
allow the staircase to find equilibrium. Weighted Up/Down
programs with 1/3 step size ratios reach 10 reversals, a com-
mon ending condition, after approximately 40 trials (García-
Pérez 1998). A 1/1 rule was employed with larger step sizes
until the first reversal occurred to accelerate the procedure
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2533Virtual Reality (2023) 27:2529–2539
1 3
to reaching equilibrium (Kingdom and Prins 2016). All Up/
Down staircases were run concurrently and presented in a
randomised order (Bechara etal. 1997). As visual responses
are broadly logarithmic (Varshney and Sun 2013), the Up/
Down staircases operated on tick rates transformed by the
natural logarithm, and step sizes were performed in incre-
ments of 0.05 log-units. All Up/Down staircases began at 4.1
log-units (60.34Hz). Each participant performed 480 trials
and the experiment lasted approximately 40min.
4.2 Participants
Sixteen individuals volunteered for the first experiment, of
which four were female and twelve were male. The partici-
pants’ age varied from 20 to 83, with an average of 40±18.
All involved possessed normal or corrected to normal vision.
4.3 Materials
The experiment was performed in a darkened, empty room to
reduce external distractions. For the VR condition, an HTC
Vive Pro HMD (1440
×
1600p 90Hz) was used and Vive
Wand Controllers for hand tracking. For the desktop condi-
tion, an Acer XB270HU G-Sync enabled monitor (2560
×
1440p 144Hz) was used. All experiments were run from
a PC with an Intel Xeon E5 2690 CPU, 32GB of memory
and a NVIDIA GeForce Titan Xp. Temporal Anti-Aliasing
was applied throughout all trials, in order to reduce flicker-
ing which may have otherwise affected responses(Jimenez
etal. 2011; Almeida etal. 2019). All other post-processing
techniques were disabled.
All trials were performed using a plain darkened tex-
tureless scene, constructed in Unity version 2021.2.8f1, to
reduce external stimuli. The stimulus was positioned 6.25m
in front of the participant and would travel a straight path
perpendicular to the facing direction. Other paths were
explored in the pilot study and a straight path was found
to be most natural. Similar to a theatre stage, the displayed
stimulus would travel from one side of the scene to the
other, appearing from behind one wall before disappearing
behind the other, repeating the same path until a response
was provided by the participant. After receiving an answer,
an inter-trial interval of 2s was shown in which no stimulus
was present. The direction of motion was randomised for all
trials to negate any potential directional biases. Likewise,
the controls for responding true or false were randomised,
though kept constant for each participant to avoid confusion
and to reduce the quantity of lapse results due to misclicks.
Stimuli would travel past the participant at two distinct
velocities, the low velocity was selected to be 1.4m/s as
this is equal to average human walking speed (Mohler etal.
2007) and a higher velocity of 2.5m/s was chosen as the
pilot study suggested it appeared significantly faster than the
alternative stimulus without appearing unnatural and nega-
tively influencing immersion throughout the experiment.
Both of these velocities lie within the band of greatest sen-
sitivity found by Orban etal. (1984) from their experiment
exploring velocity differential detection.
Two different stimuli were presented to participants, in
order to investigate the influence of visual noise from a more
complex moving stimulus. The simple stimulus was a dark
grey, 0.5m radius sphere without textures, meanwhile the
complex stimulus was a photogrammetry of a human, pur-
chased from the RenderPeople asset store. The two stimuli
are depicted in Fig.2. The human model was rigged to use a
walking animation for the low velocity and a jogging anima-
tion for the high velocity.
4.4 Procedure
Participants were informed about the proceedings of the
experiment, after which they gave informed consent. After
providing their age, gender, and previous VR experience at
their own discretion, they were randomly assigned to per-
form the VR or desktop task first. Before the experiment
began, two examples were shown, firstly a stimulus with
a low tick rate (12Hz) to demonstrate the noticeable jitter
within the movement. Secondly, a high tick rate example
(200Hz) was presented to explain how motion will appear
smooth at sufficiently high tick rates. Following the two
Fig. 2 Two different stimuli
were presented in Experiment
1. Left: The human stimulus
Right: The sphere stimulus
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2534 Virtual Reality (2023) 27:2529–2539
1 3
examples, participants were given an opportunity to ask
questions before the main experiment began, after which no
interaction with the participant occurred until the experi-
ment concluded. After the completion of the first half of the
experiment, participants took a 10min break before continu-
ing with the alternate VR or desktop task.
