The Line Motion Illusion: The Detection of Counterchanging Edge and Surface Contrast

Abstract

A version of the line motion illusion (LMI) occurs when one of two adjacent surfaces changes in luminance; a new surface is perceived sliding in front of the initially presented surface. Previous research has implicated high-level mechanisms that can create or modulate LMI motion via feedback to lower-level motion detectors. It is shown here that there also is a non-motion-energy, feedforward basis for LMI motion entailing the detection of counterchange, a spatial pattern of motion-specifying stimulus information that combines changes in edge contrast with oppositely signed changes in background-relative surface contrast. It was concluded that (1) in addition to LMI motion, edge/surface counterchange could be the basis for perceiving continuous object motion, (2) counterchange detection is the likely basis for third-order motion perception (Lu & Sperling, 1995a), and (3) motion energy and counterchange mechanisms could be composed of different arrangements of the same spatial and temporal filters, the former detecting motion at a single location, the latter detecting the motion path between pairs of locations.

Full text

The Line Motion Illusion: The Detection of Counterchanging
Edge and Surface Contrast
Howard S. Hock
Florida Atlantic University
David F. Nichols
York University
A version of the line motion illusion (LMI) occurs when one of two adjacent surfaces changes in
luminance; a new surface is perceived sliding in front of the initially presented surface. Previous research
has implicated high-level mechanisms that can create or modulate LMI motion via feedback to
lower-level motion detectors. It is shown here that there also is a non-motion-energy, feedforward basis
for LMI motion entailing the detection of counterchange, a spatial pattern of motion-specifying stimulus
information that combines changes in edge contrast with oppositely signed changes in background-
relative surface contrast. It was concluded that (1) in addition to LMI motion, edge/surface counterchange
could be the basis for perceiving continuous object motion, (2) counterchange detection is the likely basis
for third-order motion perception (Lu & Sperling, 1995a), and (3) motion energy and counterchange
mechanisms could be composed of different arrangements of the same spatial and temporal filters, the
former detecting motion at a single location, the latter detecting the motion path between pairs of
locations.
Keywords: motion, line motion illusion, counterchange, edges and surfaces, morphing
Supplemental materials: http://dx.doi.org/10.1037/a0016876.supp
The standard version of the line motion illusion (LMI) occurs
when a square is presented; sometime later, a bar is presented
adjacent to it (Figure 1a). Although the entire bar is presented
simultaneously, motion is perceived away from the square, across
the space occupied by the bar. It appears as if a surface is
continuously sliding in front of the background when the bar is
presented, and as if a surface is continuously “pulling back” to
reveal the background when the bar is removed (Figure 1c).
Most accounts of LMI motion perception have proposed that is
determined by such high-level mechanisms as attention, impletion/
morphing, and grouping/parsing. For Hikosaka, Miyauchi, and
Shimojo (1993a, 1993b, 1993b), LMI motion is induced by a
gradient of attention-speeded processing that spatially spreads
from the attention focused on the initially presented square. Be-
cause attention decreases with increasing distance from the square,
changes in bar luminance near the square are detected before they
are detected further from the square. Motion would begin where
the luminance change is first detected and end where it is detected
soon afterward. Attentionally tracking a feature (Cavanagh, 1992),
say an edge, from the initially presented square to the far end of the
subsequently presented bar, also could result in the perception of
LMI motion. It also is thought that LMI motion can result from
impletion/morphing processes that create perceptual continuity by
“filling in” detected discontinuities in location or shape with
continuous motion (Downing & Treisman, 1997; Holcombe, 2003;
Tse, Cavanagh, & Nakayama, 1998), and further, that the direction
of the motion is determined by prior operations that group the bar
with one adjacent surface and parses it from others (Tse et al.,
1998). All of the above could create or modulate LMI motion by
providing feedback to lower-level motion detectors.
The experiments reported in this article determined whether
there also is a feedforward basis for LMI motion that does not
require the mediation of these higher-level mechanisms. It was
anticipated that the to-be-detected, motion-specifying stimulus in-
formation would entail changes in the fundamental properties of
objects, their surfaces and boundaries, rather than “objectless”
first- and second-order motion energy (Sperling & Lu, 1998).
1
The
detection of LMI motion therefore would be consistent with their
third-order system for the perception of object motion; i.e., motion
based on attentionally modifiable changes in salience/activation at
different spatial locations (Lu & Sperling, 1995b; Ho, 1998; Bla-
ser, Sperling, & Lu, 1999; Lu & Sperling, 2001).
It will be shown that changes in edge contrast (the difference in
luminance at the boundary separating two surfaces), and simulta-
neous changes in surface/background contrast (i.e., the difference
in luminance between a surface and its background) are the stim-
ulus events that specify LMI motion. The proviso is that the
changes in contrast must be opposite in sign. That is, edge or
1
In Lu and Sperling’s (1995a) three-systems theory, first-order motion
entails changes in the spatial distribution of luminance, and second-order
motion entails changes in the spatial distribution of luminance contrast,
both irrespective of the shape of the objects that vary in luminance or
contrast.
Howard S. Hock, Department of Psychology, Florida Atlantic Univer-
sity; David F. Nichols, Centre for Vision Research, York University.
We thank Gregor Scho¨ner for discussion regarding the counterchange
account for the perception of continuous motion. We also thank Elan
Barenholtz for his helpful suggestions for an earlier version of this manu-
script, and Alan Kersten for his careful reading of the final version.
Correspondence concerning this article should be addressed to Howard
S. Hock, Department of Psychology, Florida Atlantic University, Boca
Raton, FL 33431. E-mail: hockhs@fau.edu
Journal of Experimental Psychology: © 2010 American Psychological Association
Human Perception and Performance
2010, Vol. 36, No. 4, 781–796
0096-1523/10/$12.00 DOI: 10.1037/a0016876
781

a) Standard LMI Stimuli Generalized LMI Stimuli
Frame 1
Frame 2
Increase in Bar Luminance (Inc)
a) b)
Frame 1
Frame 2
Decrease in Bar Luminance (Dec)
c) d)
Standard LMI Generalized LMI
Bright
Bar
Dim
Bar
Proportion of Trials Motion is Perceived
e)
1.0
0
0.2
0.4
0.6
0.8
Change in Bar Luminance (cd/m )
2
1.471.1
Counterchange
Counterchange
Attention
Attention
Counterchange
Counterchange
Attention
Attention
Counterchange
Counterchange
Attention
Attention
Counterchange
Counterchange
Attention
Attention
100% in
100% in
Counter-
Counter-
change
change
Direction
Direction
100% in
100% in
Counter-
Counter-
change
change
Direction
Direction
99% in
99% in
Counter-
Counter-
change
change
Direction
Direction
Figure 1. Experiment 1: (a– d) Standard and generalized stimuli for the line motion illusion (LMI). Although small
fixation dots were presented equally often on the left edge, right edge, and in the center of the bar for every stimulus, they
are shown here only in the locations for which attention-determined LMI motion (because of gradients of attention-speeded
processing or attentive tracking) would be in the direction opposite to the direction of counterchange-determined motion.
Both directions are indicated by horizontal arrows. The direction of the counterchange-specified motion is determined by
oppositely signed changes in edge contrast and surface-to-background luminance contrast (or alternatively, oppositely signed
changes in edge contrast). Changes in the bar’s contrast with the background are indicated by thick vertical arrows. Changes
in contrast at the bar’s edges are indicated by thin vertical arrows. (e) The proportion of trials during which LMI motion was
perceived, averaged over the three participants; the results for luminance increments and decrements are combined (the gray
bars). The error bars indicate ⫾1SEM. Superimposed on the gray bars is the percentage of the motion-perceived trials for
which motion was in the counterchange-specified direction.
782 HOCK AND NICHOLS

