Hierarchical integration of individual motions
in locally-paired-dot stimuli
Osamu Watanabea,∗, Masayuki Kikuchib
aDepartment of Computer Science and Systems Engineering, Muroran Institute of
Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan
bSchool of Computer Science, Tokyo University of Technology, 1404-1
Katakura-machi, Hachioji, Tokyo 192-0982, Japan
Recent psychophysical studies suggest that there are two types of motion integra-
tion processes in human visual system, i.e., the local and the global integration
process. The existence of the local integration process is suggested by the vector-
average perception in locally-paired-dot (LPD) stimuli. Here, we investigated the
relationship between the two motion integration processes by measuring the sig-
nal detection thresholds in three corresponding stimuli: (1) standard random-dot
kinematograms (RDKs), (2) LPD stimuli the individual dot motions of which were
identical to those of RDKs, and (3) pairwise-averaged stimuli the individual dot
motions of which corresponded to the vector-averages of locally-paired motions in
LPD stimuli. We found that the thresholds in LPD stimuli were similar to those in
pairwise-averaged stimuli rather than in RDKs. In addition, when dots were paired
appropriately, observers could detect coherent motions in LPD stimuli even if the
proportions of signal dots were less than the detection thresholds in corresponding
RDKs. These results suggest that the local and global integrations of individual
motions are carried out hierarchically, and that the global motion perception in
LPD stimuli does not depend on individual dot motions directly, but depends on
locally integrated motions.
Key words: Motion integration, Global motion, Transparent motion,
Locally-paired-dot stimulus, Threshold
∗Corresponding author. Tel: +81-143-46-5421; fax: +81-143-46-5499.
Email address: E-mail address: email@example.com (Osamu
Preprint submitted to Vision Research
For several decades, the motion integration mechanism in human visual system
has been studied with various motion stimuli. It is known that the motion inte-
gration mechanism contributes to discriminate global directions of random-dot
kinematograms (RDKs) such as Fig. 1a; the directions of individual dot mo-
tions are broadly distributed. From this type of global flow displays, observers
can discriminate a mean direction of motions as well as individual dot motions
(e.g., Watamaniuk & Sekuler, 1992; Watamaniuk, Sekuler, & Williams, 1989).
The integration mechanism also plays an important role in coherent motion
detection in RDKs that contain randomly moving (or noise) dots as well as
coherently moving (or signal) dots (e.g., Fig. 2a). Motion detection thresh-
olds in these coherence type displays have been widely adopted as a measure
of performance in visual motion processing across conditions (see Braddick,
1995; Scase, Braddick, & Raymond, 1996).
When RDKs contain two dot streams with different directions (Fig. 1b), ob-
servers can perceive two global motions simultaneously. This transparent mo-
tion perception suggests that the brain does not always integrate all dot mo-
tions into one global motion. In order to investigate how the brain represents
two distinct motions at the same time, Qian, Andersen, and Adelson (1994)
employed locally-paired-dot (LPD) stimuli as illustrated in Fig. 1c. The indi-
vidual dot motions in LPD stimuli are identical to those in RDKs that lead
to motion transparency. The only difference between them is the distribu-
tions of dots; in LPD stimuli, dots moving toward different directions are not
randomly distributed but plotted in closely spaced pairs. LPD stimuli with
opposite directions of motions produce no motion perception. Furthermore,
in the case that two motion directions are non-opposed, one again does not
perceive transparency, but a unitary global motion determined by the vector-
average of two motions (Curran & Braddick, 2000). These results indicate
that the motion detection mechanism in the brain is affected by the distribu-
tion of dot positions, and suggest that there is a local integration process for
co-located motion signals as well as the global integration process.
