Full text of DOI:10.1007/s00417-002-0458-y

Graefe’s Arch Clin Exp Ophthalmol
(2002) 240:704–709
C L I N I C A L I N V E S T I G AT I O N
DOI 10.1007/s00417-002-0458-y
Christina Schmitt
Miriam Kromeier
Michael Bach
Interindividual variability
of learning in stereoacuity
Guntram Kommerell
Abstract Background: In the evalu- with a marked interindividual vari-
Received: 14 November 2001
Revised: 13 February 2002
Accepted: 18 February 2002
Published online: 24 July 2002
© Springer-Verlag 2002
ation of therapies aiming at binocu-
lar vision, for instance by the use of
prisms or orthoptic training in the
case of heterophoria, stereoacuity is
often the primary outcome measure.
To assess therapeutic effects it is
ability. In some subjects the stereo-
acuity improved by a factor of >30
and in others it did not improve at
all. The median of the learning factor
was 1.7. There was no significant
difference between novices and ex-
necessary to separate them from per- perienced subjects. Conclusion: The
ceptual learning with repeated test-
ing. Learning stereoacuity has been
investigated only in a few studies
with up to six subjects. Methods: To
great interindividual variability of
learning in stereoacuity has impor-
tant implications for therapeutic tests
that use stereoacuity as an outcome
ascertain the interindividual variabil- measure: To distinguish therapeutic
ity of learning in stereoacuity we
examined 24 subjects, 12 with and
12 without experience in psycho-
effects from improvements due to re-
peated testing, each subject’s indi-
vidual learning behaviour has to be
physical experiments. In a two-alter- taken into account, for example by
native forced-choice paradigm, sub-
jects reported whether a vertical bar
appeared in front of or behind a ref-
erence frame. Estimates of stereo
threshold were obtained using an
adaptive staircase procedure (“best
PEST”). Results: We found a highly
starting out with an adequate training
phase. The number of test repetitions
required to reach a fairly constant
level appears to be similar among in-
dividuals: in our paradigm most of
the learning occurred within the first
six blocks with 100 target presenta-
C. Schmitt · M. Kromeier · M. Bach (
G. Kommerell
Abteilung Neuroophthalmologie
und Schielbehandlung,
Universitäts-Augenklinik,
Killianstrasse 5, 79106 Freiburg, Germany
e-mail: Bach@aug.ukl.uni-freiburg.de
Fax: +49-761-2704052
)
✉
significant learning effect (P<0.0001) tions each.
haviour with respect to both its amount and the time
course.
Stereoacuity is a form of hyperacuity, a term coined
Introduction
Stereopsis is regarded as the most refined feature of
binocular vision. Accordingly, quantification of stere- by Westheimer [27] to describe the ability of the visual
opsis by measuring stereoacuity is a suitable means of system to detect spatial relations with the precision of a
evaluation for therapeutic measures whose aim is to fraction of a photoreceptor’s diameter. It is well known
achieve binocular vision. For example, if one were to that the various forms of hyperacuity can improve with
compare the efficacy of orthoptic training with that of practice. This has been documented for vernier [5, 6, 7,
prisms or surgery in patients suffering from heteropho- 14, 17, 19, 25], curvature [5] and orientation acuity [5].
ria, it would be important to recognise perceptual learn- Concerning stereoacuity, only a few subjects have been
ing during repeated testing. Therefore it is necessary to examined, and improvement by learning has not been
know the interindividual variability of the learning be- found in all of them. Kumar and Glaser [14] presented

705
three subjects with a large number of different stereo
stimuli. They observed learning effects, but in each sub-
ject stereoacuity improved with another kind of stimulus.
Fahle and Henke-Fahle [6] studied six subjects. Only in
four of them did stereoacuity become better. Fendick and
Westheimer [8] studied the learning behaviour of two
subjects with stereo targets imaged on the fovea and in
peripheral regions. In the periphery the stereoacuity im-
proved in both subjects, in the fovea only in one of them.
In view of the limited knowledge of training effects in
stereoacuity we investigated 24 subjects, 12 with and 12
without experience in psychophysical experiments.