surface/background contrast must decrease at one location, speci-
fying the start of the motion, and surface/background or edge
contrast must increase at a second location, specifying the end of
the motion. In addition, it will be argued that the detection of these
changes in contrast are likely to constitute the informational basis
for the perception of continuous object motion. This would be
consistent with Gibson’s (1968) assertion that motion is specified
by a spatial pattern of change rather than by sequential changes in
retinal location.
Evidence that motion can be specified by patterns of change has
been reported for the perception of apparent motion by Hock,
Gilroy, and Harnett (2002). They showed that apparent motion is
perceived when there are oppositely signed changes in luminance
contrast for two nonadjacent surfaces. Motion begins at the surface
where there is a decrease in luminance relative to that of the
background and ends at the surface where there is an increase in
background-relative luminance contrast. This evidence for the
detection of counterchanging luminance contrast was obtained
with generalized apparent motion stimuli (Hock, Kogan, & Espi-
noza, 1997; Johansson, 1950), stimuli for which motion is per-
ceived between pairs of nonadjacent surfaces that remain simul-
taneously visible while they change in luminance. (Standard
apparent motion is a special case in which one of the alternating
luminance values for each surface is equal to the luminance of the
background. As a result, a surface disappears at one location and
reappears at another.) Hock et al. (2002) showed that neither the
detection of motion energy (Adelson & Bergen, 1985) nor the
tracking of a stimulus feature over time by shifting attention from
one location of the feature to another (Cavanagh, 1992) are nec-
essary for the perception of generalized apparent motion.
2
These results for a pair of nonadjacent surfaces suggest that
counterchange detection is a viable mechanism for the perception
of LMI motion for a pair of adjacent surfaces. Motion can be
perceived between pairs of simultaneously visible, nonadjacent
surfaces when oppositely signed changes in luminance contrast
occur at the same time. Neither changes in the location occupied
by a surface nor sequential changes in luminance are necessary for
the perception of motion. This is apt for LMI stimuli. When an
unchanging surface is continuously present, and an adjacent sur-
face appears, disappears, or changes in luminance, neither of the
surfaces changes their location, and whatever the stimulus infor-
mation that is responsible for LMI motion perception, it need not
be sequential. The experiments reported in this article therefore
determined whether the counterchange principle, first observed for
nonadjacent surfaces, also applies to the LMI motion perceived for
adjacent surfaces.
Investigating the line motion illusion is challenging because
there are many potential contributions to the perception of motion.
In addition to identifying the stimulus information whose detection
provides a feedforward basis for the perception of LMI motion, the
experiments that follow also determine whether the perception of
LMI motion requires gradients of attention-speeded processing
(Hikosaka et al., 1993a, 1993b), attentive tracking (Cavanagh,
1992), exogenously oriented attention (Posner, 1980), impletion/
morphing “filling in” processes that create continuity when there
are discontinuous changes in luminance and/or shape (Downing &
Treisman, 1985; Holcombe, 2003; Tse et al., 1998), or the detec-
tion of motion energy (Adelson & Bergen, 1985). How parsing/
grouping (Tse et al., 1998) affects LMI motion perception is the
subject of a forthcoming article (Hock & Nichols, in preparation).
Generalized Line Motion Stimuli
In the standard version of the LMI stimulus, the square appears
to continuously change its global shape by expanding into new
spatial locations upon the presentation of the bar (Figure 1a) and
contracting back to its initial locations upon the removal of the bar
(Figure 1c). This “morphing” of global shape (Holcombe, 2003;
Tse et al., 1998), though perhaps sufficient for LMI motion when
a surface suddenly appears or disappears, is not necessary for its
perception. This is because LMI motion is perceived for general-
ized LMI stimuli even though changes in global shape do not
occur; the bar always is visible and only its luminance changes, as
in Figures 1b and 1d. (Analogous to apparent motion stimuli, the
standard LMI stimulus is a special case of the generalized LMI
stimulus for which one of the luminance values of the bar equals
the background luminance.) The motion perceived for the gener-
alized LMI stimulus is phenomenologically similar to the motion
perceived for standard LMI stimuli. It appears as if a new surface
is moving in front of and covering the initially presented surface
when the bar’s luminance increases, and as if the initially pre-
sented surface is “pulling back” to reveal the surface behind it
when the bar’s luminance decreases. (See supplemental Figures 1b
and 1d in the online supplemental materials.)
The perception of motion for generalized LMI stimuli also
dispels the argument that LMI motion is indistinguishable from
classical apparent motion (Downing & Treisman, 1997). There are
no changes in location for these stimuli, and any inference of
motion from a rapid sequence of events can easily be eliminated by
simultaneously presenting the square and the bar for an indefi-
nitely long period of time before there is a change in bar lumi-
nance. LMI motion is perceived regardless of this duration.
Experiment 1
In addition to providing initial evidence that LMI motion can
result from the detection of counterchange, this experiment deter-
mined whether high-level morphing can produce LMI motion that
continuously “fills in” discontinuous changes in shape (Holcombe,
2003; Tse et al., 1998). It also showed that exogenously oriented
attention is not necessary for the perception of LMI motion and
2
The possibility that apparent motion between two simultaneously vis-
ible, nonadjacent surfaces depends on the detection of motion energy was
ruled out with stimuli for which luminance increased unequally for the two
surfaces such that there was a change in the location of the surface with the
higher luminance (i.e., there was a small increase in luminance for what
initially was the lighter of the two surfaces, and a much larger increase in
luminance for what initially was the darker of the two surfaces). There is
motion energy for such stimuli, but motion is not perceived because there
is no counterchange. The possibility that the motion perceived between two
simultaneously visible surfaces depends on attentive tracking (Cavanagh,
1992) was ruled out with stimuli for which the lighter of two nonadjacent
surfaces always remained at the same location, so there were no trackable
features. Motion nonetheless is perceived because of the presence of
counterchange when luminance decreases for the darker surface and in-
creases for the lighter surface, or vice versa.
783
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

confirmed earlier reports that attentional gradients and attentive
tracking also are not necessary for the perception of LMI motion.
Counterchange
As illustrated in Figures 1a through 1d, changes in the bar’s
luminance create changes in edge contrast and changes in surface-
to-background luminance contrast for both the standard and gen-
eralized versions of the LMI stimulus. When the bar’s luminance
increases, edge contrast decreases at the square/bar boundary, the
bar’s contrast with the background increases, and edge contrast
increases at the far end of the bar. Counterchange-determined
motion would be from the decrease to the increase in contrast; it is
rightward in Figures 1a and 1b. When the bar’s luminance de-
creases, edge contrast increases at the square/bar boundary, the
bar’s contrast with the background decreases, and edge contrast
decreases at the far end of the bar. Counterchange-determined
motion therefore is leftward in Figure 1c and 1d.
Morphing
As indicated previously, the fact that motion can be perceived
for generalized LMI stimuli indicates that morphing, the “filling
in” of detected changes in the shape of LMI stimuli with a moving
surface (Holcombe, 2003; Tse et al., 1998), is not necessary for the
perception of LMI motion. This is because motion can be per-
ceived for generalized LMI stimuli, stimuli for which there are no
changes in shape to detect. Although morphing is not necessary, it
is possible that it is sufficient for LMI motion perception. To test
this, we included standard LMI stimuli in this experiment for
which the bar was very dim. Changes in edge and surface-to-
background contrast were minimal for this stimulus, so if LMI
motion were perceived, it would be attributable to morphing rather
than the detection of counterchange.
Attention
Hikosaka et al. (1993a, 1993b) have proposed that LMI motion
is the result of a gradient of attention-speeded processing that
emanates from the perceiver’s locus of attention. For standard LMI
stimuli, the gradient would spread from the initially presented
square such that parts of the bar that are closer to the square
receive more attention, and therefore are processed faster than
parts of the bar that are further from the square. Motion would be
perceived because the more quickly processed parts of the bar
reach threshold before the more slowly processed parts. Another
possibility is that motion is perceived as a result of the perceiver
shifting attention during the course of tracking a feature from one
location to another (Cavanagh, 1992). Such could be the case for
the standard version of the LMI stimulus, for which a feature, like
an edge, can be attentionally tracked from the boundary of the
initially presented square to the far boundary of the subsequently
presented bar.
The dependence of LMI motion on either a gradient of attention-
speeded processing or attentive tracking has been challenged by
the observation that motion is perceived toward the square when
the bar is removed, as in Figure 1c. If attention were focused on the
square, attention-determined motion would be in the opposite
direction, away from the locus of attention (Downing & Treisman,
1997; Tse & Cavanagh, 1995). The location of the perceiver’s
locus of fixation/attention was varied in this experiment in order to
further assess whether attentional gradients or attentive tracking
are necessary for the perception of LMI motion. Attention-
determined LMI motion would be indicated if motion were per-
ceived away from the fixation dots in Figure 1. For these fixation
locations, the attention-determined motion direction would be op-
posite to the motion direction determined by counterchange.
Finally, Shimojo, Miyauchi, and Hikosaka (1997) have shown
that exogenously oriented attention (attention attracted to a loca-
tion by a transient change in stimulation) is sufficient to create the
perception of LMI motion. That is, when attention is attracted to
where one end of a bar is about to be presented, LMI motion is
perceived away from that end when the bar is presented. In this
experiment we show that exogenously oriented attention is not
necessary for LMI motion perception. To do so, we eliminated the
possibility that the appearance of the fixation dot would serve as an
exogenous orienting cue. This was done by keeping the fixation
dot continuously present in the same location in the center of the
screen, whether an LMI stimulus was present or not (the stimulus
was shifted relative to the unchanging fixation dot in order for the
fixation dot to be aligned with different stimulus locations). Par-
ticipants were instructed to fixate and maintain attention on the
fixation dot. They presumably did so, but it also is possible that
their attention was oriented elsewhere while they maintained fix-
ation (Posner, 1980). That is, an exogenous orienting cue, say the
appearance of the square, might have attracted their attention when
the first frame of the LMI stimulus was presented. If so, perceived
motion would be away from the location of the square, regardless
of whether there was an increase or decrease in bar luminance.
Method
In this and the remaining experiments, stimuli centered on the
screen of an NEC MultiSync FP955 monitor were viewed from a
distance of 30 cm, which was maintained with a head restraint.
Each trial was composed of a 2,000-ms first frame and a 400-ms
second frame. The stimuli varied with respect to whether: (1) they
were standard or generalized, (2) the square was to the left or right
of the bar, (3) the bar’s luminance increased or decreased (for the
standard version, the lower luminance value corresponded to the
background luminance), (4) the luminance changes of the bar were
large or small, and (5) the fixation dot was on the left edge, center,
or right edge of the bar. The orthogonal combination of these
variables created 48 distinct trials, each of which was repeated
three times to form blocks of 144 order-randomized trials.
The square (1 ⫻1°; luminance ⫽89.3 cd/m
2
) and bar (1 ⫻4°;
variable luminance) were lighter than the dark background (0
cd/m
2
). The bar’s luminance changed between 0 and 75.4 cd/m
2
or
between 0 and 4.3 cd/m
2
for the standard LMI stimuli, and be-
tween 4.3 and 75.4 cd/m
2
or between 4.3 and 5.7 cd/m
2
for the
generalized LMI stimuli. For both versions, the luminance of the
bar always was discriminable from the luminance of the square.
The location of the stimulus was shifted from trial to trial in order
to maintain the constant central location of the fixation dot.
Participants. Eleven students at Florida Atlantic University
participated in up to three of the five experiments (three in Exper-
iments 1, 2, 3, and 5; four in Experiment 4). All had normal or
784 HOCK AND NICHOLS