In the present paper, we investigate the relationship between the two motion
integration processes in human visual system, i.e., the local and the global
integration process. We measured motion detection performances in three
signal-noise motion displays as follows: (a) RDKs, (b) LPD stimuli the all
parameters of which were identical to those of RDKs except for dot distribu-
tions, and (c) pairwise-averaged stimuli generated by replacing each dot pair
in LPD stimuli with a single dot the motion vector of which was determined by
the vector-average of the paired motions (see Fig. 2). It is considered that the
performance of the signal motion detection in LPD stimuli depends on both
local and global integration processes, whereas only the global integration
process contributes to the signal detection in RDKs. Therefore, the difference
between the signal detection thresholds in RDKs and the corresponding LPD
stimuli would reflect the effect of the local integration process.
Assuming that paired motions in LPD stimuli are locally integrated prior
to the global motion integration, global motions observers perceive in LPD
stimuli would not be determined by individual dot motions directly, but by
the distribution of the locally integrated motions. Therefore, if this hierarchical
integration assumption holds, thresholds in LPD stimuli would depend on the
properties (e.g., coherence levels and/or distributions of signal directions) of
locally integrated motions rather than those of individual dot motions. In
the case that the properties of individual and locally-integrated motions are
different, it is expected that there would be differences between the thresholds
in RDKs and the corresponding LPD stimuli, although component dots in
each stimulus are identical. Furthermore, this assumption predicts that the
thresholds in LPD stimuli should be similar to those in the pairwise-averaged
stimuli, generated by averaging local pairs in advance, rather than in the
RDKs. Contrary to this, if the global motion detection in LPD stimuli is
based on individual dot motions, thresholds in LPD stimuli should be similar
to those in the corresponding RDKs rather than in the pairwise-averaged
stimuli. In the series of experiments, we employed LPD stimuli the properties
(e.g., coherence levels) of which after local integration were different from those
of the corresponding RDKs. Comparing the thresholds in LPD stimuli with
those in pairwise-averaged stimuli as well as those in RDKs, we examine the
hierarchical relationship between the local and global integration processes.
Here we describe the basic methods for all experiments. More specific details
will be provided for each experiment.
All experimental stimuli were displayed on a SONY CPD-G220 color moni-
tor, driven by an ATI FireGL2 graphic board in a host computer. Experiments
were conducted in a darkened room. Observers sat in a chair in front of the
monitor and viewed the screen binocularly from a distance of 85 cm. The spa-
tial resolution of the monitor was 49.5 pixel/deg, and a refresh rate was 64Hz.
Observers used a chin rest throughout the experiments and were instructed
to maintain fixation on a small cross at the center of the screen. The fixation
cross was visible for 500 ms prior to each trial and remained on the screen for
the stimulus duration.
Five observers participated in all experiments; one was the author (OW), and
the others were naive to the conceptual basis of the experiments. All had
normal or corrected-to-normal visual acuity.
Stimuli were composed of moving dots presented within a stationary virtual
aperture of a diameter 7.8 deg. RDKs and LPD stimuli consisted of 200 dots,
resulting in a dot density of 4.2 dots/deg2. The luminances of dots and the
background were 68.5 cd/m2and 1.1 cd/m2, respectively, which gave a Michel-
son contrast of 97 %. Each dot subtended about 2.4 arcmin and moved at a
speed of 2 deg/s. Signal dots moved coherently, whereas the directions of noise
dots were chosen from a rectangular distribution, covering the full 360 deg.
In RDKs, each dot was located randomly, whereas dots moving in different
directions were plotted in closely spaced pairs in LPD stimuli. The pairwise-
averaged stimuli were generated by replacing each dot pair in LPD stimuli
by a single dot the motion vector of which was determined by the vector-
average of the paired motions. Therefore, pairwise-averaged stimuli consisted
of 100 dots (the dot density was 2.1 dots/deg2), and the speed of each dot
did not exceed 2 deg/s. A dot lifetime was set to 78 ms to correspond to a
dot trajectory length of 0.16 deg, well within the range that transparency was
abolished in LPD stimuli (Qian, Andersen, & Adelson, 1994; Curran & Brad-
dick, 2000). When a dot reached the end of its lifetime, its replacement was
plotted at a randomly chosen location. In addition, in the cases of RDKs and
pairwise-averaged stimuli, the lifetimes of individual dots began and ended
asynchronously. In the case of LPD stimuli, two dots in each pair appeared
and disappeared at the same time, and their motion paths crossed at the
midpoint of their trajectories.
