Perception, 1996, volume 25, pages 109-119
Haptic aftereffect of curved surfaces
Ingrid M L C Vogels, Astrid M L Kappers, Jan J
Koenderink
Helmholtz lnstituut, Princetonplein 5, 3584 CC Utrecht, The
Netherlands
Received 15 May 1995, in revised form 14 November 1995
Abstract. A haptic aftereffect of curved surfaces
is demonstrated. Two spherical surfaces were
presented sequentially to human subjects. They rested one hand on
the first (conditioning) surface.
After a fixed conditioning period they transferred their hand to
the second (test) surface and judged
whether the test surface was convex or concave. In experiment I
the curvature of the conditioning
surface was varied; the subject's judgment of convexity or concavity
of the test surface was strongly
shifted in the direction opposite to the curvature of the
conditioning surface (negative aftereffect).
Therefore, subjects judged a flat surface to be concave after being
exposed to a convex surface. After a
conditioning period of 5 s the shift was about 20% of the curvature
of the conditioning surface.
In experiment 2 the duration of the conditioning period was
varied; the magnitude of the aftereffect
could be described by a first-order integrator with a time constant
of 2 s. In experiment 3 the time
interval between the conditioning period and the touching of
the second surface was varied; the
magnitude of the aftereffect could be described by an exponential decay
with a time constant of 40 s.
It is concluded that the haptic aftereffect of curved surfaces is an
important effect that occurs almost
instantaneously and lasts for an appreciable period.
1 Introduction
Probably all modalities give rise to aftereffects. Gibson (1937) was one
of the first to
emphasise this similarity between the senses. In his paper he
described several exam-
ples of visual, tactual, and gustatory stimuli which lead to
adaptation with negative
aftereffects. Adaptation and aftereffect, both of which are caused
by prolonged exposure
to a constant stimulus, are in fact two
distinct phenomena. Adaptation affects the
perception of the stimulus itself. Aftereffects are defined as a
change of the 'physical
phenomenal correspondence' of the stimulus dimension
occurring after prolonged
stimulation. The term adaptation is often used as a synonym
for various ill-defined
terms such as normalisation, satiation,
habituation, or fatigue. Such careless usage
often leads to unfortunate misunderstandings. For instance,
Gibson (1937) assumed
that adaptation and aftereffect are two facets of a
single process, whereas Colheart
(1971) argued that they may be quite separate effects. In
this paper we use the men-
tioned conventions.
In modalities such as vision or hearing, adaptation
and aftereffects have been
investigated intensively. In haptic perception, which relies on both
the cutaneous sense
and kinesthesis, these phenomena have received
considerably less attention, although
they have already been known phenomenologically for a
long time. Here a number of
examples of studied haptic aftereffects is presented. We
certainly do not aim to be
complete.
It is well known that tepid water feels cold to a hand
previously exposed to hot
water. Abbott (1914) mentioned that the phenomenal
'neutral' temperature appears to
be so adaptable that it can be raised as high as 39
°C, whereupon 37 °C feels cold
and it can fall as low as 11 °C, whereupon 12 °C feels warm.
Thalman (1922) applied
a cord of rough material to the
underside of the bare forearm of human subjects.
The cord moved in a constant direction and with a constant
velocity. As soon as the
movement stopped, subjects perceived a movement
in the opposite direction both
when the cord was removed from the arm and when the cord
remained in contact with
110
IMLC Vogels, A M L Kappers, J J Koenderink
the arm. Wohlgemuth (1911) and Hazlewood (1971) failed
to find evidence in support
of a tactile movement aftereffect. Recently, Hollins
and Favorov (1994) demonstrated
that the texture of the surface applied to the skin might
determine the occurrence or
nonoccurrence of the aftereffect. When subjects cupped their hand around
a moving
drum which was covered with a smooth microtexture
combined with a square wave
of low spatial frequency, the aftereffect
was especially effective. The vividness and
duration of the aftereffect increased
over the range of adaptation durations explored
(30 180 s). Gibson (1933) found that after 3 min of
moving the fingers over a curved
cardboard edge a straight edge felt curved in the opposite
direction. Nafe and Wagoner
(1941) investigated pressure adaptation. They showed
that tactile sensation produced
by a weight resting on the skin disappeared when the
rate at which the weight sank
into the skin had decreased below
a minimum rate required to stimulate. The removal
of the weight produced a clear tactile sensation.
Koehler and Dinnerstein (1947)
showed that when the width of a test bar felt with
one hand had to be matched with
the other hand, the matching depended
on a satiation bar previously felt with the
tested hand. A satiation object smaller than the
test object enlarged the matched width
of the test bar; a wider satiation object had the opposite
effect. Gibson (1963) investi-
gated the aftereffect of the perception of
vergence. He found that two parallel palm
boards felt divergent after they had been held
convergent for some time, and felt
convergent after being held divergent. In order to make the surfaces feel
parallel they
had to be rotated over about 50 to 10°, according
to the amount of convergence or
divergence of the hand during adaptation. After
an adaptation period of 12 s the
aftereffect did not show any increase with time and after
a so-called recovery period of
56 s the aftereffect still had no tendency to decrease. Hahn
(1966) investigated vibro-
tactile adaptation by two different methods. In the first
method he measured the
absolute threshold, which is the just-noticeable amplitude of
the sinusoidal vibration.
