P
M
Humans can separately perceive
distance, velocity, and acceleration
from vestibular stimulation
Markus von der Heyde, Bernhard E. Riecke, Douglas. W. Cunningham, and Heinrich H. Bülthoff
Max−Planck−Institute for Biological Cybernetics
Tübingen
Germany
email: [email protected], web: www.kyb.tuebingen.mpg.de
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distance [m]
Purpose
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If the vestibular system is providing a spatial reference frame, one of the
central questions is which motion parameters are used to specify the change
in body position.
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velocity [m/s]
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Methods
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perceived X distance
perceived X velocity
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block 3: vel.
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perceived H distance
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i
The coefficients (Di, Vi, Ai) describe for each experimental condition the
subjects’ (i) response Ji across all 30 factorial combinations (see Fig. 7).
There was no substantial difference between judgments of translational
and angular movements.
Conclusions
One can derive distance and
velocity from the vestibular
cues.
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Despite the fact that the vestibular system measures acceleration only, peak
velocity and traveled distance can be obtained from it. Furthermore, it is
particularly unclear why the acceleration judgment looks like a velocity
judgment. One possible explanation is that since velocity is encoded at a
very early stage (in the vestibular nerve), it may replace or mask the
acceleration signal.
In sum, the vestibular system is providing a good spatial reference frame,
which does enable spatial updating.
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perceived distance
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real acceleration [m/s2]
perceived velocity vs. real acceleration
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real distance [m]
perceived velocity vs. real distance
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real distance [m]
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real velocity [m/s]
perceived velocity vs. real velocity
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real acceleration [m/s ]
perceived acceleration vs. real acceleration
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real velocity [m/s]
perceived acceleration vs. real velocity
perceived acceleration
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perceived acceleration
perceived acceleration
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perceived velocity
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perceived distance vs. real acceleration
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perceived distance
perceived distance vs. real velocity
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real velocity [m/s]
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real acceleration [m/s2]
Figure 5: Perceived values vs. physical stimulus. The nine graphs show the data of one typical subject in
the Y (left-right translation) condition. The rows contain the data for distance, velocity, and acceleration
judgments, respectively. Each column plots those data against the physical distance, velocity, and acceleration of the stimulus. Therefore, the diagonal displays the subject’s answers correlated to the physical
stimuli. Each plot displays the data twice: the left-hand side groups the data for identical peak acceleration
and the right-hand side groups the same data for identical distance.
perceived distance
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real acceleration [m/s2]
model fit for perceived distance
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real acceleration [m/s2]
(perceived − model) distance
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real acceleration [m/s2]
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real acceleration [m/s2]
(perceived − model) velocity
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real acceleration [m/s2]
model fit for perceived acceleration
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(perceived − model) acceleration
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real acceleration [m/s2]
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perceived acceleration
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real acceleration [m/s2]
model fit for perceived velocity
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perceived velocity
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real distance [m]
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real distance [m]
real distance [m]
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real distance [m]
A model, which assumes a linear combination of distance, velocity, and
acceleration, was fitted to the individual data with minimal error (see Fig. 6
for an example of the subjects’ responses, the model fit, and the difference
(error) between them).
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perceived velocity
The correlation of perceived and real velocity was linear and showed no
systematic influence of distances or accelerations. High accelerations were
drastically underestimated while accelerations close to threshold were
overestimated, showing a logarithmic dependency (see Fig. 5(i)). The judged
acceleration was close to the velocity judgment but clearly distinct from
distance judgments.
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perceived H acceleration
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real distance [m]
Subjects judged the distance, velocity, and acceleration quite consistently,
but with systematic errors (see Fig. 5). The distance estimates showed a
linear scaling towards the mean response and were independent of
accelerations. The histograms of the verbal responses reflect this tendency
towards the mean (see Fig. 4).
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real distance [m]
perceived acceleration vs. real distance
real distance [m]
Figure 3: Experimental design. This example shows the order of blocks for the X (forward-backward)
condition for one subject. After a short introduction to the purpose of the experiment and the task, this
subject was asked to judge acceleration in the first block. These 240 trials (60 trials in 4 repetitions) were
followed by a break and than the next two blocks with a break between them. The 60 trials of each repetition
were randomized over the 5*6 conditions in both directions. Each individual trial had a maximum length of
4 seconds followed by a brief period during which the subject gave the verbal judgment to the experimenter.