Methods
Subjects
Medical students and employees of our department were asked to
join a screening procedure. They had to comply with the following
three conditions: Corrected visual acuity at least 20/20 with each
eye, difference of visual acuity between both eyes not more than a
factor of 1.26, and absence of strabismus, ascertained with the uni-
lateral cover test. Screening was continued until 24 subjects were
recruited. They were between 19 and 57 years of age with the me-
dian at 27 years. A first group comprised 12 volunteers who had
never participated in a psychophysical experiment (KH, KS, BH,
KK, CW, AL, KB, PE, ML, TF, MG, HG). A second group com-
prised 12 employees of our department who had often taken part
in psychophysical experiments, but had never performed the ste-
reoacuity test employed here or participated in any other study of
stereoacuity. Among these were three orthoptists (TK, UZ, HL),
two physicians (FP, BS), five postgraduates of various sciences
(AR, TH, SH, JK, PM) and two laboratory assistants (MS, CK).
Subjects were informed that the goal of the experiment was to as-
certain the reproducibility of a stereoacuity test. As an introduc-
tion to the task, they viewed several sample stimuli with a dispari-
ty of about 500 arcsec. All subjects gave informed consent to take
part in the experiments.
Fig. 1A, B Freiburg Stereoacuity Test. A vertical bar appears with
variable disparity either in front of or behind a reference frame.
The size of the bar and the frame are kept at a constant factor rela-
tive to the disparity of the bar. To obscure monocular cues the bar
is randomly displaced to the left or right. A Example of fine stereo
disparity. B Example of gross stereo disparity
Apparatus
We used the Freiburg Stereoacuity Test [3]. The essential features
of this test are the following: The stimulus is presented at a dis-
tance of 4.5 m on a visual display unit (GD403, Richardson Elec-
tronics) 36 cm wide and 27 cm high, with a resolution of 800×600
pixels and a frame rate of 120 Hz. The monitor is driven from the
mainboard graphics card of a standard computer (Macintosh G4).
The separation for the right and left eye is achieved by a pair of
ferroelectric liquid crystal shutter goggles (FE1, Cambridge Re-
search Systems). The shutter goggles are synchronised to the mon-
itor frequency so that every second image is presented to the right
and left eye, respectively. Each eye receives its image at a fre-
quency of 60 Hz, which is just above flicker fusion frequency.
The stereo target consists of a vertical bar that is surrounded by
a frame (Fig. 1). A pattern with random black-and-white squares
surrounds the frame (edge length 180 arcsec). The size of the bar
and the frame are kept constant relative to the disparity of the bar.
The inner frame width is 8 times the disparity and the inner frame
height 10 times the disparity. The length of the vertical bar is 70%
of the inner frame height, so that a gap remains between the top
and the bottom of the bar and the inner frame edge. To obtain suf-
ficient stimulus width and length at small disparities, the frame
height is kept at a minimum of 3600 arcsec and the frame width at
800 arcsec. To mask monocular cues, the bar is not centred with
respect to the frame but placed randomly, trial by trial, to the right
or left of the centre by the amount of the actual disparity. The dis-
tance between the bar and the left or right inner frame edge is
3 times the disparity, but is clamped to a minimum of 300 arcsec
for disparities below 100 arcsec to comply with the spatial re-
quirement for fine stereoacuity [16].
At the viewing distance of 4.5 m each pixel subtends 20 arc-
sec. Disparities smaller than the width of a pixel are attained by
“anti-aliasing” [1,22]: The margins of the vertical bar are
smoothed with a gradual transition of the luminance following a
Gaussian profile. The Gaussian profile has a standard deviation of
2 pixels. The profile can be shifted to the right or left by fractions
of a pixel. Anti-aliasing requires accurate control of luminance,
taking into account the inherent non-linearity of cathode ray tubes.
For that reason the monitor is “gamma corrected” [2] to achieve a
linear grey scale centred on a mean luminance of 220 cd/m2. The
goggles transmit approximately 14% of the light, resulting in a
mean luminance of 31 cd/m2 as seen by the subject.