In the second method he measured the subjective magnitude,
by matching the sensa-
tion in the adapted finger to that in the contralateral finger.
Increasing the time of
vibrotactile stimulation resulted in an increase of the threshold
and a decrease of the
subjective magnitude. Both methods showed the
same temporal course of adaptation.
Adaptation continued to increase after a period of 20 min.
Not only simple aftereffects, like previous examples, but also
contingent aftereffects
have been demonstrated in the haptic modality In contingent
aftereffects, a correlation
between two stimulus dimensions is established during
an inspection period, and
during a subsequent test period the
appearance of an object on one dimension is
dependent on the location on the other dimension. If
a narrow inspection block,
located on the subject's left, and a wide block, located
on the right, are alternately
grasped by a subject between the fingers of
a single hand then an intermediate test
block presented on the left is perceived wider than
an equal block on the right (Walker
and Shea 1974). The perceived width of the test block is contingent
on the location of
the block. If a rectangular inspection block is oriented with its
long side horizontally
and with its short side vertically, and if a subject alternately
grasps this block horizon-
tally and vertically, then the horizontal side of
a subsequently presented square test
block is perceived shorter than the vertical side (Walker 1977).
Here the perceived size
of a test block is contingent on the orientation of the block.
Thus, many haptic stimuli give rise to
an aftereffect. Because the haptic sense is
particularly important for the recognition and manipulation of
objects, it would be
useful if the haptic sense provided us with veridical information
about the shape and
curvature of environmental objects. Because aftereffects could affect
veridicality,
it
would be of interest to know whether aftereffects
occur when subjects touch curved
three-dimensional objects. Such an aftereffect of curved surfaces
has not been reported
in the literature.
Haptic aftereffect of curved surfaces
111
It is known that in general the categorisation of curvature of
one-dimensional strips
is not veridical. Hunter (1954) and Davidson (1972) let subjects judge
whether strips
were convex, concave, or straight. All
subjects judged the straight strips to be curved
and the strips which were judged to be straight typically corresponded to a
curved
strip. So, straight was not judged to be straight. It is conceivable that in
the case of the
judgment of curved surfaces, the surface which is judged to be flat (phenomenal
flatness)
also corresponds to a curved surface. The interesting question is, however,
whether the
phenomenal flatness, veridical or not, is constant over time. The experiments
reported
here are designed to investigate this. In the first experiment we
investigated whether the
categorisation of curvature is influenced by a previously touched curved
surface. Two
spherical surfaces (a conditioning surface and a test surface) were presented
sequentially.
We measured which curvature of the test surface was judged to
be flat for several
differently curved conditioning surfaces. We found an aftereffect; the
phenomenal
flatness depended on the curvature of the conditioning surface. In
experiment 2 we
investigated how much time was needed to build up the aftereffect.
The magnitude of
the aftereffect was measured for several different periods of time
during which the
conditioning surface was touched (conditioning period). In experiment 3 we
investigated
whether the aftereffect was maintained or whether it disappeared
after the touching
had ceased. The magnitude of the aftereffect was measured for
several time intervals
between the conditioning period and the touching of the test surface.
2 Experiment 1
In the first experiment we tested whether judgments of convexity or
concavity of a
spherical surface are influenced by the curvature of a previously touched
surface. The
results of this experiment can give us an idea of how haptic curvature
information is
processed. Does the haptic system possess an absolute internal reference for curvature
or does recalibration occur? The results are
also important for other haptic experiments:
does it make sense to let subjects judge the absolute curvature when aspects
of haptic
curvature perception are being investigated?
2.1 Method
2.1.1 Experimental setup. The stimuli had a spherical upper
surface, either convex or
concave, and a flat bottom which rested on a
table (see figure 1). The diameter of the
stimuli was 20 cm and the total height ranged between 2.5 and 6.5 cm.
This height
was not directly related to the curvature,
because we randomised the base height.
20 cm
Figure 1. Example of a convex spherical stimulus. All stimuli had a flat bottom
and a diameter
of 20 cm. The height difference H between the total height of the stimulus
and the base
height B was 2 cm for the largest curvature (4 m-I) and 0.125 cm for the
smallest curvature
(0.25 m-'). The total height ranged between 2.5 and 6.5 cm.
H
B
112
IMLC Vogels, A M L Kappers, J J Koenderink
The curvature ranged from 4 m-1 to 4 m-1 and two successive curvatures differed
by a factor -12- (the whole set of curvatures being 4, 2.8, 2, 1.4, 1, 0.7, 0.5,
0.35, 0.25, 0, 0.25, 0.35, 0.5, 0.7, 1, 1.4, 2, 2.8, and 4 m-1). Curvature is convention-
ally expressed as reciprocal radius, so a sphere with radius 2
m has a curvature of
0.5 m-1. A plane has zero curvature and the curvature of the tip of
a needle would
tend to infinity. A positively curved surface is called convex,
a negatively curved surface
is called concave.