4.5 Results
Each participant’s 25%, 50%, and 75% measurements were
fitted through a Levenberg-Marquardt fitting algorithm (Lev-
enberg 1944) to determine their PF for each of the eight
combinations of medium
×
complexity
×
velocity. The PFs
are reported as threshold
𝛼
and slope
𝛽
, and descriptive sta-
tistics are provided in Table1.
From the calculated set of thresholds and slopes, a Sha-
piro-Wilk normality test (Shapiro and Wilk 1965) was per-
formed on all the separate combinations of variables and
normality was found for all cases.
A three-way mixed ANOVA was performed on the
thresholds and slopes for all participants. For the main effect
of medium, sensitivity to tick rate was significantly higher
within VR than on a desktop monitor and the effect size cal-
culated by partial omega squared analysis displayed a large
effect (p < 0.01,
𝜔2
p
=
0.407). Reverting the log-transfor-
mation, the desktop mean threshold translates to 42.9Hz,
whilst the VR mean threshold is 64.1Hz. For the main
effect of complexity, no statistical significance was found (p
= 0.873,
𝜔2
p
=
−
0.063), with mean thresholds at approxi-
mately 52Hz. Negative effect sizes were obtained (Okada
2017) and the mean difference between the two conditions
was 0.024 whilst the 95% confidence interval was (
−
0.153,
0.201), therefore the null hypothesis cannot be rejected. For
the main effect of velocity, significance was displayed (p
=
0.020,
𝜔2
p
=
0.223), with sensitivity decreasing for increased
velocities, from 65.4Hz at 1.4m/s to 42.1Hz at 2.5m/s. No
statistical significance was found for slopes under any con-
ditions. Similarly, no significance was found for any cross-
variable interaction for thresholds or slopes. Analysis on the
participants’ data found there to be no significant difference
(p>0.05) for age, gender, or previous VR experience.
Tukey post-hoc tests for means comparison agreed with
the single variable ANOVA results, suggesting that for
thresholds, a significant difference was found for medium
(p<0.01) and velocity (p=0.020), whilst no statistical
significance was found for complexity (p=0.785) or slopes
under any conditions.
5 Experiment 2: renement
Since complexity did not display any significance in the first
experiment, in the second experiment it was disregarded and
a spherical stimulus was used for all trials. Therefore, a 2
×
2
factorial design was employed, where velocity and medium
were both evaluated as within-participant variables. As such
the total number of trials remained at 480, but now with both
velocities presented to every participant.
The same up/down methodology targeting the 25%, 50%,
and 75% thresholds as Experiment 1 was utilised. The exper-
imental procedure for the participant was also identical to
Experiment 1, with a single stimulus presented per trial and
participants were given the same task of identifying whether
the movement of the stimulus appeared smooth.
Eleven participants volunteered for the second experi-
ment, none of whom took part in the first experiment. Two
were female and nine were male. The average age of the
participants was 20.1 years. All had normal or corrected to
normal vision.
5.1 Results
For each of the four medium
×
velocity combinations, the
same Levenberg-Marquardt fitting procedure was applied
as in Experiment 1. Descriptive statistics are provided in
Table2.
To compare the results, two-way repeated measures
ANOVA was performed and effect sizes were calculated
from partial omega squared. Both medium (p
=
0.040,
𝜔2
p
=
0.406) and velocity (p< 0.001,
𝜔2
p
=
0.737) displayed
a significant effect upon the threshold, though no signifi-
cant interaction effect was found for medium
×
velocity
(p
=
0.650,
𝜔2
p
=

−
0.094). Sensitivity increased in VR in
comparison with desktop, and similarly higher tick rates
Table 1 Descriptive statistics for Experiment 1
Variable
𝛼
Mean
𝛼
SD
𝛽
Mean
𝛽
SD
Desktop 3.756 0.113 4.781 1.248
VR 4.157 0.131 4.072 1.578
Sphere 3.968 0.098 4.426 1.474
Human 3.945 0.146 4.426 1.352
Velocity low 4.176 0.140 4.325 1.482
Velocity high 3.736 0.104 4.528 1.344
Table 2 Descriptive statistics for Experiment 2
Variable
𝛼
Mean
𝛼
SD
𝛽
Mean
𝛽
SD
Desktop 3.463 0.325 7.339 5.565
VR 3.856 0.344 2.670 0.882
Velocity low 3.539 0.326 5.510 5.123
Velocity high 3.780 0.411 4.499 4.049
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2535Virtual Reality (2023) 27:2529–2539
1 3
were required for motion to appear smooth at increasing
velocities.