3 Experiment 1: Threshold for uni-directional signal
The general aim of this study is to investigate the relationship of the local
and the global motion integration process by comparing the signal detection
performances in RDKs, LPD stimuli, and pairwise-averaged stimuli. In Exper-
iment 1, we introduced a novel LPD display the dot pairs of which consisted
of a signal and a noise dot (Fig. 2b). Previous studies reported that observers
cannot perceive component motions in LPD stimuli composed of two coher-
ent motions (Qian, Andersen, & Adelson, 1994; Curran & Braddick, 2000).
Therefore, there is a possibility that observers cannot detect the directions of
signal motions in the present LPD display.
In this experiment, the RDK corresponded to a simple coherence-type display
that was composed of signal dots moving in the same direction and noise dots
moving in random directions (Fig. 2a). In the LPD stimulus, all signal dots
were paired with a noise dot (Fig. 2b). If each local pair in the LPD stimuli is
averaged prior to the global motion integration as described in Introduction,
the global motions observers perceive in LPD stimuli should be similar to
those in the corresponding pairwise-averaged stimuli (Fig. 2c). Although the
directions of the pairwise-averaged motions were broadly distributed, the mean
direction of them was identical to the signal motion direction1. This pairwise-
averaged stimulus is similar to global-flow displays as shown in Fig. 1a. It
is known that observers can discriminate a mean direction of motions from
this type of RDKs (Watamaniuk & Sekuler, 1992; Watamaniuk, Sekuler, &
Williams, 1989). Therefore, if the hierarchical integration assumption holds,
the directions of signal motions would be perceived in the present LPD stimuli.
In the first experiment, we examine whether the signal motions can be dis-
criminated in this locally-paired signal-and-noise dot stimuli by measuring the
direction discrimination threshold. We also measure the thresholds in the cor-
responding RDKs and pairwise-averaged stimuli, and compare them with the
threshold in LPD stimuli.
All signal dots in RDKs and LPD stimuli moved toward a single direction. In
LPD stimuli, all signal dots were paired with a noise dot, because, in general,
each dot in LPD stimuli should be paired with a dot moving toward different
1Let the motion vector of each dot be (v cosθ,v sinθ), where v and θ represent
the speed and the direction of the dot motion, respectively. The pairwise-averaged
motion of a signal-noise pair is represented as ((v cosθS+ v cosθN)/2,(v sinθS+
v sinθN)/2), where θSand θNare the directions of the signal and the noise motion,
respectively. Note that all dots had the same speed in the present experiment.
Because the direction of noise motion θN distributes uniformly, the mean motion
vector of the pairwise-averaged motions is given by ((v/2)cosθS,(v/2)sinθS). The
mean direction is equal to the signal direction, although the mean speed is only a
half of the signal speed.
direction. Therefore, in the case that the proportion of signal dots was less
than 50 %, some of dot pairs were composed of two noise dots. For example,
when the proportion of signal dots was 25 %, half of dot pairs consisted of a
signal and a noise dot, and the others two noise dots.
In pairwise-averaged stimuli, we regarded the dots that corresponded to signal
contained pairs in LPD stimuli as “signal” dots, because the mean direction
of these motions was equal to the direction of a signal motion as described
previously. Similarly, the dots corresponding to noise-only pairs were regarded
as “noise” dots, as these dots moved toward random direction. We will plot
the direction discrimination threshold in the pairwise-averaged stimuli with
respect to the percentage of the above mentioned signal dots. Note that the
signal proportions in the pairwise-averaged stimuli become twice as large as
those in the corresponding LPD stimuli. For example, when a signal proportion
of an LPD stimulus was 25 %, half of the dot pairs contained a signal dot,
and therefore, the proportion of “signal” dots in the corresponding pairwise-
averaged stimulus became 50 %.