2.1.2 Subjects. Three naïve paid subjects, about 20
years old, participated in this
experiment; one was a strongly left-handed female (GD) and two
were strongly right-
handed males (MH and EK). The degree of left/right-handedness is defined by Coren
(1993). None of the subjects reported any haptic deficiencies.
2.1.3 Procedure. Subjects were seated behind a curtain in front of
a table. They put
their right hand under the curtain so that they could touch the stimuli without seeing
them. In each trial subjects put their hand on a surface (conditioning surface) for
a fixed
conditioning period of 5 s. After that period they transferred their hand
to a second
surface (test surface). Subjects had to decide whether this second surface
was convex
or concave. They were not allowed to move their hand over the surfaces. All stimuli
were in the same position with respect to the thorax when they were touched. Seven
conditioning surfaces were used, with curvatures of 4, 2, 1, 0,
1, 2, and 4 m-1.
In order to measure the phenomenal flatness we presented each conditioning surface
together with nine differently curved test surfaces. Each combination of conditioning
surface and test surface was presented 15 times. The total number of presentations
was thus 945 (7 conditioning surfaces x 9 test surfaces x 15 presentations). All presen-
tations were randomly distributed over seven sessions. Each session took about 1 h,
so for each subject the experiment involved 7 h in total.
We adapted the range of test surfaces to the curvature of the surface judged
to
be flat. This was done by means of a pilot experiment in which
we estimated which
surface was judged to be flat for each conditioning surface and each subject. The nine
test surfaces were chosen symmetrically around this phenomenal flat surface. In this
way
the range of test surfaces was optimised for each conditioning surface.
2.2 Results
In figure 2 we present the results in the case of a flat conditioning surface (0 m-1) for
subject GD. The percentage of convex judgments is plotted against the
curvature of
the test surface. The psychometric function is fitted with
an error function, according
to the Levenberg Marquardt method (Press et al 1988). This method minimises x2.
Figure 2 is a typical example of how well the function fits the data (x2
= 3642).
The fit can be characterised by two parameters: the shift and the threshold. The shift
corresponds to the value of the 50% point. In our analysis the shift of the psycho-
metric curve is called 'phenomenal flatness' because the curved surface for which
convex and concave judgments are equally frequent is assumed to be perceived as flat.
The threshold, in this case the threshold of curvature detection, is inversely
propor-
tional to the steepness of the curve and corresponds to the difference between the
values of the 50% and 85% points. Because the psychometric
curve is symmetrical,
the threshold also corresponds to the difference between the values of the 50%
and
15% points.
It can be seen that in figure 2 the value of the 50% point is
not zero. In this
example, the surface which is perceived as flat corresponds to
a geometrically concave
surface. For all three subjects phenomenal flatness corresponded
to a surface with
negative curvature.
1
Haptic aftereffect of curved surfaces
113
100:
807
60.
threlold
40.:
0
20
0
)1
shift
-1 0
-0.5
0.0
0.5
1 0
Curvature/m-1
Figure 2. The percentage of convex judgments for a flat conditioning
surface as a function of
the curvature of the test surface, for subject GD. A psychometric
function is fitted to the data
points (x2 = 3642). The shift, which corresponds to the value of the 50%
point, is 0.18 m-1.
This indicates that a geometrically flat surface is not judged to be flat. The
threshold for curva-
ture detection, which corresponds to the difference between
the values of the 50% and 85% (or
15%) points, is 0.32 m-1.
Figure 3 shows the results in the case of all conditioning surfaces for subject GD.
For clarity the fitted curves are plotted without the data points. Most
values of X2 are
somewhat smaller than the value of figure 2; x2 varies between 105 and 16 323
for
subject GD, 260 and 7650 for subject MH, and 740 and 4480 for subject
EK.
The shapes of the psychometric curves look rather similar. Although it seems as
if the
steepness of the curves decreases with increasing curvature,
this is not significant.
For the other two subjects the steepness did not systematically increase or
decrease.
The threshold is
thus independent of the curvature of the conditioning surface.
The average thresholds are 0.25 ± 0.04 in-', 0.24 ± 0.03 m-1, and 0.21 ± 0.04 m
for
subjects GD, MH, and EK respectively.
The position of the curves, ie the value of the phenomenal flatness, is not constant.
The curves are horizontally shifted with respect to each other, the order being the same
100
80 -
20 -
0
1 5
1.0
0.5
0.0
0.5 1.0
1 5
Curvature/m-1
Figure 3. Psychometric curves for seven differently curved conditioning surfaces (-4, 2, 1, 0,
1, 2, and 4 m-1) for subject GD. The values of x2 are, from left to right, 105, 593, 322, 3642,
1469, 3567, and 16 323. The thresholds of the seven curves are almost similar; the average
is 0.25 ± 0.04 m-1. The values of the phenomenal flatness are clearly different; the stronger the
conditioning curvature the larger the shift of the phenomenal flatness. This indicates that
phenomenal flatness depends on previous exposure to curved surfaces.
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