the stimulus is presented briefly, observers report motion in the direction opposite that ..... circles, for comparison, show direction-of-motion discrimination of.
Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A
G. B. Henning and A. M. Derrington
1759
Direction-of-motiondiscrimination with complex patterns: further observations G. Bruce Henning SRI/David Sarnoff Research Center, Princeton, New Jersey 08540 A. M. Derrington Department
of Physiological Sciences, The Medical School, Newcastle-upon-Tyne,
England
Received June 10, 1987; accepted June 3, 1988 Moving one component of a stimulus comprising two sinusoidal gratings of the same orientation sometimes results
in mistaken judgments of the direction of motion. If the component with the higher spatial frequency moves and the stimulus is presented briefly, observers report motion in the direction opposite that which actually occurs. The illusory, or backward, motion appears whether the movement producing it occurs smoothly or as a discrete jump at the midpoint of the stimulus presentation. At durations at which motion appears reversed, smooth and discrete motion are indistinguishable. Measurement of the speed of the illusory motion by a cancellation technique permits comparison with results from classical induced-motion paradigms; the classical effect, obtained with spatially separated components, is smaller but in the same direction as the errors in perceived direction of motion that we measure. We suggest that the errors in judging the direction of motion may result from interactions among motion
detectors tuned to the different spatial-frequency components of the stimulus.
INTRODUCTION The direction in which a briefly presented, vertical sinusoidal grating appears to move can be reversed by the addition of a static component of lower spatial frequency.' In the
presence of a component of lower spatial frequency, the combined pattern appears to move in a direction opposite that in which the moving component actually moves; the same motion viewed without the lower-spatial-frequency grating is seen correctly.
The illusion occurs when the stimulus duration is briefless than approximately 100 msec. At durations greater than 200msec, the higher-frequency grating is seen correctly
ments of the direction of motion are relative judgments in which the relative motion is ascribed to the lower-frequency component. But data for different observers were inconsistent. Further measurements, although not contradictory, reveal a more complicated picture.
METHOD The stimuli and experimental procedures were identical to those described by Derrington and Henning.' Vertically orientated spatial patterns were generated on a television display (Joyce Electronics, Cambridge) by using a computerized version of the method of Schade."1
The cross-sec-
as moving in the direction in which it actually moves-even
tional luminance profile of the (one-dimensional) stimuli
in the presence of a static low-frequency grating. The short stimulus durations required to produce the effect suggest the operation of what is often termed the low-level motion
consisted of the sum of one or more sinusoids of the same
system.
23
However, current models of low-level motion
processing4-8 do not readily predict the effect, and even our
orientation. Each component could be made to move independently to the left or to the right and at different speeds. The display subtended 7.5 by 6.25 deg at the observers' eyes,
and the presentation of a stimulus did not alter its mean
suggested modifications of the models to allow them to pre-
luminance (160 cd/M2 ).
dict the illusion are not particularly compelling. It seemed possible that a single-channel, gradient-based motion-detection system might account for the illusion.l The mechanism was developed from that proposed by Limb
Each component of the stimulus was generated by reading numbers from a list, stored in a PDP 11/73 computer, to a 12-bit digital-to-analog converter. The digital-to-analog converters generating the analog signal for the 95-kHz raster
and Murphy 9 and by Fennema and Thompson' 0 for extracting regions with different velocities from successive frames of video displays. In this paper, we first show that system has characteristics different from those of our observers and that it can therefore be rejected as a model of the mechanism
were altered on every line, and approximately 500 lines were
underlying human performance. Then, to determine the magnitude of the illusory motion,
we measure the amount and direction of real motion required to cancel it. Preliminary measurements were not inconsistent with the notion that, at short durations, judg0740-3232/88/101759-08$02.00
displayed on each frame. Smooth motion of any component was introduced by changing the starting position in its list by a small amount
at the beginning of each frame (every 8
msec). If a single step displacement was required, the starting position was changed at the beginning of a frame in the middle of a presentation. In most of our experiments, the two components of the stimulus were added together and the sum used to modulate the contrast of the display. However, in one experiment, analog switches synchronized with the © 1988 Optical Society of America
1760
J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
vertical scan were used to switch between the two compo-
nents so that one component appeared in a band across the center of the display and the other in bands at the top and bottom. The duration of the stimuli was manipulated by adjusting the time constant, a, of the Gaussian'2 temporal envelope (truncated at 1.024 sec) that modulated the contrast of both components of the stimulus. The observers (usually the authors) were required to discriminate between leftward and rightward motion in a standard two-alternative forced-choice task: A stimulus in which one or more of the components moved in some direc-
tion was presented in the first observation interval of each trial. After a pause, and in the second observation interval of the trial, the direction of motion was reversed. The observer's task was to press a key to indicate the interval in which the stimulus moved leftward; a second press began the next trial. Different types of stimulus presentation were randomly interleaved, and the number of correct responses was recorded separately for each type of stimulus.