J = D Distance + V V elocity + A Acceleration + Error
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Results
Judgments were correlated
with distance, velocity, and
acceleration.
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% judgements
% judgements
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perceived velocity
perceived distance
random order of
60 trials
movement: subj. judgement: movement: subj. judgement:
1−4sec
<15sec
1−4sec
<15sec
Figure 1: The Stewart-Platform motion simulator. The subject is seated
blindfolded and with headphones on the platform. The platform is able to
move in all 6DOFs independently.
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real distance [m]
4 rep. of 60 trials
5*6 cond. in 2 directions
...
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perceived H velocity
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perceived Y acceleration
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perceived distance vs. real distance
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Figure 4: Histograms of subjects’ responses. The red bars represent the mean percentage of the subjects’
responses. The green bars refer to the standard error of the mean, with the ”whiskers” depict one standard
deviation. The blue “stars” show the right answer percentages.
each rep.:
random order of
60 trials
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real distance [m]
block 2: dist.
4 rep. of 60 trials
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real distance [m]
block 1: acc.
4 rep. of 60 trials
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% judgements
% judgements
% judgements
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perceived Y velocity
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perceived Y distance
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break
break
intro
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% judgements
The vestibular stimuli consisted of Gaussian−shaped translatory or rotatory
velocity profiles with a duration of less than 4 seconds (see Fig. 2). The
movement was always confined to one degree of freedom per session (X:
translation forward−backward, Y: translation left−right, H: turn around
vertical body axis). The full two−factorial design covered 6 peak
accelerations above threshold and 5 distances with 4 repetitions (see Fig. 3).
In three separate blocks, subjects were asked to verbally judge on a scale
from 1 to 100 the distance traveled or the angle turned, as well as the
maximum velocity and maximum acceleration.
perceived X acceleration
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% judgements
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Twelve blindfolded naive volunteers (ages between 19 and 29) participated
in three sessions of a psychophysical experiment using a Stewart−Platform
(see Fig. 1). The subjects were seated on the platform and moved on
predefined trajectories. Auditory cues were excluded during the entire
experiment.
Figure 2: The vestibular stimuli. The translation profiles were created from the Gaussian-shaped velocity
profiles. The acceleration describes a function close to a sinusoidal profile. The plot shows the factorial
combination of 5 distances (5, 10, 15, 20, 25 cm) and 6 accelerations (0.1, 0.2, 0.4, 0.6, 0.8, 1.6 m=s2 ).
Profiles with the same maximum peak acceleration are plotted in the same color.
% judgements
We asked for distance, velocity,
and acceleration judgments.
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The vestibular system is known to measure changes in linear and angular
position as acceleration. Can humans judge these vestibular signals as
acceleration itself and integrate them to reliably derive velocity and distance
estimates?
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acceleration [m/s ]
What spatial information can
be derived from vestibular
cues?
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real acceleration [m/s2]
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Figure 6: Model fit to the data. The nine graphs show the same data as Fig. 5. This time, each plot in
the first row displays one block of the experiment. The color encodes the mean of the subject’s judgments
across all factorial combinations. The second row is the result of the fitted model to the individual data of
the first row. Finally, the last row depicts the difference between the model and the actual data.
Session: X block: dist.
Session: X block: vel.
Session: X block: acc.
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Session: Y block: dist.
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Session: Y block: vel.
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Session: H block: dist.
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Session: H block: vel.
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Session: Y block: acc.
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Figure 7: Coefficients of the model. The nine graphs display the mean of the coefficients from the model
(see Fig. 6) for all nine experimental conditions. The rows show the three sessions: X (forward – backward
translation), Y (left – right translation, and H (turn around the body’s vertical axis). The columns show the
different experimental blocks of each session (distance, velocity and acceleration judgment). The bars refer
to the standard error of the mean, and the ”whiskers” depict one standard deviation.