To measure the signal detection performance, we employed a single-interval
two-alternative-forced-choice (2AFC) paradigm. In each trial, a signal direc-
tion was randomized to be either leftward or rightward, and observers were
asked to indicate the direction of the signal motion. Each stimulus was pre-
sented for 400 ms.
Direction discrimination thresholds were measured with an 1-up/4-down stair-
case procedure that converged on 84 % correct level; four successive correct
responses were required to decrease the proportion of signal dots while one
incorrect response increased the proportion. The staircase started at a signal
proportion of 50 % in both RDKs and LPD stimuli. The step-size in signal
proportion was 8 % until the second reversal, 4 % until the fourth reversal, 2 %
until the sixth reversal, and 1 % thereafter. In the pairwise-averaged stimuli,
the initial level and the step-size were twice as large as those in LPD stim-
uli. Each experimental run continued until twelve reversals were collected, but
only the last six reversals were used in data analysis. All subjects completed
two experimental runs with each stimulus, so that each estimate of threshold
was based on twelve reversals.
Figure 3a represents the average thresholds for five observers in RDKs and
LPD stimuli. The direction discrimination thresholds in RDKs and LPD stim-
uli were 16.8 % and 20.1 %, respectively. Although the threshold in LPD stim-
uli was greater than that in RDKs, this result indicates that signal directions
could be detected when signal dots were paired with noise dots; while previous
studies showed that observers could not perceive component motion directions
when signal dots were paired with dots moving in another direction coherently.
Note that the thresholds obtained in the present study were higher than those
obtained in some previous studies. For example, Scase, Braddick, and Ray-
mond (1996) reported that the coherence thresholds in RDKs were around
5–10%. Although we cannot simply compare the present results with the pre-
vious ones because the stimulus parameters are different, this difference is
most likely due to the performance level that corresponds to the threshold
values. In the present study, threshold values correspond to 84% correct lev-
els, whereas the thresholds reported by Scase, Braddick, and Raymond (1996)
correspond to 71%. In addition, Baker, Hess, and Zihl (1991) reported that the
direction discrimination ability declines with decreasing dot lifetime. There-
fore, introducing dot lifetime would also raise the coherence threshold in the
Figure 3b shows the direction discrimination threshold in pairwise-averaged
stimuli. To compare the thresholds in LPD and pairwise-averaged stimuli, the
threshold in LPD stimuli was replotted as the percentage of the total number
of dot pairs that contain a signal dot. The threshold in pairwise-averaged
stimuli was 39.0 % in average.
An ANOVA showed that the effect of stimulus type was significant (F(2,8) =
4.467,p < 0.05). Post hoc multiple comparisons with Tukey’s test showed that
a difference was significant between RDK and LPD conditions (p < 0.05).
The results showed that observers could perceive the directions of signal mo-
tions that were paired with noise motions. These results can be explained by
assuming the hierarchy of motion integration stages; paired motions in LPD
stimuli are locally integrated first, and then observers perceive the global direc-
tion of the pairwise-averaged motions. This hierarchical integration assump-
tion argues that the motion perception in the present LPD stimuli is similar
to that in the global flow displays such as Figs. 1a and 2c.
The results confirmed the prediction that observers can detect the signal di-
rection of the locally-paired signal-and-noise motions. However, another pre-
diction, that is, the thresholds in LPD stimuli should be similar to those in
pairwise-averaged stimuli rather than in RDKs, is still unclear. The three
threshold values obtained in this experiment were similar. Although the sta-
tistical difference was found between the thresholds in RDKs and LPD stimuli,
the statistical test could not found a significant difference between RDKs and
pairwise-averaged stimuli. Therefore, to examine the latter prediction, it is nec-
essary to employ the RDKs and the corresponding LPD stimuli the threshold
values of which would be greatly different.