corrected-to-normal vision, and all were naı¨ve with respect to the
purposes of the experiments.
Procedure. The 3 participants in this first experiment were
tested on three blocks of trials. They were instructed to maintain
their attention at the fixation dot during the entire block of 144
trials. After each trial, they first indicated whether or not they
perceived motion and, if they did, whether the direction of the
motion was rightward or leftward.
Results
Differences in the frequency of LMI motion perception between
trials with increased and decreased bar luminance were not statis-
tically significant in this experiment or the experiments that fol-
low. The results for increases and decreases in bar luminance are
therefore combined within each experiment.
With one exception, motion perception in Experiment 1 was at
ceiling or floor, regardless of fixation location, the one exception
occurring for 1 participant, who perceived motion for 65% of the
standard LMI trials with the dim bar. There was little effect of
fixation location for these trials, so the data were combined for the
three fixation locations, and for trials in which the square was to
the left or right of the bar. The combined data, averaged over the
3 participants, is presented in Figure 1e (for each participant there
were 108 trials for each of the four conditions). The interaction
between stimulus type (standard vs. generalized) and the magni-
tude of the stimulus change (large vs. small) was statistically
significant, F(1, 2) ⫽62.51, p⬍.02, indicating that the size of the
luminance change had a greater effect for generalized compared
with standard LMI motion.
Counterchange. Motion always was perceived for the stan-
dard LMI stimuli when the bar was relatively bright, and it almost
always was perceived for the generalized LMI stimuli when there
was a large change in bar luminance. For all these stimuli, LMI
motion almost always was in the direction consistent with coun-
terchange, although it could not be determined in this experiment
whether the motion was due to the detection of counterchanging
edge and surface-to-background contrast or the detection of coun-
terchanging edge contrast on the opposite ends of the bar.
Morphing. Motion was not perceived for the generalized LMI
stimuli when the change in bar luminance was barely detectable,
likely because the changes in edge and surface-to-background
contrast were too small to activate motion detectors responsive to
counterchange. However, changes in edge and surface-to-
background contrast also were very small for the standard LMI
stimuli with very dim bars, yet LMI motion almost always was
perceived. Indeed, motion was perceived for the standard LMI
stimuli no matter how dim we made the bar, so long as it was
detectable. It could be concluded that in the absence of counter-
change detection, morphing motion that continuously “fills in”
detected discontinuities in shape can be sufficient for the percep-
tion of LMI motion (Holcombe, 2003; Tse et al., 1998).
Attention. Motion almost always was perceived toward the
locus of fixation/attention for the stimuli illustrated in Figure 1. It
would have been perceived away from these fixation locations if it
were the result of either attentive tracking or a gradient of
attention-speeded processing that spreads from the locus of fixa-
tion/attention. Indeed, regardless of where the perceiver was at-
tending, attention-determined motion would have been in the same
direction, away from the locus of attention, regardless of whether
the bar was presented or removed, or whether its luminance was
increased or decreased. The same would be the case if attention
were exogenously attracted to a stimulus feature other than the
fixation dot; LMI motion always would be away from the location
of this feature. The evidence that the perceived LMI motion was in
counterchange-determined directions (opposite directions for in-
creases and decreases in bar luminance) rather than attention-
determined directions (the same direction for increases and de-
creases in bar luminance) confirmed that neither gradients of
attention, attentive tracking, nor exogenous orientation of attention
are necessary for the perception of LMI motion.
Experiment 2
We have proposed that there is a feedforward basis for LMI
motion perception that entails the detection of motion-specifying
stimulus events and, therefore, does not require the mediation of
higher-level mechanisms. However, Downing and Treisman
(1997) have claimed the opposite. They argue that the perception
of LMI motion does not involve motion detection, and is instead
the result of a high-level impletion process that modifies discon-
tinuous stimulus changes “. . . in terms of the most likely real
world state of affairs” (p. 768). From this point of view, when a
discontinuous change in surface luminance is detected for gener-
alized LMI stimuli, an impletion process would smooth the dis-
continuity by creating the perception of continuous LMI motion.
Little if any motion was perceived for the generalized LMI stim-
ulus in Experiment 1 when there was a small change in bar
luminance, but this result was not sufficient to argue for or against
impletion because the luminance change was barely detectable. In
this experiment, a range of luminance changes was introduced, all
of which were clearly detectable (confirmed by multiple observ-
ers). If LMI motion were based on impletion, it would have been
perceived for all of these changes in bar luminance.
Method
Using generalized LMI stimuli, the magnitude of the change in
bar luminance was varied while the bar’s average luminance was
kept approximately constant. The luminance of the square was
96.4 cd/m
2
, and the bar luminance varied between 28.2 and 31.4,
24.3 and 36.1, 21.4 and 39.4, or 18.7 and 44.2 cd/m
2
. The orthog-
onal combination of: (1) the size of the change in bar luminance,
(2) whether the square was to the left or right of the bar, (3)
whether the bar’s luminance increased or decreased, and (4)
whether the fixation dot was on the left edge, center, or right edge
of the bar, created 48 distinct trials, each of which was repeated
three times to form blocks of 144 order-randomized trials. Three
participants were tested on three blocks of these 144 trials (for
each participant there were 108 trials in each of the four
luminance-change conditions).
Results
The proportion of trials for which LMI motion was perceived,
averaged over the 3 participants, increased with the size of the
change in bar luminance (Figure 2). This effect was statistically
significant, F(3, 6) ⫽26.96, p⬍.001. The motion was in the
785
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