6 Building themodel
From the results of the second experiment, a model was
developed to describe the variation within the entire sam-
pling group. Because complexity was disregarded after the
first experiment, the model was defined for medium and
velocity only.
Logistic regression via maximum likelihood estimation
is the most common technique for estimating a group PF
from a collection of results (Akaike 1998; Prins 2019). How-
ever, it did not accurately describe the collective sampling
group from these experiments. This is because the method
consistently underestimated the slope of participants, result-
ing in maximum likelihood estimates with slope param-
eters significantly lower than the measured data, such as
𝛼VR 2.5 m/s =3.93
and
𝛽VR 2.5 m/s =0.91
, and with
R2
=0.037.
We present an alternative method for combining the col-
lective sampling group based upon the decomposition of
means and standard deviations (Altman etal. 2000). The
logistic function can be described as a cumulative distribu-
tion function and the derivative of this logistic function pro-
duces the probability distribution function of the threshold,
with a defined standard deviation (Warren etal. 2022). The
derivative of Eq.3 is the logistic distribution scaled by 0.99
due to the lapse rate assumption
and as such the slope
𝛽
can be converted into a standard
deviation
𝜎
through the variance of the logistic distribution
By converting the slope into a standard deviation of the
threshold, it enables the results of individual participants
to be combined through the decomposition of means and
standard deviations. The combined threshold and standard
deviation can be transformed back into a PF through Eq.5,
thus producing a PF for the whole sampling group.
(4)
d
Ψ
dx
=0.99 𝛽e
−𝛽(x−𝛼)
(1+e
−𝛽(x−𝛼)
)2
(5)
𝜎
2=
1
0.99
2
𝜋
2
3𝛽
2
.
The merged data for the conditions of medium
×
velocity
are listed in Table3 and depicted in Fig.3. The models for
𝛼
and
𝛽
clearly display the results from Table2, with VR
requiring higher thresholds over a desktop and threshold
increasing for higher velocities.
The Bayesian Information Criterion (BIC) is a popu-
lar method for evaluating the suitability of various mod-
els attempting to describe a set of psychophysical results
(Schwarz 1978). The BIC can be transformed into a Schwarz
weight for probability-based optimal model selection
(Wagenmakers and Farrell 2004). Four different models
were developed and evaluated through the BIC analysis.
Model 1 is the null model in which no variables hold any
influence. Model 2 and 3 are models where significance is
displayed for only medium or velocity, respectively. Finally,
Model 4 is for the medium
×
velocity condition where
medium and velocity are both significant.
The Schwarz weights for each model are displayed in
Table4. The model with the highest probability is Model 4
with the medium
×
velocity condition (p = 1.000). Because
Model 4 was selected with the highest Schwarz weight, it
can be concluded that both velocity and medium have a sig-
nificant effect on sensitivity with respect to tick rate, which
is in line with the ANOVA results. The BIC for Model 2 is
lower than for Model 3, suggesting medium has a stronger
Table 3 Models for medium
×
velocity conditions Variables (m/s)
𝛼
𝛽
Desktop 1.4 3.347 3.388
Desktop 2.5m/s 3.578 2.697
VR 1.4m/s 3.731 2.320
VR 2.5 3.981 2.074
Fig. 3 Predictive models for medium
×
velocity conditions
Table 4 BIC results from Experiment 2
Model BIC Schwarz weight
1. Null 7397 0.000
2. Medium 7226 0.000
3. Velocity 7320 0.000
4. Medium
×
velocity 7176 1.000
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2536 Virtual Reality (2023) 27:2529–2539
1 3
influence on sensitivity than for the different velocities. This
can also be observed through the
𝛼
values in the predictive
model, where changing the display medium evokes a change
in the threshold of
Δ𝛼≈0.4
log-units, whilst changing the
velocity only induces a shift of
Δ𝛼≈0.25
log-units.
A simpler, velocity-independent model may be easier
to implement for most networks, as it removes the require-
ment to calculate the velocity relative to the viewer, thus
the Model 2 parameters are provided here. For the desktop
condition,
𝛼desktop =3.463
and
𝛽desktop =2.932
, whilst for the
VR condition,
𝛼VR =3.856
and
𝛽VR =2.162
.