4 Experiment 2: Threshold for bi-directional signal
In the second experiment, we measured the coherence thresholds in bi-directional
signal displays as schematically illustrated in Fig. 4. The RDK consisted of
orthogonal signal motions and noise motions (Fig. 4a). In the corresponding
LPD stimulus, each signal dot was paired with a signal dot, and each noise
dot was paired with a noise dot (Fig. 4b). Therefore, the pairwise-averaged
stimulus became a uni-directional RDK (Fig. 4c). In these stimuli, observers
perceive transparent motion in the RDK and unitary motions in the others.
The proportions of signal dots (filled dots in Fig. 4) in these three stimuli
were equal in this experiment. Note that, in the RDK and the LPD stimulus,
a half of signal dots moved in one direction while the other half moved in the
orthogonal direction, whereas all signal dots move in the same direction in the
Previous studies reported that extracting motion signals in transparent RDKs
was far harder than in uni-directional RDKs. Edwards and Greenwood (2005)
showed that the proportion of each coherent motion required to perceive trans-
parency was about three times higher than the coherence threshold in uni-
directional RDKs. This finding suggests that the perception of motion trans-
parency has a high processing cost associated with the need to detect and rep-
resent two overlapping motions simultaneously (see also Braddick, Wishart,
& Curran, 2002). Contrary to this, when observers were not required to per-
ceive overlapping motions simultaneously, the performance of coherent motion
detection in bi-directional RDKs was similar to that in uni-directional RDKs
(Edwards & Nishida, 1999; Hibbard & Bradshaw, 1999). In other words, at the
threshold level, the proportion of each coherent motion in bi-directional RDKs
was similar to the coherence threshold in uni-directional RDKs. However, even
if the ability to detect a threshold-level signal was not affected by the presence
of a secondary supra-threshold signal when transparency perception was not
required, observers cannot detect coherent motions the proportions of which
were less than the uni-directional threshold.
On the other hand, if signal dots in a transparent RDK are paired as illustrated
in Fig. 4b, it is predicted that observers can perceive motion coherency when
no coherent signal exceeds the uni-directional threshold. In the case of Fig.
4, the proportion of signal dots moving in a particular direction in the LPD
stimulus is equal to a half of the proportion of signal dots in the pairwise-
averaged stimulus. The hierarchical integration assumption argues that the
performance of coherent motion detection in LPD stimuli would be similar
to that in pairwise-averaged stimuli. Because the pairwise-averaged stimulus
has a single coherent motion, it is predicted that observers can detect motion
coherency when the proportion of each coherent motion in the LPD stimulus
is equal to a half of the uni-directional threshold. Therefore, although the
stimulus parameters (e.g., dot density and speed) are different between the
RDK and the pairwise-averaged stimulus, it is expected that the signal level
that is required to perceive motion coherency in the LPD stimulus would be
far smaller than that in the transparent RDK.
In RDKs and LPD stimuli, half of the signal dots moved in one direction, and
the other half in the orthogonal direction. Each local pair in LPD stimuli was a
two-signal or a two-noise pair; no signal-noise pair was allowed. The directions
of signal motions were fixed at upper and lower right (45 deg and −45 deg), or
upper and lower left (135 deg and −135 deg). Therefore, perceived directions in
LPD and pairwise-averaged stimuli became rightward (0 deg) or leftward (180
deg). In each two-noise pair, one motion direction was determined randomly,
and another was restricted to the orthogonal direction. Therefore, the direction
difference of each local pair was 90 deg, and the speed of pairwise-averaged
motions was 1.4 deg/s.
In pairwise-averaged stimuli, dots corresponding to two-signal and two-noise
pairs were regarded as signal and noise dots, respectively. Note that, in RDKs
and LPD stimuli, we will plot the coherence thresholds with respect to the
percentages of the total number of dots that were assigned as signal dots
(e.g., the percentage of all filled dots in Fig. 4). Unlike Experiment 1, the
proportions of signal dots in pairwise-averaged stimuli were equal to those in
the corresponding LPD stimuli and RDKs.