counterchange-specified direction for an average of 89% of the
motion-perceived trials (the magnitude of the luminance change
did not significantly affect the frequency of with which LMI
motion was perceived in the counterchange direction, F⬍1.0).
If impletion were necessary for the perception of LMI motion,
the frequency with which it was perceived would not have de-
pended on the magnitude of the luminance change. Impletion-
determined LMI motion would have been perceived equally often
for all the magnitudes of luminance change in this experiment
because they all were detectable, and therefore sufficient for the
initiation of a “filling in” impletion process that would create the
perception of LMI motion. Instead, the results were consistent with
LMI motion perception being based on counterchange detection
mechanisms whose activation depends on the magnitude of
motion-specifying changes in edge and surface contrast.
Experiment 3
The results of Experiments 1 and 2 were consistent with the
perception of LMI motion being based on the detection of coun-
terchange. One possibility is that the counterchange entails a
change in edge contrast combined with an oppositely signed
change in surface-to-background contrast for the bar. Another is
that it entails oppositely signed changes in edge contrast on the two
sides of the bar. Although the latter remains a possibility, it is
precluded as the basis for LMI motion in this experiment and the
experiment that follows because edge contrast always changed in
the same direction on both sides of the bar. LMI motion is
nonetheless perceived, so if the motion were determined by the
detection of counterchange, it would have to be counterchange
based on changes in edge and surface/background contrast.
The stimuli were generalized versions of a stimulus from Faub-
ert and von Gru¨nau (1995). They were composed of two squares
with equal luminance and a connecting bar between them, all
presented against a background that either was black or white
(Figure 3). The bar was visible for the entire trial, and its lumi-
nance always was discriminable from the luminance of the flank-
ing squares (both squares were lighter or both were darker than the
bar). The bar’s luminance either increased or decreased during the
second frame of each trial, so depending on whether the back-
ground was black or white, the luminance change for the bar either
increased or decreased its contrast with the background.
When the background was black and the squares were lighter
than the bar, the changes in contrast at the square/bar boundaries
and the change in the bar’s contrast with the background were
oppositely signed. This counterchange was expected to result in
the perception of converging LMI motion when the bar’s lumi-
nance increased (Figure 3a). That is, edge contrast was reduced at
the bar’s boundaries with the squares (the two locations where
motion begins), and the contrast of the bar with the background
increased (the common ending location for the two converging
motions). Conversely, counterchange detection was expected to
result in the perception of diverging LMI motion when the
luminance of the bar decreased (Figure 3b). That is, the contrast
of the bar with the background decreased (the common starting
location for the two motions) and edge contrast increased at
both of the bar’s boundaries with the squares (the two end
locations of the diverging motion). However, changes in edge
contrast and bar/background contrast were same-signed when
the squares were darker than the bar (Figures 3c and 3d), so
little motion perception was anticipated. (See supplemental
Figures 3a and 3d in the online supplemental materials.)
The reverse was expected when the background was white. Now
when the squares were darker than the bar, changes in edge
contrast and bar/background contrast were oppositely signed. This
counterchange was expected to result in the perception of diverg-
ing motion when the bar’s luminance increased (Figure 3g) and
converging motion when the bar’s luminance decreased (Figure
3h). However, changes in edge contrast and bar/background con-
trast were same-signed when the squares were lighter than the bar
and the background was white (Figures 3e and 3f). For these
stimuli, relatively little perception of LMI motion was anticipated.
Method
A square was presented on both sides of the bar (same spatial
dimensions as in Experiment 1). For the black background (0
cd/m
2
), the luminance of both squares was 6.3 or 89.3 cd/m
2
and
the bar’s luminance changed from 19.1 to 60.9 cd/m
2
(or vice
versa). For the white background (89.3 cd/m
2
), the luminance of
both squares was 0 or 57.3 cd/m
2
and the bars luminance changed
from 8.3 to 41.3 cd/m
2
(or vice versa). The fixation dot always was
aligned with the center of the bar.
There were 96 order-randomized trials per block formed by the
orthogonal combination of the two luminance values of the
squares, whether the bar’s luminance increased or decreased, and
24 repetitions. Three participants were tested on two blocks of 96
trials with the black background, then two blocks of 96 trials with
the white background. After each trial, they indicated whether or
not they perceived motion and, if so, whether the motion was
convergent or divergent. For each participant, there were 96 trials
in each of the four conditions.
Results
The results, averaged over the 3 participants, are presented in
Figure 3i. Whether or not LMI motion was perceived depended on
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25 30
Luminance Change of the Bar (cd/m
2
)
Proportion of Trials Motion is Perceived
Figure 2. Experiment 2: The proportion of trials during which LMI
motion was perceived as a function of the size of the luminance change for
the bar (the results for luminance increments and decrements are com-
bined). The results are averaged over the three participants. Error bars
indicate ⫾1SEM.
786 HOCK AND NICHOLS

the combination of the background luminance (black or white) and
the luminance of the flanking squares (lighter or darker than the
connecting bar). The interaction between these variables was sta-
tistically significant, F(1, 2) ⫽1033.81, p⬍.001 (Figure 3i).
When the background was black and the squares were lighter than
the bar, increases in bar luminance resulted in the perception of
converging motion and decreases in bar luminance resulted in the
perception of diverging motion, both consistent with the detection
of counterchanging edge and surface/background contrast
(changes in edge and surface/background contrast were oppositely
signed). The minimal perception of LMI motion when the squares
were darker than the bar was consistent with the absence of
counterchange for these stimuli (changes in edge and surface-
background contrast were same-signed).
When the background was white, the results were the reverse of
those obtained with the black background, but again consistent
Increasea) Increasee)
Decreaseb) Decreasef)
Increasec) Increaseg)
Decreased) Decreaseh)
i)
Light
Squares
Dark
Squares
Light
Squares
Dark
Squares
Black Background White Background
1.0
0
0.2
0.4
0.6
0.8
Proportion of Trials Motion is Perceived
98% in
98% in
Counter-
Counter-
change
change
Directions
Directions
99% in
99% in
Counter-
Counter-
change
change
Directions
Directions
Figure 3. Experiment 3: Generalized versions of Faubert and von Gru¨nau’s (1995) LMI stimuli presented
against a black background (a– d) and against a white background (e– h). The luminance for the two flanking
squares always was the same for each trial, but varied from trial-to-trial depending on the condition. The thick
vertical arrows indicate whether the background-relative contrast of the bar increases or decreases, and the thin
vertical arrows indicate whether the luminance contrast at the edges of the bar increases or decreases. The
horizontal arrows indicate the directions of the motion predicted on the basis of edge/surface counterchange. (i)
The proportion of trials during which LMI motion was perceived, averaged over 3 participants; the results for
luminance increments and decrements are combined (gray bars). The error bars indicate ⫾1SEM. Superimposed
on the gray bars is the percentage of the motion-perceived trials for which motion was in counterchange-
determined directions.
787
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

with LMI motion being counterchange determined. That is, when
the squares were darker than the bar, diverging motion was per-
ceived for increasing bar luminance and converging motion for
decreasing bar luminance, and when the squares were lighter than
the bar, little motion was perceived, consistent with the absence of
counterchange for these stimuli (changes in edge contrast and
surface/background contrast were same-signed). As indicated ear-
lier, the perceived LMI motion in this experiment could not have
been based on the counterchange of edge contrast on the left and
right sides of the bar; both always changed in the same direction in
this experiment, regardless of the luminance of the background.
Additional results. Although there is little if any motion
perception for the generalized Faubert and von Gru¨nau (1995)
stimulus in the absence of counterchange, this is not the case for
the standard version of these stimuli (when the connecting bar
appears during only one frame). Converging LMI motion is per-
ceived when the bar is presented and diverging LMI motion is
perceived when its is removed. This was consistent with the results
for the dim bar in Experiment 1 in indicating that morphing is
sufficient for the perception of LMI motion when there is a change
in the shape of the stimulus.
Experiment 4
It has been shown thus far that a number of high-level alterna-
tives to the detection of counterchange are not necessary for the
perception of LMI motion. These include morphing, impletion,
gradients of attention-speeded processing, attentive tracking, and
exogenously oriented attention. It remains possible, however, that
LMI motion perception results from the detection of shifts in the
centroid of the luminance profile at the square/bar boundaries
(Zanker, 1994). That is, LMI motion perception requires the de-
tection of motion energy (Adelson & Bergen, 1985). For the
stimuli in the preceding experiment with light flankers (Figures 3a
and 3b), the directions specified by motion energy were consistent
with the converging motion perceived when the bar’s luminance
increased, and the diverging motion perceived when the bar’s
luminance decreased. However, if LMI motion were based on the
detection of motion energy, the same motion directions would
have been perceived for the stimuli with dark flankers in Figures
3c and 3d, unless motion energy was much weaker for the stimuli
with dark flankers. For this reason, luminance values were selected
in Experiment 4 in order to match stimuli with respect to their
first-order motion energy content (i.e., motion energy based on
spatiotemporal changes in “raw” luminance). This matching was
done by implementing Adelson and Bergen’s (1985) motion en-
ergy model, as detailed in the Appendix. If LMI motion required
the detection of motion energy, it would be perceived in the
directions specified by motion energy when the flankers were
lighter than the bar (and counterchange was present) as often as
when they were darker than the bar (and counterchange was
absent).
Method
Stimuli. The generalized LMI stimuli had the same spatial
dimensions as in Experiment 3. When both flanking squares were
darker than the bar (Figures 4c and 4d), their luminance was 28.4
cd/m
2
, the luminance of the background was 0 cd/m
2
, and the
luminance of the bar changed from 58.9 to 97.0 cd/m
2
(Weber
fraction ⫽0.65), or vice versa. When both squares were lighter
than the bar (Figures 4a and 4b), their luminance was 58.9 cd/m
2
and the luminance of the background was 16.3 cd/m
2
. Luminance
values for the bar were selected to match the light-flanker to the
dark-flanker stimuli with respect to the first-order motion energy
calculated on the basis of Adelson and Bergen’s (1985) model.
This was done with spatial filters (receptive fields) that had either
balanced or unbalanced excitatory and inhibitory zones.
Balanced spatial filters. For half of the trials with the light
flanking squares, the bar’s luminance changed between 28.4 and
54.0 cd/m
2
(Weber fraction ⫽0.90). For these luminance values,
the calculated motion energy was matched to that of the stimuli
with dark flanking squares. It should be noted, however, that the
stimulus conditions differed with respect to the Weber fraction for
the change in bar luminance; it was 0.65 for the stimuli with dark
flankers.
Unbalanced spatial filters. For the other half of the trials
with the light flanking squares, the bar’s luminance changed from
28.4 to 48.5 cd/m
2
(Weber fraction ⫽0.71), and vice versa. For
these luminance values, the calculated motion energy was matched
to that of the stimuli with dark flanking squares, and in addition,
the two conditions were similar with respect to the Weber fraction
for the change in bar luminance.
Design/procedure. There were 96 order-randomized trials per
block determined by the orthogonal combination of the luminance
of the flanking squares, whether the bar’s luminance increased or
decreased, and 24 repetitions. The 4 participants were test on two
blocks of 96 trials, one for the light and the other for the dark
flanking squares. The fixation dot always was aligned with the
center of the bar. After each trial, participants indicated whether or
not they perceived motion and, if so, whether the motion was
convergent or divergent. For each participant there were 96 trials
in each of the four conditions.
Results
LMI motion almost always was perceived for both stimulus sets
in the light-flanker condition (one stimulus set matched motion
energy for the light- and dark-flanker conditions with balanced
spatial filters, the other matched them with unbalanced spatial
filters), so the combined results for the two stimulus sets, averaged
over the four participants, are presented in Figure 4e. The major
finding was that when LMI motion was perceived, it was in the
direction specified by motion energy much less often when the
flanking squares were darker than the bar (6% of the trials)
compared with when they were lighter than the bar (98% of the
trials), t(3) ⫽87.95, p⬍.001. If LMI motion depended on motion
energy extraction, the frequency of its perception in directions
specified by motion energy would have been similar for the stimuli
with light and dark flankers.
Although it was possible to quantitatively match stimuli with
respect to first-order motion energy, uncertainty regarding an
appropriate quantitative measure of contrast precluded doing the
same for second-order motion energy. However, when the bar
changed in luminance, its contrast changed with respect to the
background (the contrast of the flanking squares with the back-
ground was unchanged), so second-order motion energy specified
motion in the same directions as first-order motion energy. None-
788 HOCK AND NICHOLS