706
Fig. 2 Stereo threshold over
the course of the nine training
blocks. Each graph represents
one of the 24 subjects, identifi-
able by their initials. The
crosses indicate the threshold
as calculated by the best PEST
after 100 trials. The solid lines
are the exponential fit func-
tions. The numbers in the top
right corners represent the
learning factors (ratio of initial
over final threshold). Subjects
are sorted by their learning fac-
tor in decreasing order. A wide
variability in amount and
course of learning is seen
Procedure and data analysis
make their decision, at the end of the test sequence about 2 s. The
next stimulus was presented after an interval of 0.5 s during which
We used a two-alternative forced-choice paradigm in which the the random square pattern covered the whole field. Data were
subject had to report whether the bar appeared in front of or be- analysed online using the “best PEST” (best parameter estimation
hind the frame. The stimulus disappeared when the subject had by sequential testing; [10, 15]). The best PEST assumes that the
made his or her choice by pressing the appropriate button on a re- psychometric function has a sigmoid form (in our design a logistic
sponse box. At the beginning, most subjects took about 10 s to function) and takes the point where the slope is steepest for the

707
threshold. After each response the best PEST calculates the most
likely threshold on the basis of all previous responses and sets the
next stimulus accordingly. After the initial 12 trials and then after
every 5th trial we presented a “bonus” trial with a disparity 5
times the current threshold estimation to keep up the subject’s mo-
tivation. Bonus trials were included in the best PEST analysis. The
value reached after 100 trials (one block) was taken as the stereo
threshold. A test session consisted of three blocks. The interval
between blocks was at least 10 min. Each subject attended three
sessions on three consecutive days, nine blocks altogether.
As will be seen, subjects differed widely in their learning be-
haviour. After several attempts of quantification with various algo-
rithms, including multiple time constants, we chose as a parsimo-
nious description an exponential fit per subject as follows:
started with a high threshold (=220 arcsec). The time
course of learning also differed widely. In three subjects
(KK, JK, PM) stereoacuity improved mainly during the
first two blocks, whereas in others it improved monoton-
ically during the nine blocks. Although most of the
learning occurred within the first six blocks, informal
testing showed that learning can continue far beyond the
ninth block. For instance, one of the authors of the pres-
ent study (CS) reached 9 arcsec at the 10th block and
levelled off at about 2 arcsec from the 30th block on-
wards. We also observed long-term retention: retesting
four of our subjects after several months showed that
they had maintained the stereoacuity reached after the
nine blocks of the formal experiment.
The proportion of “learners” and “non-learners” in
our study is compatible with the results of other authors
obtained in smaller groups. Of the two subjects studied
by Fendick and Westheimer [8], only one improved with
practice. Fahle and Henke-Fahle [6] found an improve-
ment of stereoacuity with practice in four of six subjects.
In the study conducted by Ramachandran and Braddick
[20], stereopsis improved in all 11 subjects with training,
but the task given by these authors was different from
ours: they measured the time required for perception of a
stereogram with a fixed disparity of 7.2 arcmin rather
than the disparity threshold. Kumar and Glaser [14]
found learning effects in all of their three subjects, but
each of them improved with another type of stereo
target.
The reasons for the great interindividual variation in
perceptual learning found in our study are unclear. Prior
experience in psychophysical experiments was probably
not relevant, since the performance of the 12 subjects
who had frequently participated in psychophysical ex-
periments did not differ significantly from the perfor-
mance reached by the 12 novices. The various time
courses of learning may reflect different learning mech-
anisms: Drastic improvements from the first to the sec-
ond block, e.g. in subjects KK and JK, may have been
caused by cognitive factors such as better understanding
of or concentration on the task. The more gradual im-
provements, e.g. in subjects KS, TF, BH, ML and FP,
may have been due to specific mechanisms in the prima-
ry visual cortex. This idea is supported by several stud-
ies in animals that showed cortical plasticity at adult age
after sensory deafferentiation in the somatosensory [18],
where i identifies the subject, b the block number (1–9), c1 the as-
ymptotic threshold, c1+c2 the threshold after the initial block and τ
the time constant (in blocks).