G. B. Henning and A. M. Derrington
moving in the direction opposite that in which the moving component actually moves. In neither case does the direction of apparent motion depend on the relative phase of the moving and static components. That the illusory "backward" motion does not depend on the relative starting phase of the two components is inconsistent with the notion that the observers use a mechanism analogous to our modification' of the gradient-based model of Fennema and Thompson.' 0 In a gradient-based motion detector, velocity estimates over the surface of the display are derived locally from the ratio of the rate of change of
luminance with time to the rate of change of luminance with distance. With our two-component stimuli, the velocity estimates depend on location within the stimulus but, over most of the display, can be made to predict reversed motion by assuming the internal representation of the component of (A)
10,
Short Duration *
RESULTS AND DISCUSSION
Long Durat ion
Experiment I: The Effects of Relative Phase
L U
The stimulus comprised two gratings, each with 12% contrast: a static (nonmoving) grating having a spatial frequen-
U
0
5
L
cy of 1 cycle per degree of visual angle (c/deg) and a grating of 3 c/deg that changed location in a single step at the center
of the Gaussian temporal envelope that determined the duration of the (compound) stimulus. The 3-c/deg grating moved in one direction in the first observation interval and in the opposite direction in the second; the observers' task was to indicate the interval in which leftward motion occurred. The displacement step imposed on the 3-c/deg grat-
0
ing was one quarter of its spatial period. Two different temporal envelopes were used: long duration (a = 0.27 sec) and short duration (a = 0.014 sec). The
durations were chosen because observers correctly report the direction in which the 3-c/deg grating moves at the longer duration but, at the shorter duration, see motion in the direction opposite that which actually occurs.' From observation interval to observation interval the spatial phase of the static 1-c/deg grating was chosen randomly from a set of eight equally likely phases equally spaced from
90
0
180
360
270
(B) I
10
0
0
0
0
0
0
S
S
S
S
Short Durotion * Long Duration
0
a) L
L
0
5 -
c-
0 to 360 deg. The principal variable manipulated was the phase of the 3-c/deg grating, which was fixed at one of eight
different values relative to the peak of the 1-c/deg grating. On each trial, the extent of the motion was the same, and the starting phase relation of the leftward motion was the same as the finishing phase of the rightward motion. Stimuli are denoted by the starting phase of the leftward motion. Figure 1 shows the number of correct responses as a function of the phase of the 3-c/deg grating-Fig. 1(A) for observer AH and Fig. 1(B) for observer AMD. Open symbols
show the results obtained with the longer stimulus duration; filled symbols show the results with the shorter duration. It is clear that the relative phase of the moving component has little effect on the apparent direction of motion. As in the results reported previously,' the motion of stimuli exposed for the longer duration is correctly perceived, whereas stimuli exposed for the shorter duration are consistently seen
o . 0
S
S
S
90
180
Spatial Fig. 1.