theless, motion was rarely perceived in those directions for the
stimuli in Figures 4c and 4d.
LMI motion was perceived for 99% of the trials in the light-
flanker condition, for which counterchanging edge/surface contrast
was present. The motion almost always was in the counterchange-
specified direction. However, LMI motion was perceived for only
37% of the trials in the dark-flanker condition, for which edge/
surface counterchange was not present. Because of large variabil-
ity among the participants (and few degrees of freedom), this
difference fell short of significance, t(3) ⫽2.64, p⫽.08. The
residual motion perceived in the absence of counterchange (mostly
in the non-motion-energy direction) may entail changes in the
luminance similarity of the bar with the flanking squares. This
possibility will be addressed in future research.
Baloch and Grossberg (1997). In their account of the line
motion illusion, Baloch and Grossberg (1997) proposed that LMI
motion is perceived by virtue of the sequential activation of arrays
of “bipole cells” that lie along the horizontal boundaries of the bar.
These hypothetical cells are composed of two lobes with the same
orientation preference (horizontal in this example), one on each
side of a connecting cell body. Because the stimulation of both
lobes is necessary for bipole cells to reach their threshold, those
cells that already are stimulated in one lobe by the horizontal
boundaries of the square would reach threshold more quickly when
the bar is presented (or its luminance increased) in its other lobe
compared with bipole cells that are further from the square. LMI
motion would result from the wave of boundary completion as
successive bipole cells reach threshold.
The results obtained in this experiment for stimuli with dark
flanking squares were inconsistent with Baloch and Grossberg’s
(1997) account. If the sequential activation of bipole cells were the
basis for the perception of LMI motion, the motion that was
perceived would have been convergent when the bar’s luminance
increased and divergent when the bar’s luminance decreased (these
would have been the same as the directions specified by motion
energy in Figures 4c and 4d). However, the perceived motions
were consistently in the opposite directions.
Experiment 5
This experiment provided evidence that the detection of edge/
surface counterchange is sufficient for the perception of LMI
motion under conditions in which there is detectable first-order
e)
1.0
0
0.2
0.4
0.6
0.8
Proportion of Trials Motion is Perceived
Light
Squares
Increase
c)
c)
d)
d)
Motion Energy
Motion Energy
Decrease
Dark
Squares
6% in
Motion
Energy
Directions
Increase
a)
a)
Decrease
b)
b)
Motion Energy
+
Counterchange
Motion Energy
+
Counterchange
98% in
Counterchange
and
Motion Energy
Directions
Figure 4. Experiment 4: Generalized versions of Faubert and von
Gru¨nau’s (1995) LMI stimuli presented against a dark gray background or
against a black background, Luminance values were selected such that the
stimuli with light squares (a,b) and the stimuli with dark squares (c,d) were
matched in motion energy, as computed with a detection model based on
Adelson and Bergen (1985). Background-relative edge/surface counter-
change was present only for the stimuli with light squares (a,b). The
horizontal arrows indicate the directions of the motion predicted by edge/
surface counterchange and by motion energy. (c) The proportion of trials
during which LMI motion was perceived, averaged over 4 participants; the
results for luminance increments and decrements are combined (gray bars).
The error bars indicate ⫾1SEM. Superimposed on the gray bars is the
percentage of the motion-perceived trials for which motion was in direc-
tions specified by counterchange and/or motion energy.
789
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

motion energy in the opposite direction. Two-frame generalized
LMI stimuli were created for which there was a gradient of
luminance values for the bar during one frame, and uniform
luminance for the bar during the second frame. The luminance
value for the uniform bar was equal to the lowest luminance value
of the gradient bar. As a result, the centroid of the luminance
profile shifted toward the light end of the gradient bar when it
replaced a bar that was uniform in luminance, producing first-order
motion energy toward the light end (in the leftward direction for
the stimuli illustrated in Figures 5a and 5c, and in the rightward
direction for the stimuli illustrated in Figures 5b and 5d). Con-
versely, when the gradient bar was replaced by a bar with uniform
luminance, the centroid of the luminance profile shifted toward
what was the dark end of the gradient bar, producing first-order
motion energy in that direction. The above motion energy direc-
tions were confirmed by the implementation of Adelson and Ber-
gen’s (1985) motion energy model described in the Appendix.
As can be seen in Figure 5a, edge/surface counterchange spec-
ifies motion when the gradient bar replaces the uniform bar, and
the light side of the gradient bar is adjacent to the light flanking
square. That is, edge contrast decreases at the square/bar boundary,
and except for the far end of the bar, the luminance contrast of the
bar with the background increases. However, there is no edge/
surface counterchange when the dark side of the gradient bar
appears next to the flanking square; decreases in edge contrast at
the square/bar boundary are minimal because there is little change
in the gradient bar’s luminance alongside the square (Figure 5b).
There is, as well, no edge/surface counterchange when the square
is not present (Figures 5c and 5d).
When edge/surface counterchange was not present, it was antici-
pated that motion would be in the direction specified by first-order
motion energy (e.g., the stimuli illustrated in Figures 5b, 5c, and 5d).
When edge/surface counterchange was present, it specified motion in
the direction opposite to the motion energy direction (Figure 5a). The
perception of motion in the counterchange-specified direction for this
stimulus would indicate that motion energy extraction is not necessary
for the perception of LMI motion.
Method
The square and bar, which had the same spatial dimensions as in
Experiments 1 and 2, were presented against a dark gray back-
ground (luminance ⫽11.4 cd/m
2
). The bar was either uniform in
luminance (16.8 cd/m
2
), or it was composed of a gradient of
luminance values that increased linearly from 16.8 cd/m
2
at one
end to 45.4 cd/m
2
at the other end of the bar (the slope of the
gradient was 7.2 cd/m
2
per degree of visual angle). The light
side of the gradient was either on the left or right side of the bar.
The flanking square (uniform luminance of 60.2 cd/m
2
) was ad-
jacent to the left edge of the bar for half the trials, and was not
present during the other half of the trials. There were 96 order-
randomized trials per block determined by the orthogonal combi-
nation of whether the square was present or not, whether the
uniform bar was presented before or after the gradient bar, whether
the light side of the gradient was on right or the left end of the bar,
and 12 repetitions. The fixation dot always was aligned with the
center of the bar. Three participants were tested on three blocks of
96 trials, so there were 72 trials for each participant in each
condition.
Results
The results, averaged over the three participants, are presented
in Figure 5e. Whether the flanking square was present or not, F(1,
2) ⫽10.32, p⫽.09, and whether the gradient was positive or
negative, F⬍1.0, did not significantly affect the frequency with
which LMI motion was perceived. As in the preceding experiment,
the most important data concerned the frequency with which LMI
motion, when perceived, was in the direction specified by motion
energy. When edge/surface counterchange was absent, perceived
motion was most often in the direction specified by motion energy
(Figure 5e), indicating that the extraction of first-order motion
energy is sufficient for the perception of motion for surfaces with
luminance gradients. However, even with luminance gradients,
motion energy extraction is not necessary for the perception of
LMI motion. When edge/surface counterchange was present, and it
specified motion in the direction opposite to that specified by
motion energy (as in Figure 5a), perceived motion was over-
whelmingly in the direction specified by counterchange rather than
motion energy. That is, when there was a light flanking square,
LMI motion was in the direction specified by motion energy
significantly less often when counterchange was present than when
it was absent, t(2) ⫽32.60, p⬍001. This difference between the
negative and positive gradients was significantly greater when
there was a flanking square compared with when there was not a
flanking square; i.e., the interaction between gradient direction and
whether the square was present or absent was significant, F(1,
2) ⫽41.85, p⬍.05.
A series of experimental conditions similar to those of the
current experiment previously was reported by von Gru¨nau,
Saikali, and Faubert (1995). When they presented a gradient bar on
a blank field, they found by a relatively small margin that the
direction of perceived motion was toward the dark end of the
gradient.
3
It was argued that this was because the light end was
processed more rapidly than the dark end, consistent with the
gradient of attention-speeded processing proposed by Hikosaka et
al. (1993a, 1993b). In the current study, however, motion was
perceived in the opposite direction, toward the light end of the
gradient bar when it replaced the uniform bar, perhaps because
motion energy is more readily extracted when the gradient bar is
exchanged with a uniform bar compared with presenting it on a
blank field. When a square was presented, and an adjacent gradient
bar appeared afterward, von Gru¨nau et al.’s (1995) results were
very similar to ours. That is, they found that strong LMI motion
was perceived when the square was adjacent to the light side of a
gradient bar, but not when it was adjacent to its dark side. They
argued that a more global process affected the differential process-
ing of the light and dark ends of the bar, whereas we have argued
for the detection of edge/surface counterchange. The relative merit
of the counterchange explanation follows from its ability to ac-
3
In a more recent study, Hsieh, Caplovitz, and Tse (2006) did the
opposite; i.e., they removed a previously presented gradient bar, leaving
only the blank field. Their results differed from von Gru¨nau et al. (1995)
in two respects: (1) subjects were much more consistent in reporting the
direction of the perceived motion, and (2) the perceived motion direction
depended on the luminance polarity of the background. Hsieh et al. (2006)
attributed their results to differences in decay rates within the afterimage of
the gradient bar.
790 HOCK AND NICHOLS