As there was no obvious grouping of the data by session
(which comprised three blocks), we chose to define the learning
curve in blocks. To quantify the strength of learning by a single
number, we calculated a “learning factor” for subject i as
fi(1)/fi(9). Thus a learning factor greater than 1 indicates a de-
crease in stereo threshold or an increase in stereoacuity.
Results
A repeated-measures ANOVA revealed a highly signifi-
cant learning effect (P<0.0001) and no significant differ-
ence between novices and experienced subjects. The ini-
tial stereoacuity ranged from 4.5 to 1000 arcsec with a
median at 14.7 arcsec (Fig. 2); the final stereoacuity
ranged from 2.8 to 406 arcsec, median 8.7 arcsec. The
learning behaviour varied considerably among the 24
subjects. The learning factor ranged from 34.6 to 0.6
with a median at 1.7. Three subjects had a learning fac-
tor of ≥10, ten subjects of 3.3 to 1.7, and seven subjects
of 1.5 to 1.2. In four subjects the learning factor was be-
low 1.0. The time course of learning also differed widely
among subjects. Omitting the four subjects with learning
factors below 1.0 the time constant of the fitted exponen-
tial function ranged from 0.3 to 41.5 blocks with a medi-
an at 3.5 blocks.
Discussion
In nearly all subjects the stereoacuity increased over the auditory [21], motor [23] or visual domains [9, 12].
course of the nine blocks with 100 stimulus presenta- There is also evidence for cortical plasticity associated
tions each. A general assessment of all subjects is, how- with perceptual learning in adult humans. During expo-
ever, precluded by the marked interindividual variability. sure with supra-threshold vernier stimuli [25, 26] and
In 17 of the 24 subjects the stereoacuity increased from sub-threshold stereo stimuli [24], the activity recorded
the first to the ninth block by factors between 1.4 and from scalp electrodes was found to change in parallel
34.6. In the other seven subjects factors between 0.6 and when the psychophysical threshold improved. The site
1.3 were found, which means that, for practical purposes, of the electrodes from which the maximal changes were
these subjects did not learn at all. The greatest improve- recorded suggested an origin in the primary visual cor-
ments, with factors >30, occurred in subjects who had tex.

708
Previous researchers of visual functions also conclud- an outcome measure: To distinguish therapeutic effects
ed that perceptual learning occurs in different phases. from improvements due to repeated testing, each sub-
For instance, Fahle [4] found a fast learning phase dur- ject’s learning behaviour has to be taken into account,
ing the first 30 min and a slow learning phase that ex- for example by starting with an adequate training phase.
tended up to 10 h or even beyond. In both phases the Although the amount of learning is quite variable, the
learning was very specific to the task. For example, an number of trials required to reach a fairly constant level
improvement in detecting a horizontal vernier offset was appears to be similar among individuals: in our paradigm
not transferred to a vertical offset. On the basis of this most of the learning occurred within the first six blocks
specificity, Fahle suggested that the structural basis for (600 stimulus presentations).
learning was localised in early levels of cortical process-
Are the improvements of stereoacuity reached under
ing. Karni and Sagi [13] studied learning in texture seg- laboratory conditions beneficial for everyday life? This
regation (a mechanism of figure–ground segregation). appears unlikely, since learning effects in the various hy-
The threshold levelled off within a few minutes. Further peracuity domains are limited to the type of target used
improvement only occurred after a rest of about 8 h, for the training [5, 7, 20, 25]. Moreover, one should con-
preferably overnight. Karni and Sagi suggested that the sider that improvements in a specific hyperacuity task
fast learning within the first few minutes may reflect a might be achieved by allocation of limited neural re-
task-specific routine, while slow learning occurring after sources and thus go along with a loss in similar tasks
a rest may indicate a long-term modification of perceptu- [11]. On the basis of these arguments we see no point in
al modules. In our study we did not encounter a latent therapeutic training with an apparatus designed for mea-
phase: the stereoacuity improved irrespective of the du- suring stereoacuity such as the Freiburg Stereoacuity
ration of the interval between blocks.
Test.
The great interindividual variability of learning in ste-
reoacuity revealed in our investigation has important im-
plications for therapeutic studies that use stereoacuity as
Acknowledgement Supported by the Deutsche Forschungsge-
meinschaft (KO 761/1-1).
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