To measure the coherence thresholds for the bi-directional signal condition,
we employed a two-interval 2AFC procedure like previous studies that the
observers did not have to perceive transparency in order to perform the task
(Edwards & Nishida, 1999; Hibbard & Bradshaw, 1999). On each trial, ob-
servers viewed two stimulus intervals; each lasting 400 ms and separated by an
inter-stimulus interval of 500 ms. One interval was designated as the signal-
present interval that contained signal dots as illustrated in Fig. 4, and the
other as the signal-absent (or noise-only) interval. This order was chosen at
random from trial to trial. The observers’ task was to indicate which interval
contained coherent motions.
The coherence thresholds were measured with 1-up/4-down staircase proce-
dure like Experiment 1. All subjects completed two staircases; one staircase
had rightward signal motion, and the other leftward signal motion. The stair-
case started at a signal proportion of 100 %, and the step-size in signal pro-
portion was 16 % until the second reversal, 8 % until the fourth reversal, 4
% until the sixth reversal, and 2 % thereafter. Each staircase continued un-
til twelve reversals had been completed, and the last six reversals were used
in data analysis. The coherence threshold in each stimulus was calculated by
averaging the twelve reversals from the two staircases.
Figure 5 shows the results of the experiment. The coherence thresholds in the
bi-directional RDKs, i.e., the sum of the percentages of two signal dots, was
51.5 % in average, and was about twice as high as the threshold in pairwise-
averaged stimuli (23.3%); although the stimulus parameters (e.g., dot density
and speed) were different between these stimuli, this result was consistent with
the previous result (Edwards & Nishida, 1999; Hibbard & Bradshaw, 1999).
Note that the threshold values obtained in this experiment were higher than
the previous results because of the same reason described in Section 3.2.
The threshold in LPD stimuli, i.e., the percentage of the dot pairs composed of
two signal dots, was 27.4 %. This threshold value was similar to the threshold
in pairwise-averaged stimuli rather than that in RDKs. An ANOVA showed
that the effect of stimulus type was significant (F(2,8) = 31.60,p < 0.001).
Multiple comparisons with Tukey’s test showed that the difference was signifi-
cant between the RDK and LPD conditions (p < 0.01) and between the RDK
and pairwise-average conditions (p < 0.01).
The results indicated that the coherence threshold in the LPD stimuli was
similar to that in the pairwise-averaged stimuli rather than that in the cor-
responding RDKs. Only pairing signal dots, observers could discriminate co-
herent motions in LPD stimuli even if the proportions of signal dots were less
than the coherence threshold in the corresponding RDKs. This result suggests
that the local integration for closely paired motions is unaffected by the global
proportions of signal dots.
The results of Experiments 1 and 2 suggest the hierarchical integration model
as schematically illustrated in Fig. 6. When moving dots are randomly plotted
(Fig. 6a), observers perceive a global motion of them. On the other hand,
plotting these dots in closely spaced pairs (Fig. 6b), each local pair is integrated
first, and the global motion is determined with the distribution of the pairwise-
averaged motions, not with the individual dot motions directly. In the case
of Experiment 2 (Fig. 6c), motion coherency is discriminated with the uni-
directional motion distribution resulting from the local motion integration
stage. The proportion of signal dots moving in a particular direction in the
original display (e.g., the black dots moving in the upper right direction in
the left panel of Fig. 6c) is a half of the proportion of coherent motions after
local integration (gray arrows in the middle panel of Fig. 6c). Because the
proportions of each coherent motion should be greater than the uni-directional
threshold in order to perceive coherency in bi-directional RDKs, the coherence
threshold in the corresponding RDK is greater than that in the LPD stimulus.
It should be noted that the human visual system can discriminate transparent
motions as well as unitary global motions. This fact indicates that the “global
integration stage” in this model does not always integrate all individual mo-
tions into a single motion, but carries out an adaptive integration according as
the type of an input motion distribution. In the case that a transparent RDK
is presented, this stage should integrate each signal motion separately while
the other motions are not integrated. Therefore, the global integration stage
cannot be simply modeled as a rigid algorithm such as vector-summation or
winner-take-all as suggested by Zohary, Scase, and Braddick (1996).