6.1 Application
Threshold predictions for a defined probability can be
obtained from the models through the inverse of Eq.(3),
where p is the desired response probability,
𝛼
and
𝛽
are the
model parameters from Table3, and x is the log-transformed
tick rate. Due to the nature of this function as well as the
guess rate and lapse rate assumptions, p is restricted to the
range
0<p<0.99
. Threshold predictions for a range of
common probabilities are stated in Table5.
6.2 Validation
A k-fold validation was performed to test the accuracy of
model predictions and to compare the proposed model to
the traditional maximum likelihood estimation algorithm.
One-fold or leave-one-out analysis evaluates the validity of a
model by removing a single data point and comparing it to a
predictive model developed without the removed data point.
The method applied here will compare the validity of tick
rate predictions through the Wasserstein distance (Wasser-
stein 1969). The Wasserstein distance compares two curves
through the absolute difference integrated over all space and
for cumulative distribution functions, it can be defined as
∫ℜ
∣PF
model
−PF
true
∣d
x
.
This metric was calculated for both the proposed model
and the maximum likelihood method and out of the 44 total
(6)
x
=
−ln
(
0.99
p
−1
)
𝛽
+𝛼
,
data points, 43 were more closely modelled by the proposed
model. The proposed model had average Wasserstein dis-
tance of 0.353 with a standard deviation of 0.157, whilst
the maximum likelihood model had an average Wasserstein
distance of 0.694 and a standard deviation of 0.279. This is
due to the maximum likelihood model consistently under-
estimating the slopes of individuals, resulting in large errors
at the higher response probabilities. The individual results
of various conditions were equally compared, and the larg-
est differences were found in the desktop 2.5m/s condition
with an average of 0.406 log-units, whilst the best predicted
was the VR 1.4m/s condition with an average difference of
0.296 log-units. From the results of this validation, it can be
concluded that the proposed model more closely predicts
the individual results of participants when compared to the
traditional maximum likelihood estimation technique.
7 Discussion
The results of these two experiments support our hypotheses
that medium and object velocity display a significant effect
upon perceived smoothness of tick rate; however, no sig-
nificance was found for the visual complexity of a stimulus.
VR consistently required higher tick rates for motion to
appear smooth in comparison with the desktop equivalent,
thus we accept H1. VR has been found to elicit stronger
sensations of presence within virtual environments when
compared to computer desktops (Shu etal. 2019), and
human perception has been shown to be more sensitive in
VR, with Niu etal. observing participants were more sensi-
tive to surface roughness and specularity in VR (Niu and
Lo 2022). Table5 quantifies the requirement for higher tick
rates in VR. The results suggest that the minimum required
tick rate lies at 29Hz for a desktop application and at 42Hz
for a VR application. However, for the majority of the popu-
lation to consistently perceive the motion as smooth, the
model predicts 56Hz would be required for a desktop whilst
VR would need 113Hz. The 113Hz prediction exceeds the
maximum frame rate of the HMD (90Hz), thus a tick rate
to match the frame rate of the HMD may be applied without
detriment to the experience.
H2 predicted that participants would be more sensitive
to complex objects, however, Complexity displayed no sig-
nificant effect upon tick rate thresholds, therefore H2 can-
not be accepted. Two different stimuli types were presented
in Experiment 1. The first was a simple sphere, whilst the
second was a human avatar displaying increased complex-
ity due to the motion of the hands and feet in the walking
animation. ANOVA results found no significance for the
complexity variable, therefore our findings suggest that tick
rate may be controlled independently of the visual intri-
cacy of an object. For this study, the visual complexity was
Table 5 Threshold predictions based upon a probability of perceived
smoothness. All values have the log-transformation reverted and have
units of Hz
Prob (%) Desk. 1.4m/s Desk. 2.5m/s VR 1.4m/s VR 2.5m/s
50 28.60 36.08 42.08 54.14
75 39.79 54.64 68.17 92.88
90 56.09 81.10 112.55 162.74
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2537Virtual Reality (2023) 27:2529–2539
1 3
investigated in relation to update frequency; however, further
research should be performed into the complexity of stimuli.
For objects with complex geometry, more data must be sent
each update and therefore will require greater bandwidth
to maintain the same tick rate. In bandwidth constrained
scenarios, complex objects would be forced to shift down
the presented models to remain within the limitations of
the bandwidth; therefore, a predictive model could be built
based upon the size of the data transmitted and bandwidth
availability, to find the balance between reducing the com-
plexity of the object and reducing the tick rate to minimise
the impact on the participant’s experience.