Direction-discrimination
270
360
Phose
performance of human observers
judging the direction of motion of a pattern comprising a static 1-c/ deg grating and a 3-c/deg grating that changes its phase at the midpoint of the presentation interval by 90 deg (one fourth of its spatial period). The number of correct responses is plotted for observer AH in (A) [for observer AMD in (B)] as a function of the starting phase of a moving 3-c/deg component (measured relative to the peak of the static 1-c/deg component). Open circles show results with long presentations (Gaussian temporal envelope with a = 0.27 sec). Filled circles show results with brief presentations (a = 0.014 sec).
Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A
G. B. Henning and A. M. Derrington
1761
used at each duration. Speeds corresponding to temporal frequencies of 12.2 and 2.44 Hz were used at the shortest duration. The successof these precautions was indicated by the fact that discrimination of smooth from abrupt motion was independent of speed at each duration; consequently, the data for the two speeds have been combined. Figure 3 shows the percentage of correct discriminations based on 100trials as a function of a, the time constant of the
Ir
0
temporal envelope.
Data for the two observers are shown in
separate panels: open circles show the results obtained with 1-c/deg gratings; open diamonds, the results with 3-c/deg -1
0
each observer's performance in discriminating direction of 90
180
Spatial
270
360
Phase
Fig. 2. Effect of spatial phase on the decision variable of the modified gradient model' as a function of the spatial phase of a moving 3-
c/deg component measured relative to the peak of the static 1-c/deg component.
The data indicated by the filled symbols show
gratings.
8
Positive values of the decision variable indicate mo-
tion in the same direction as that of the moving component of the pattern; negative values indicate motion in the opposite direction.
motion with single jumps of one quarter of the period of a 3c/deg grating in the presence of a static 1-c/deg grating (from Fig. 4 of Ref. 1). The results confirm our informal observa-
tions; the observers were unable to discriminate smooth from discrete motion at signal durations determined by time constants less than -50 msec, and it is at these durations that the illusory motion predominates. A common explanation of our failure to make a discrimi-
nation is that the information on which the discrimination might be based is not available to the observer either higher spatial frequency to have much less contrast than that of the lower-frequency component. Under these conditions, the model predicts that direction-of-motion judgments should depend strongly on the relative phase of the two components, and the phase dependence derived from the model is indicated in Fig. 2.
The ordinate of Fig. 2 shows the decision variable derived
through lack of sensitivity or through masking.13 -' 6
If we
assume that a motion-detection system has no information about stimuli that produce no changes in luminance over time, then the result implies that the motion system cannot discriminate a temporal motion impulse from a rectangular pulse of the same area lasting -100 msec. This corresponds approximately to the blur time inferred by Burr and Ross17
from the model as a function of the starting phase of the 3-c/
deg grating. Values greater than zero correspond to correct-
100
ly seen motion; values less than zero correspond to illusory or
AMD
backward motion. Figure 2 demonstrates that the model predicts that direction-of-motion discrimination should show a strong dependence on phase, a dependence that is clearly not part of our observers' behavior. We therefore
75 _ L LI
reject the model. One characteristic of the steplike motion used in this experiment is that it appears to be smooth and continuous at the short durations for which the illusory motion occurs. Experiment II established and measured this effect.
50L 25L 0
0
Experiment II: Discrimination of Smooth from Abrupt Motion
100
The stimuli in Experiment II were simple sinusoidal gratings of either 1 or 3 c/deg.
In one observation interval, the
grating moved abruptly either leftward or rightward by one quarter of its spatial period. The motion occurred as a singlejump at the center of the Gaussian temporal envelope that determined the stimulus duration. In the other observation interval, the stimulus moved smoothly (that is, in small, equal spatial steps made every 8 msec at the beginning of each frame). The observers' task was to indicate the interval in which the smooth motion had occurred. To prevent our observers from attempting to perform the discrimination on the basis of the distance traveled by the stimulus during the observation interval, the speed of the smoothly moving grating was made inversely proportional to the duration of the grating. Then, to remove any potential cue resulting from failure to match velocities in the two observation intervals, two speeds that differed by a factor of 5 were
49 CU
L ,L
r
75L
:00 100 200 Time Constant (msec)
G81E
50L
0o
25L 0
- --- --- I
I-I
200 300 Time Constant (msec) Fig. 3. Discrimination between discrete and continuous motion for 0
100
1-c/deg (open circles) and 3-c/deg gratings (diamonds) as a function
of the time constant of the Gaussian temporal envelope. The filled circles, for comparison, show direction-of-motion discrimination of a stimulus comprising a static 1-c/deg grating and a 3-c/deg grating
that changes phase by 90 deg at the midpoint of the observation interval.