The present model assumes that the global percept in LPD stimuli is led by
the global integration stage. Because the motion distribution that the global
integration stage receives determines whether bi-directional motions are per-
ceived or not in this model, it is predicted that transparency can be perceived
from the LPD stimulus of which the output of the local integration stage is
identical to a motion distribution of a transparent RDK (Fig. 6d), although it
is known that transparency was vanished when moving dots are locally paired
(Qian, Andersen, & Adelson, 1994; Curran & Braddick, 2000). In the following
experiment, we examine this model prediction.
5 Experiment 3: Transparent LPD stimuli
Experiment 3 was conducted to confirm the model prediction that LPD stim-
uli composed of two sets of locally-paired dots lead to the percept of motion
transparency. Figure 7 schematically illustrates the LPD and the correspond-
ing pairwise-averaged stimuli utilized in this experiment; the left and the right
panel represents a horizontal and a vertical motion stimulus, respectively. The
component motions in the two LPD stimuli were identical, and the only dif-
ference between them was the manner of dot pairing. If all moving dots are
positioned randomly, it is obviously impossible to determine the orientation of
transparent motion because two orientations of transparency were present2.
On the other hand, if the percept of the LPD stimuli is identical to that of
the corresponding pairwise-averaged stimuli, observers could distinguish the
orientation of transparent motion.
Signal dots in LPD stimuli were moved in four directions; upper right (45
deg), lower right (−45 deg), upper left (135 deg), and lower left (−135 deg).
Each dot pair was a signal-only or a noise-only pair; there was no local pair
composed of a signal and a noise dot. The mean direction of each noise-only
pair was determined randomly, but the direction difference of the two motions
was fixed at 90 deg. Note that we will plot the coherence thresholds with
respect to the percentages of the total number of dots that were assigned as
We employed a single-interval 2AFC with 1-up/4-down staircase procedure
to measure the orientation discrimination thresholds in LPD and pairwise-
averaged stimuli. Observers were asked to indicate the orientation of trans-
parent motion, i.e., horizontal or vertical. Each stimulus was presented for 400
ms. The staircase started at a signal proportion of 100 %, and the step-size
in signal proportion was 16 % until the second reversal, 8 % until the fourth
reversal, 4 % until the sixth reversal, and 2 % thereafter. Each experimental
run continued until twelve reversals were collected, but only the last six re-
versals were used in data analysis. All subjects completed two experimental
2Some psychophysical studies suggested that the maximum number of overlap-
ping motions observers can perceive simultaneously is two (Edwards & Greenwood,
2005) or three (Andersen, 1989). However, in the present experiment, it was not
tested whether observers could perceive four orthogonal directions of motions si-
multaneously in the corresponding RDKs, as examining the limit of transparency
perception is beyond the purpose of the present study.
runs with each stimulus, and each estimate of threshold is based on twelve
5.2 Results and discussion
The results are illustrated in Fig. 8. Observers could distinguish the orientation
of transparent motions in the LPD stimuli, and there was no significant dif-
ference between the orientation discrimination thresholds in the LPD and the
pairwise-averaged stimuli (t4= 0.59, p > 0.05). Because component dot mo-
tions in the horizontal and the vertical LPD stimuli were the same, observers
would distinguish the orientations of transparent motions by the manner of
dot pairing. The results obtained agreed with those expected by the model;
the output of the local integration stage can lead to the percept of motion
transparency. In light of the result of Experiment 1 and 2, the present result
is not surprising but could be a confirmatory finding of hierarchical motion
In the present study, we have measured the motion detection thresholds in
RDKs, LPD stimuli, and pairwise-averaged stimuli for three conditions, i.e.,
uni-directional, bi-directional, and quad-directional signal conditions. Com-
paring the thresholds in these stimuli, we examined the effects of the local
integration process on the motion detection performance. The experimental
results showed that the thresholds in LPD stimuli were similar to those in
pairwise-averaged stimuli, while there were differences between the thresh-
olds in RDKs and LPD stimuli. These results suggest that individual motion
signals are integrated hierarchically; motion signals in each local region are
integrated prior to the global motion integration, and global motions are de-
termined based on the distributions of locally integrated motions. In addition,
the results showed that, when dots were paired appropriately, observers could
detect coherent motions in LPD stimuli even if the signal proportions were less
than the threshold in the corresponding RDKs. Therefore, it is suggested that
the local integration process is unaffected by the global information concerning
the proportions of signal dots.