Edge/surface
Edge/surface
Counterchange
Counterchange
(motion energy
(motion energy
is in opposite
is in opposite
direction)
direction)
a) Negative Gradient
a) Negative Gradient
Frame 1
Frame 1
Frame 2
Frame 2
b)
b)
e)
e)
1st
st
-Order Motion Energy
-Order Motion Energy
Frame 1
Frame 1
Frame 2
Frame 2
Frame 1
Frame 1
Frame 2
Frame 2
Frame 1
Frame 1
Frame 2
Frame 2
Frame 2
Frame 2
1st
st
-order
-order
motion energy
motion energy
Edge/surface
Edge/surface
counterchange
counterchange
1st
st
-order
-order
motion energy
motion energy
1st
st
-order
-order
motion energy
motion energy
1st
st
-order
-order
motion energy
motion energy
No Edge/Surface Counterchange (only motion energy)
No Edge/Surface Counterchange (only motion energy)
Proportion of Trials Motion is Perceived
Proportion of Trials Motion is Perceived
1.0
1.0
0
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
Square is Present
Square is Present
Square is Absent
Square is Absent
c) Negative Gradient
c) Negative Gradient
b) Positive Gradient
d) Positive Gradient
Negative
Negative
Gradient
Gradient
Positive
Positive
Gradient
Gradient
Negative
Negative
Gradient
Gradient
Positive
Positive
Gradient
Gradient
No counter-
No counter-
change
change
No counter-
No counter-
change
change
No counter-
No counter-
change
change
3% in
3% in
Motion
Motion
Energy
Energy
Direction
Direction
98% in
98% in
Motion
Motion
Energy
Energy
Direction
Direction
60% in
60% in
Motion
Motion
Energy
Energy
Direction
Direction
90% in
90% in
Motion
Motion
Energy
Energy
Direction
Direction
Figure 5. Experiment 5: (a,b) Generalized LMI stimuli for which the bar is presented adjacent to a lighter
square. The bar either is uniform in luminance or is composed of a gradient of luminance values, the lowest
of which corresponds to the luminance of the uniform bar. (c,d) Same stimuli as above, except that the
square is not present. The thick vertical arrows indicate whether the luminance of the bar increases or
decreases in its contrast with the background, and the thin vertical arrows indicate whether the luminance
contrast at the edges of the bar increases or decreases. The horizontal arrows indicate the directions of
motion predicted on the basis of edge/surface counterchange (when it is present), as well as the direction
of motion predicted by the motion energy in the stimulus. (e) The proportion of trials during which LMI
motion was perceived, averaged over 3 participants; the results for changes from the uniform to the gradient
bar, and vice versa, are combined (gray bars). The error bars indicate ⫾1SEM. Superimposed on the gray
bars is the percentage of the motion-perceived trials for which the motion was in the motion energy
direction.
791
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

count, not just for observations with the gradient bars, but also for
results obtained for bars with uniform luminance.
General Discussion
The primary objective of this study was to determine whether there
is motion-specifying stimulus information whose detection is suffi-
cient for the perception of LMI motion for pairs of adjacent surfaces.
If so, it would provide a feedforward basis for LMI motion that does
not require the mediation of higher-level mechanisms, and as indi-
cated in the introduction, a mechanism that potentially could account
for the perception of continuous object motion.
Edge/Surface Counterchange
The results of the reported experiments indicate that motion for
generalized LMI stimuli is specified by a nonsequential pattern of
oppositely signed changes in edge contrast and surface-to-
background contrast. (Either the detection of edge/surface coun-
terchange or morphing could result in motion perception for stan-
dard LMI stimuli.) Counterchange-specified motion begins where
edge contrast decreases and ends where background-relative sur-
face contrast increases, or it begins where background-relative
surface contrast decreases and ends where edge contrast increases.
Although edge/surface counterchange is sufficient for LMI mo-
tion, motion can nonetheless be perceived for stimuli without
edge/surface counterchange. For example, Hsieh, Caplovitz, and
Tse (2005) showed that LMI motion, once established, can be
maintained as a series of LMI motions that reverse in direction
while the bar alternates between different hues (and luminance
levels). There was no edge/surface counterchange stimulating
these motion reversals. In addition, LMI motion can be perceived
in the absence of edge/surface counterchange when attention is
drawn to one of the boundaries of a to-be-presented surface by an
auditory or tactile orienting cue (Shimojo et al., 1997). In the
current study, there was evidence that in the absence of counter-
change, morphing (Experiment 1; additional results for Experi-
ment 3) and changes in similarity for a pair of adjacent surfaces
(Experiment 4) were sufficient for the perception of LMI motion.
All reflect changes in perceptual organization being perceptually
realized as LMI motion (Hock & Nichols, in preparation).
Attention
Studies of attention allocation often distinguish between endog-
enously and exogenously oriented attention (Posner, 1980; Nakayama
& Mackeben, 1989). The former entails the intentional orientation of
attention to a location, and the latter the non-intentional attraction of
attention to a location by a transient change in stimulation. The
endogenous orientation of attention appears to be neither necessary
nor sufficient for the perception of LMI motion. Shimojo et al.’s
(1997) experiments with transient orienting cues have shown that
endogenously oriented attention is not necessary, and Christie and
Klein (2005) have shown that it is not sufficient for the perception of
LMI motion (see also Chica, Charras, & Lupianez, 2008).
The above-mentioned study by Shimojo et al. (1997) indicated
that exogenously oriented attention is sufficient to create the
perception of LMI motion. It is, however, not necessary for its
occurrence. In all the experiments in the current article, the pos-
sibility that the fixation dot would exogenously attract attention
was eliminated by continuously presenting it at the same location,
regardless of whether the LMI stimulus was present or not. If,
despite our instructions to maintain attention on the fixation dot,
attention were exogenously drawn to a feature of the LMI stimulus
(e.g., the square presented during the first frame), motion would
a)
+
-+
-
+
Decrease
Subunit
Increase
Subunit
-+
-
+
Frame 1
(2,000 ms)
Frame 2
(400 ms) +
-+
Increase
Subunit
Decrease
Subunit
-+
-
+
Frame 1
(2,000 ms)
Frame 2
(400 ms) +
-
+
Increase in Bar Luminance b) Decrease in Bar Luminance
Figure 6. Schematic of counterchange model as applied to the perception of: LMI motion. (a) For increases in
bar luminance. (b) For decreases in bar luminance.
792 HOCK AND NICHOLS