The results from this study support H3, because Velocity
displayed a significant effect in both experiments; however,
the direction of the effect changed between Experiment 1
and Experiment 2. In the first experiment, velocity was a
between-participant variable and results suggested that
sensitivity decreased for increasing velocities, whilst in the
second experiment velocity changed to a within-participant
variable, and sensitivity changed to increase for increasing
velocities. The difference observed in our experiments is
likely to be due to the difference in methodology between
experiments. In the first experiment, only one velocity was
presented to each participant, whereas in the second experi-
ment both velocities were shown and as such judgements of
smoothness could be made relative to how smooth the other
stimulus class appeared. It is this change in relative percep-
tion that may have caused the shift in results. This contradic-
tion of results is not unique to this study. McDonnell etal.
(2007) found for animations at higher velocities, a higher
frequency was required, whilst Hulusić etal. (2011) found
increased velocities were perceived as smoother in compari-
son with lower velocities, however, only for trials with no
multimodal stimuli. As participants in a virtual environment
are likely to be exposed to multiple velocities in a short dura-
tion, and thus relative perception can affect their experience,
the results from the within-participant evaluation are more
likely to accurately describe participant sensitivity to tick
rate in a practical application. The predictions from Table5
suggest that a faster moving stimulus required a 26% to 30%
higher tick rate for both mediums.
8 Conclusions andfuture work
The influence of tick rate upon human perception of smooth-
ness was investigated and predictive models were developed.
Over the course of two experiments, three key variables were
studied through a 1 alternative forced choice psychophys-
ics methodology, the display medium, the velocity, and the
complexity of the object.
The results suggest that VR requires significantly higher
tick rates before motion appears smooth, and similarly
sensitivity increases for higher velocities. The complexity
of the object had no significant effect on tick rate sensitiv-
ity. The predictive models developed here could be used
to predict participant tick rate thresholds at any desired
probability and they establish a set of guidelines for appro-
priate tick rates in the future applications based upon the
conditions in the scene. An important observation is that
the majority of the predictions from the models lie sig-
nificantly below the 90Hz frame rate of the HMD, there-
fore tick rate may be decoupled from frame rate and thus
operate at sub-frame rate frequencies without negatively
affecting participant experience.
There are likely to exist other variables not investigated
in this study, which may also exert an influence upon an
individual’s PF. VR enables binocular vision unlike a
monitor, and in this work stimuli were only presented at
one distance from the observer, so further research could
be performed to establish whether a changing distance
from the observer will affect perception. Throughout these
experiments, the stimulus was always the focal point of the
participant’s attention and attention has previously been
shown to significantly affect temporal sensitivity (Carver
and Brown 1997). Additional research could evaluate
whether objects within a virtual environment that are not
the centre of attention could update at sub-threshold fre-
quencies without any perceptible difference to a user.
Alongside exploring new variables, the present vari-
ables could be expanded to explore greater extremities of
conditions. Participants were only tested on two differ-
ent media, VR and desktop, so further research could be
performed to expand these results to different levels of
immersive media, from a small mobile phone screen to
Mixed Reality headsets such as the Microsoft HoloLens.
Additionally, only two velocities were presented, selected
as velocities that are likely to be encountered in a vir-
tual environment. The testing range could be expanded
to explore more extreme values and such results could be
compared to the results from Orban etal. (1984) to estab-
lish whether tick rate smoothness follows a similar shape.
In this experiment, the PFs for each participant were
evaluated from the 25%, 50%, and 75% thresholds; how-
ever, the shape of the curve at more extreme thresholds
such as 10% and 90% were not explored. As a result, in
a practical implementation of this model, there is greater
uncertainty in the true position of the high probability
thresholds. Therefore, further research needs to be per-
formed to establish whether the logistic function is the
true shape of the PF or an alternative sigmoidal function,
such as the Weibull or Cumulative Normal distribution
functions would more closely describe the data for prob-
abilities closer to certainty.
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2538 Virtual Reality (2023) 27:2529–2539
1 3
Funding This research was funded by the EPSRC DTP fund and the
Leete Award from the Worshipful Company of Engineers.
Data availability The datasets generated during the current study are
available from the corresponding author on reasonable request.
Declarations
Conflict of interest The authors have no competing interests to declare
that are relevant to the content of this article.
Ethical approval Ethical approval was granted by BSREC (BSREC
143/20-21) and informed consent was received from every participant.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article’s Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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