It should be noted that the present results cannot reveal the neural mechanism
for the local and the global motion integration in detail, and many open issues
remain, including neural representation of locally integrated motions. We have
focused on the motion perception in LPD and pairwise-averaged stimuli at
threshold signal level. However, there is a possibility that the neural represen-
tations of LPD stimuli are not the precise equivalent of those of the correspond-
ing pairwise-averaged stimuli. Curran and Braddick (2000) reported that, in
the case of no noise condition, the precision of motion direction discrimination
in LPD stimuli is worse than that in RDKs. This result would suggest that the
neural representation of a locally integrated motion is not completely identical
to a single dot motion. Further investigations should include measuring the
precision of direction discriminations in LPD and pairwise-averaged stimuli at
supra-threshold signal levels.
In addition, Vidny´ anszky, Blaster, and Papathomas (2002) pointed out the
similarity between the perceptions of LPD stimuli and motion aftereffects
(MAEs) induced by transparent motions (Mather, 1980; Verstraten, Freder-
icksen, & van de Grind, 1994), and argued that these integrated motion per-
ceptions result from similar mechanisms. The relationship between the MAE
resulting from adaptation to transparent motion and the local integration
process discussed in the present paper is the question for further research.
This research was supported in part by Grant-in-Aid for Scientific Research
from MEXT, Japan.
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Fig. 1. Schematic illustrations of motion stimuli utilized to investigate the mecha-
nism of global motion integration. The large arrows represent perceived directions
of global motions. (a) An RDK stimulus the motion directions of which are broadly
distributed. (b) A transparent motion stimulus. Observers can perceive two global
motions simultaneously. (c) An LPD stimulus. Dots moving toward different direc-
tions are locally paired. Observers perceive a unitary global motion determined by
the vector-average of two motions.
Fig. 2. Schematic illustrations of the motion stimuli used in Experiment 1. Filled
circles represent coherently moving (or signal) dots, and open circles noise dots.
(a) An RDK stimulus. (b) The corresponding LPD stimulus generated by pairing
a signal and a noise dot. (c) A pairwise-averaged stimulus generated by replacing
each dot pair in the LPD stimulus with a single dot (gray circles) the motion vector
of which is determined by the vector average of the paired motions.
Fig. 3. Result of Experiment 1. (a) Direction discrimination thresholds for
uni-directional motion signals in RDKs and LPD stimuli. The thresholds are plotted
as the percentage of signal dots. Error bars represent ±1 standard errors. (b) Direc-
tion discrimination thresholds in LPD and pairwise-averaged stimuli. The threshold
in the pairwise-averaged stimuli is plotted as the percentage of the dots that corre-
spond to signal contained pairs in LPD stimuli (see text). In order to compare the
thresholds in LPD and pairwise-averaged stimuli, the threshold in LPD stimuli is
replotted as the percentage of the total number of dot pairs that contain a signal
Fig. 4. Schematic illustrations of bi-directional motion stimuli used in Experiment
2; (a) RDK, (b) LPD stimulus, and (c) pairwise-averaged stimulus.
Fig. 5. Result of Experiment 2; coherence thresholds in RDKs, LPD stimuli, and
Fig. 6.Aschematicmodelforthe hierarchical motion integration.
Fig. 7. Schematic illustration of the stimuli used in Experiment 3; (a) transparent
LPD stimuli and (b) the corresponding pairwise-averaged stimuli.
Fig. 8. Result of Experiment 3; orientation discrimination thresholds for transparent
LPD and pairwise-averaged stimuli.
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