always have been in the same direction, away from the location of
the attention-attracting feature, regardless of whether the lumi-
nance of the bar increased or decreased. This, however, was never
observed. Different motion directions always are perceived for
increases vs. decreases in bar luminance, verifying the conclusions
of Downing and Treisman (1997) and Tse and Cavanagh (1995)
that neither gradients of attention-speeded processing nor attentive
tracking are necessary for the perception of LMI motion.
Third-Order Motion and The Detection of
Counterchange
Lu and Sperling (1995a, 2001) have presented substantial evidence
for a three-systems theory of motion perception. Whereas the first-
and second-order motion systems entail the extraction of motion
energy, the third-order system is based on attentionally modulated
changes in salience/activation created by stimulus attributes changing
at different spatial locations. For example, Blaser et al. (1999) tested
motion perception with a directionally ambiguous stimulus in which
a red/green sine grating was presented during the odd-numbered
frames (phase shifted by 180° with successive presentations), and a
contrast-modulated noise grating was presented during the interven-
ing even-numbered frames (phase shifted by 90° in relation to the
preceding red/green grating). They found that attention to either red or
green resulted in motion being perceived in the direction specified by
that color. Attention was exogenously cued in their study. It was
drawn to successive locations of the attended color as it reappeared
during successive frames, amplifying the input to detectors signaling
motion in that direction.
Evidence that the perception of LMI motion for two adjacent
surfaces can be determined by exogenously oriented attention
(Shimojo et al., 1993), that it is unaffected when the square and
adjacent bar are presented separately to the two eyes (Faubert &
von Gru¨nau, 1995; Hikosaka et al., 1993b), and that it does not
require the extraction of motion energy (Experiments 4 and 5 of
this study) all point to its perception by Lu and Sperling’s (1995a)
third-order motion system. Parallel evidence that the perception of
apparent motion between a pair of nonadjacent surfaces can be
influenced by exogenously attracted attention (Hock et al., 2002;
Stelmach, Herdman, & McNeill, 1994), that it can be perceived
when the two surfaces are presented separately to the two eyes
(e.g., Braddick, 1980), and that it does not require the extraction of
motion energy (Hock et al., 2002) likewise points to its perception
by the third-order motion system. Finally, evidence that the coun-
terchange principle applies to the perception of both LMI motion
and apparent motion suggests that oppositely signed stimulus
changes at pairs of spatial locations provide feedforward input to
the third-order system and, further, that counterchange detection
might constitute an attentionally modulated, feature-invariant mo-
tion signaling mechanism for the third-order system.
A computational model for the detection of counterchanging
activation has recently been developed by Hock, Scho¨ner, and
Gilroy (2009). The model is composed of a pair of subunits that
respond biphasically to changes in input activation.
4
One subunit
responds with excitation to decreases in input activation at one
spatial location and the other responds with excitation to increases
in input activation at another spatial location. Motion is signaled
by the multiplicative combination of the transient outputs of these
4
Biphasic detectors create transient responses to changes in input
activation by giving positive weight to recent inputs and negative
weight to older inputs. For the “Decrease” subunit, a recent decrease in
input activation receives positive weight (excitation) and the preceding
input activation receives negative weight (inhibition). For the “In-
crease” subunit, a recent increase in input activation receives positive
weight (excitation) and the preceding input activation receives negative
weight (inhibition).
a)
-+
-
+
-
+
-
+
-+-
+
b)
b)
-
+
-+
-
+
-
+
-
+
-
+
Activation
Decreases
Activation
Decreases
Activation
Decreases
Activation
Decreases
Activation
Increases
Activation
Increases
Time
Time
Space
Space
Figure 7. (a) Temporal discontinuities at each spatial location traversed by
the leading and trailing boundaries of the moving object create a cascade of
counterchanging edge/surface contrast. Rightward motion is specified at the
leading boundary by the combination of decreased edge contrast (downward
arrows) and increased surface/background contrast (upward arrows). Right-
ward motion is specified at the trailing boundary by the combination of
decreased surface/background contrast (downward arrows) and increased edge
contrast (upward arrows). (b) Schematic of counterchange model as applied to
the perception of continuous object motion.
793
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

“Decrease” and “Increase” subunits to changes in input activation;
both subunits must be excited at the same time in order for motion
to be perceived.
The evidence in the current article for edge/surface counter-
change as the basis for LMI motion is consistent with edge filters
(elongated receptive fields with one excitatory and one inhibitory
lobe) providing the input to a biphasic “Decrease” or “Increase”
subunit and center/surround filters (with excitatory centers and
inhibitory surrounds, or vice versa, depending on the luminance
polarity of the background) providing the input to a biphasic
“Increase” or “Decrease” subunit. A schematic of the model shows
how these spatial filters would account for the direction of the LMI
motion perceived when one of two adjacent surfaces increases
(Figure 6a) or decreases in luminance (Figure 6b).
Counterchange and Continuous Object Motion
When an object moves continuously across a darker back-
ground, luminance discontinuously increases at the leading edge of
the object and discontinuously decreases at its trailing edge
(Figure 7a). These temporal discontinuities create a cascade of
simultaneous edge/surface counterchanges that specify motion in
the same direction at both the leading and trailing edges of the
object. At the first moment in time depicted in Figure 7a, there is
edge contrast at the boundary separating the leading edge of the
object from the background, and there is no surface luminance just
in front of the object. As the object moves rightward, the edge
contrast at the previous boundary location decreases to zero (the
downward arrow in Figure 7a) and the previously vacant space in
front of the object now is occupied by the object, increasing the
surface/background contrast luminance at that location (the up-
ward arrow in Figure 7a). Counterchange-determined motion is
similarly specified at the trailing edge of the object.
Counterchanging edge and surface contrast could therefore consti-
tute the stimulus information that specifies continuous object motion,
and counterchange detection could be the basis for its perception. As
illustrated in Figure 7b, the increase in activation for the edge filter
when the leading boundary of the moving object enters the edge
filter’s excitatory lobe is followed a moment later by a decrease in its
activation when it enters the edge filter’s inhibitory lobe. Soon after-
ward (depending on the object’s speed), the activation of the center/
surround filter is increased when the moving object enters its excita-
tory center. Counterchange-specified rightward motion is signaled at
the leading boundary of the moving object by this combination of
decreased activation for the edge filter and increased activation for the
center/surround filter. Counterchange-specified rightward motion is
similarly signaled at the trailing boundary of the moving object by the
combination of decreased center/surround activation and increased
edge filter activation.
The stimulus depicted in Figure 8a demonstrates that the detec-
tion of a spatial pattern of oppositely signed changes in edge and
-+
-
-
-+
b)
-
-+
Activation
Decreases
Activation
Decreases
Activation
Increases
+
Frame 1
(2,000 ms)
Frame 2
(50 ms)
Frame 3
(1,000 ms) +
+
-+
-
-
-+
a)
-
-+
Activation
Decreases
Activation
Decreases
Activation
Increases
+
Frame 1
(2,000 ms)
Frame 2
(50 ms)
Frame 3
(1,000 ms) +
+
Figure 8. Stimuli demonstrating how the detection of edge/surface counterchange could result in the perception
of motion for the leading boundary of a continuously moving object.
794 HOCK AND NICHOLS