1762
J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
G. B. Henning and A. M. Derrington
and to what might be expected from the bandwidth of either of the two low-temporal-frequency mechanisms derived from flicker-frequency discrimination experiments' 8 19 or inferred from flicker-adaptation studies.2 0
grating moved is plotted as a function of the temporal fre-
quency of the 1-c/deg grating. Negative temporal frequencies indicate speeds of the 1-c/deg grating moving in the direction opposite that of the 3-c/deg grating; positive temporal frequencies indicate motion in the same direction as that of the 3-c/deg grating. For short durations, it is clear that the observers require the 1-c/deg component to move in the same direction as the 3-c/deg grating in order to cancel the apparent motion. The results obtained with the longer stimulus duration are shown in the two right-hand panels (note the 10-fold increase in the
Our observers found it difficult to estimate the velocity of
the illusory motion other than to note that it seemed brisk. Experiment III measured the velocity of the illusory motion by adjusting the velocity of the lower-frequency component to find the speed at which the observers were unable to specify the direction of motion. Experiment III: Canceling the Illusory Motion
scale of the abscissa).
The stimulus had two components with the spatial frequencies and contrasts used in Experiment I. The 3-c/deg grat-
ble those at short durations, but the temporal frequency of the 1-c/deg grating that produces equal numbers of leftward- and rightward-moving responses is much closer to
ing moved smoothly at a speed of 4 deg of visual angle per second (12.2 Hz), and the speed of the 1-c/deg grating was
zero.
manipulated. The direction of motion of both gratings was changed between the two observation intervals of each trial, but their speeds in the two intervals were the same. Motion
The smooth curves are least-mean-squares fits of the cumulative normal distribution to the data. The fits were calculated by probit analysis. We take the mean of the cumulative Gaussian as the temporal frequency of the lowfrequency grating that results in equal numbers of judgments of leftward and rightward motion and call that temporal frequency the canceling frequency. There are some similarities between aspects of the illusory motion that we have been studying and the phenomena of induced motion. Before considering the implications of the cancellation experiment, we compare our results with those obtained in a conventional induced-motion paradigms.
of the 1-c/deg grating in the same direction as the 3-c/deg
grating is indicated by positive speed or temporal frequency; motion in the opposite direction, by negative speed or temporal frequency. Two different durations were used: long (a = 0.27 sec) or short (a = 0.014 sec). The results for each observer are shown separately in the two columns of Fig. 4. In the two left-hand panels (short
durations) the number of trials on which the observers reported seeing motion in the direction in which the 3-c/deg AMD 0.014
The data for longer durations resem-
40 AMD 0.27
Sec
L U
40
E
30
301
20
20_
C 10
10L
Sec
,_ 4J
3 0
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n
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-10
no
40
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0
10
Sec
ThL
-1
0
1
G8H 0. 27 Sec
40
U
30
301
4J20
20L
m 10
10K
0> 0
0
C
-10
0
Temporal Frequency Fig. 4.
Cancellation of illusory motion.
-1
10
(H z)
Direction discrimination
0
Temporal Frequency
1
(Hz)
as a function of the temporal frequency of a 1-c/deg grating added to a
moving 3-c/deg grating that had a temporal frequency of 12.2Hz. The left-hand panels show results for brief presentations; those on the right for long presentations. (Note the tenfold expansion of the temporal frequency scale in the right-hand panels.) The solid curves are bestfitting cumulative Gaussians calculated by probit analysis.