surface-to-background contrast is a likely basis for the perception
of continuous object motion. There are only increases in luminance
for this three-frame stimulus, which simulates the motion percep-
tion at the leading boundary of a continuously moving object.
Frame 1 (2,000 ms) begins with the activation of an edge filter by
the thin light and dark bars that presumably fall in its excitatory
and inhibitory lobes. During Frame 2 (50 ms), luminance increases
for the thin dark bar on the right, decreasing the activation of the
edge detector, and during the Frame 3 (1,000 ms), the rectangular
surface appears to the right of the thin bars, activating a center/
surround filter at that location. Rightward motion is perceived across
the gap between the thin bars and the rectangular surface to its right,
consistent with how edge/surface counterchange would signal motion
for the leading edge of a continuously moving object. (See supple-
mental Figure 8a in the online supplemental materials.) Rightward
motion likewise is perceived across the gap when the rectangular
surface on the right appears during Frame 1 and increases in lumi-
nance during Frame 3, as in Figure 8b, showing that changes in
location are not required for perceiving this analog of continuous
object motion. (See supplemental Figure 8b.)
Counterchange and Motion Energy Detection
The counterchange model proposed for the perception of LMI
motion and continuous object motion has essentially the same com-
ponent filters as Adelson and Bergen’s (1985) motion energy model,
but in a different arrangement. Both have “odd” spatial filters (edge
detectors for the counterchange model) and “even” spatial filters
(center/surround detectors for the counterchange model), and both
have biphasic (bandpass) temporal filters that respond to changes in
luminance. For motion energy detection, the “odd” and “even” spatial
filters are aligned at the same spatial location and the bandpass
temporal filters for each respond to same-signed changes in input
activation. The motion energy detector thereby determines whether
there is motion at a single point in space. For counterchange detection,
the “odd” and “even” spatial filters are at different spatial locations,
and the bandpass temporal filters for each respond to oppositely
signed changes in input activation. The counterchange detector there-
fore determines whether there is motion between two points in space;
that is, from the location with the decrease in activation to the location
with an increase in input activation.
These different filter configurations could serve parallel percep-
tual functions. For example, the point-by-point computation of
motion direction, as determined by motion energy analysis, could
provide a suitable basis for the spatial integration that is necessary
for the detection of global optic flow, while the motion path of an
object that has been parsed from the background could be deter-
mined by counterchange. This distinction between two qualita-
tively different kinds of motion information is consistent with
Sperling and Lu’s (1998) description of first- and second-order
motion energy systems as “objectless,” and the third-order system
as the basis for the perception of object motion.
References
Adelson, E. H., & Bergen, J. R. (1985). Spatiotemporal energy models for
the perception of motion. Journal of the Optical Society of America, 2,
284 –299.
Baloch, A. A., & Grossberg, S. (1997). A neural model of high-level
motion processing: Line motion and formotion dynamics. Vision Re-
search, 37, 3037–3059.
Blaser, E., Sperling, G., & Lu, Z. L. (1999). Measuring the amplification
of attention. Proceedings of the National Academy of Science USA, 96,
11681–11686.
Braddick, O. J. (1980). Low-level and high-level processes in apparent
motion. Philosophical Transactions of the Royal Society of London,
Series B, 290, 137–151.
Cavanagh, P. (1992). Attention-based motion perception. Science, 257,
1563–1565.
Chica, A. B., Charras, P., & Lupianez, J. (2008). Endogenous attention and
illusory line motion depend on task set. Vision Research, 48, 2251–2259.
Christie, J., & Klein, R. M. (2005). Does attention cause illusory line
motion? Perception & Psychophysics, 67, 1032–1043.
Downing, P. E., & Treisman, A. M. (1997). The line-motion illusion:
Attention or impletion? Journal of Experimental Psychology: Human
Perception and Performance, 23, 768 –779.
Faubert, J., & von Gru¨nau, M. (1995). The influence of two spatially
distinct primers and attribute priming on motion induction. Vision Re-
search, 35, 3119 –3130.
Gibson, J. J. (1968). What gives rise to the perception of motion? Psycho-
logical Review, 75, 335–346.
Hikosaka, O., Miyauchi, S., & Shimojo, S. (1993a). Voluntary and
stimulus-induced attention detected as motion sensation. Perception, 22,
517–526.
Hikosaka, O., Miyauchi, S., & Shimojo, S. (1993b). Focal attention pro-
duces illusory temporal order and motion sensation. Vision Research, 33,
1219 –1240.
Ho, C. E. (1998). Letter recognition reveals pathways of second-order and
third-order motion. Proceedings of the National Academy of Science
USA, 95, 400 – 404.
Hock, H. S., Gilroy, L., & Harnett, G. (2002). Counter-changing lumi-
nance: A non-Fourier, non-attentional basis for the perception of single-
element apparent motion. Journal of Experimental Psychology: Human
Perception and Performance, 28, 93–112.
Hock, H. S., Kogan, K., & Espinoza, J. (1997). Dynamic thresholds for the
perception of single-element apparent motion: Bistability from local
cooperativity. Perception & Psychophysics, 59, 1077–1088.
Hock, H. S., & Nichols, D. F. (2009). State-dependent dynamic grouping:
A high-level mechanism for the perception of motion. Manuscript in
preparation.
Hock, H. S., Scho¨ner, G., & Gilroy, L. (2009). A counterchange mecha-
nism for the perception of motion. Acta Psychologia, 132, 1–21.
Holcombe, A. O. (2003). Occlusion cues resolve sudden onsets into mor-
phing or line motion, disocclusion, and sudden materialization. Journal
of Vision, 3, 562–572.
Hsieh, P. J., Caplovitz, G. P., & Tse, P. U. (2005). Illusory rebound motion
and the motion continuity heuristic. Vision Research, 45, 2972–2985.
Hsieh, P. J., Caplovitz, G. P., & Tse, P. U. (2006). Illusory motion induced
by the offset of stationary luminance-defined gradients. Vision Research,
46, 970 –978.
Johansson, G. (1950). Configurations in event perception. Uppsala, Swe-
den: Almqvist & Wiksells Boktryckeri AB.
Lu, Z. L., & Sperling, G. (1995a). The functional architecture of human
visual motion perception. Vision Research, 35, 2697–2722.
Lu, Z. L., & Sperling, G. (1995b). Attention-generated apparent motion.
Nature, 377, 237–239.
Lu, Z.-L., & Sperling, G. (2001). Three-systems theory of human visual
motion perception: Review and update. Journal of the Optical Society of
America A, 18, 2331–2370.
Nakayama, K., & Mackeben, M. (1989). Sustained and transient compo-
nents of focal visual attention. Vision Research, 29, 1631–1647.
Posner, M. I. (1980). Orienting of attention. Quarterly Journal of Exper-
imental Psychology, 32, 3–25.
795
THE LINE MOTION ILLUSION: DETECTING COUNTERCHANGE

Shimojo, S., Miyauchi, S., & Hikosaka, O. (1997). Visual motion sensation
yielded by non-visually driven attention. Vision Research, 37, 575–
1580.
Sperling, G., & Lu, Z. L. (1998). A systems analysis of visual motion
perception. In T. Watanabe (Ed.), High-level motion processing: Com-
putational, neurobiological, and psychophysical perspectives (pp. 154 –
183). Cambridge, MA: MIT Press.
Stelmach, L., Herdman, C., & McNeill, R. (1994). Attentional modulation
of visual processes in motion perception. Journal of Experimental Psy-
chology:Human Perception and Performance, 20, 108 –121.
Tse, P., & Cavanagh, P. (1995). Line motion occurs after surface parsing.
Investigative Ophthalmology and Visual Science, 36, 1919.
Tse, P., Cavanagh, P., & Nakayama, K. (1998). The role of parsing in
high-level motion processing. In T. Watanabe (Ed.), High-level motion
processing: Computational, neurobiological, and psychophysical per-
spectives (pp. 154 –183). Cambridge, MA: MIT Press.
von Gru¨nau, M., Saikali, Z., & Faubert, J. (1995). Processing speed in the
motion-induction effect. Perception, 24, 477– 490.
Zanker, J. M. (1994). Modeling human motion perception. I. Classical
stimuli. Naturwissenschaften, 81, 156 –163.
Appendix
Motion Energy Detection Model
Computations were done in Matlab 7.4.0, on a Macbook running
OS X, 10.4.11. Space and time were sampled discretely with
increments of .02° and 10 ms, respectively. The spatial and lumi-
nance values were as in the experiments. Temporal values were
modified in order to isolate the luminance-change portion of the
trials; 4-s intervals were successively assigned to an initial blank
field, the first frame of the two-frame trials, the second frame of
the two-frame trials, and a final blank field.
The spatial and temporal filters, as well as the algorithm to
calculate motion energy, were as in Adelson and Bergen (1985). In
executing the model, the time course of the stimulus was con-
volved with all four combinations of “even” and an “odd” spatial
filters (Equations 1 and 2), and two temporal filters with a slight
temporal offset between them (Equations 3 and 4). The spatial
scaling factor for the filters, ␴
s
, was chosen to be 0.5, which gives
a strong response in the correct direction for a basic LMI stimulus
with the same spatial dimensions as in the experiments; narrower
filters produce a weak response and broader filters respond most
strongly to motion in the wrong direction. The parameters for the
temporal filters were k
1
⫽0.014 and k
2
⫽0.017, which give a
maximal response to sine wave stimuli moving at 10 Hz.
seven ⫽
⫺x2⫹␴s
2
␴s
5
冑
2␲e
⫺x2
2␴s
2(1)
sodd ⫽
⫺x3⫹3x␴s
2
␴s
7
冑
2␲e
⫺x2
2␴s
2(2)
t1⫽k1te⫺k1t
冉
1
6⫹共k1t兲2
120
冊
(3)
t2⫽k2te⫺k2t
冉
1
120 ⫹共k2t兲2
5040
冊
(4)
Following this linear spatial and temporal filtering of the stim-
ulus, the outputs of the four combinations of spatial and temporal
filters were squared to give a directional output at each point in
space and time. The magnitude and direction of the motion re-
sponse at the square/bar boundaries was the maximum response
within 0.5° of the edge of the square/bar boundary and within
3,000 ms of the change from the first to the second frame of each
trial.
Also created was a modified version of Adelson and Bergen’s
(1985) motion energy detector. In the original version, the positive
and negative portions of the spatial receptive field are balanced,
i.e. they sum to zero for a uniform field. In the modified version
they are imbalanced such that the inhibitory portion has 75% of the
magnitude of the excitatory portion. As a result of the imbalance,
the response to a change in the luminance level of a uniform field
depends on its initial luminance level, as per Weber’s law (Equa-
tions 5 and 6). The model is the same in all other respects.
seven
imb ⫽1
␴s
冑
2␲e
⫺x2
2␴s
2⫺0.75
2␴s
冑
2␲e
⫺x2
2共2␴s兲2(5)
sodd
imb ⫽x
␴s
3
冑
2␲e
⫺x2
2␴s
2⫺0.75x
共2␴s兲3
冑
2␲e
⫺x2
2共2␴s兲2(6)
Received January 14, 2009
Revision received April 27, 2009
Accepted May 5, 2009 䡲
796 HOCK AND NICHOLS