G. B. Henning and A. M. Derrington
L 40AMD
Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A
0.014
Sec. Split
40 AMD 0.27
-u40 E
0
3
1763
0
_0~~~~~ 30_
0
C310 _ >oI
1
m
-10
10
0
GBH 0.014 Sec. Split
L 40
-1
0
1
GBH 0.27
40
D C
30
30K
20 K
20K
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)
En- I
-
-10
Temporal
-
0
I
o
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Frequency
10
(Hz)
n
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I
0
Temporal
Frequency
1
(Hz)
Fig. 5. Cancellation of induced motion. Direction discrimination as a function of the temporal frequency of a 1-c/deggrating displayed in a horizontal strip 2 deg high and extending across the center of the display. A 3-c/deg grating moving at 12.2 Hz was displayed in 2-deg-high horizontal strips above and below the central strip and separated from it by gaps of -0.3 deg. Other details as in Fig. 4.
Experiment IV: Induced Motion
In Experiment IV the display was divided into three horizontal strips, each of which subtended 2 deg of visual angle
in height. Gaps of 0.3 deg separated the top and bottom strips from the central strip. The stimulus in the top and bottom strips of the display was the inducer-a 3-c/deg grating moving leftward in one observation interval and rightward in the other at a speed of 4 deg of visual angle per second (a temporal frequency of 12.2 Hz). The stimulus
that filled the center section of the display (1-c/deg grating) was the test stimulus; we manipulated its speed. The direction of motion was reversed between the observation intervals of each trial, and the observers were required to report the direction in which the 1-c/deg grating moved. Two stimulus durations (a = 0.014 and a = 0.27 sec) were used.
Figure 5 showsthe number of trials on which the observers reported the 1-c/deg grating to be moving in the same direc-
tion as the 3-c/deg grating (inducer) as a function of the temporal frequency of the 1-c/deg grating. Motion in the split-screen case at short durations is in the same direction as the illusory motion with superimposed stimuli, but, measured in terms of the canceling motion, it is a little more than a factor of 2 weaker.
There is almost no induced motion at
the longer stimulus duration. This result is consistent with
the work of Levi and Schor. 2 ' Figure 6 summarizes the data of Figs. 4 and 5. It shows
the temporal frequency of the 1-c/deg grating at which the observers are unable to discriminate direction of motion as a
function of the time constant of the Gaussian temporal window. The insets illustrate one frame of the two display types. At the longer duration, there is little induced motion either with the whole field or with the split-screen display. At the shorter duration, the speed of the induced motion with the split-screen is about 2 deg of visual angle per second. This is less than one half of the speed obtained when the test and the inducer were superimposed. With superimposed components, the induced motion has a velocity (4.8 deg/sec) almost equal to that of the 3-c/deg grating (4.07 deg/sec).
The similarity of the speed of the moving component and the measured speed of the illusion suggests that the observers might be judging relative motion: First, the speed of the 1-c/deg grating that canceled the motion induced by the moving 3-c/deg grating was nearly the same as that of the 3c/deg grating. Second, the canceling 1-c/deg grating moved in the same direction as the 3-c/deg grating; that is, cancella-
tion occurred when there was almost no relative motion between the components of the stimulus. This observation might be taken to suggest either that the low-level-motion system signals relative motion or that motion information for short-duration
signals is interpreted
by the low-level-
motion system as if it were information about relative motion. In order to explore the notion that our observers might, in effect, be judging relative motion, we extended the cancellation experiment by using 2-, 3-, and 6-c/deg gratings as the
J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
1764
U>5 I-_
G. B. Henning and A. M. Derrington
AMD o
0
C
S
]hJF
111
D
o 4_
GBH *
Whole
AMD 0
I1IiiituitiSpl i t
L
GBH *
lower-frequency component corresponding to equal numbers of leftward- and rightward-moving judgments (determined from the 40-observation-per-point psychometric functions by probit analysis) as a function of the spatial frequency of the lower-frequency component. The parameter is the spatial frequency of the higher-frequency grating. On the coordinates
0 E .@
I-
-o 1 oj Dj0
09 o
-o 0 1
test
at the same velocity as the 2-, 3-, and 6-c/deg inducing
0. 30
0. 20
0. 10
0. 00
I
I
I
I
_
of Fig. 7, a (one-dimensional)
object moving at a constant velocity has its spatial-frequency components on a straight line through the origin. This is simply because an object moving at constant velocity past a point in space produces temporal frequencies that are proportional to the spatial frequencies that constitute the object. The slope of the line is determined by the direction and speed of the motion. Consequently, test objects moving
L
gratings should lie on the solid, short-dashed, and long-
Time Constont (sec) Fig. 6. Summary of Figs. 4 and 5: magnitude of induced motion (measured as the mean of the best-fitting cumulative Gaussian curve) for displays in which the test pattern (a 1-c/deg grating) and the inducing pattern (a 3-c/deg grating moving at 12.2 Hz) were either summed arithmetically over the whole display (circles and
upper inset) or spatially separated so that the test pattern occupied a 2-deg-high strip extending across the middle of the display and the
dashed lines, respectively.
Our data do not fall exactly on
those lines, but, for one branch of each set of data at least, they are not sufficiently discrepant to justify our rejecting out of hand the notion that the observers judge relative motion and attribute the resulting motion to the lowerfrequency object.
inducing pattern occupied the top and bottom of the display (diamonds and lower inset). Results for two observers are plotted for long (a = 0.27 sec) and short (a = 0.014 sec) presentations. (Plots of different conditions are horizontally offset for clarity.)
higher-frequency components with lower-frequency components of 0.25, 1, 2, 3 and 4 c/deg. The temporal frequency of the moving high-frequency component was 12.2 Hz in all
cases, and both high- and low-frequency components were presented within a brief Gaussian envelope (a = 0.014 sec).
Figure 7 shows the temporal frequency (in hertz) of the
DISCUSSION The apparent reversal in the direction of motion of briefly presented compound stimuli does not depend on the relative phase of the components of the stimulus. Thus, since the gradient-detection model that we had tentatively considered in a previous paper1 predicts phase dependence, the model must be rejected. Furthermore, the fact that the reversed motion occurs when the moving and static components are separated in space makes it possible to speculate
Reversed Motion with Di ffevrnt 9
9-
AMD
SF Pacirs GBH
N
N
//
Inducing 6 c/deg 3 c/deg 2 c/deg
6 L1
CCU A_ D
0 / ,
Inducing
SF
0
0
3 c/deg
0
.7
/
LL
2 c/deg
9
/ 3
aT
SF
6 c/deg
6
0
,7 I0
,/
0L L 0
0
0
E G)
0
1
2
3
Test Spatial Frequency
4
(C/deg)
0
1
2
3
Test Spatial Frequency
4
(C/deg)
Fig. 7. Magnitude of induced motion. The temporal frequency of the lower-frequency, or test, grating corresponding to the mean of the bestfitting cumulative Gaussian for different combinations of test and inducing spatial frequencies. All patterns occupied the whole display and were presented briefly (a = 0.014 sec). The temporal frequency of the inducing grating was always 12.2 Hz. The lines radiating from the origin indicate the locus, on these coordinates, of (one-dimensional) constant velocity objects of 2.03 deg/sec (solid lines), 4.07 deg/sec (long-dashed lines) and 6.10 deg/sec (short-dashed lines). SF, spatial frequency.
G. B. Henning and A. M. Derrington
that the percept may perhaps result from the combination of the outputs of different mechanisms responding to the different components. We shall consider two possible reasons for the reversal; neither of them is particularly compelling,
but each merits some consideration. The first is that the observers track the moving component in some way. The second concerns the way in which the determination of the
speed of motion might depend on estimates of temporal frequency obtained at different spatial frequencies. Tracking the Moving Component Since the illusory motion occurs for stimulus durations less than 50 msec and since eye movements have at least a 90msec latency, 22 it seems unlikely that eye movements play a crucial role in producing the illusion, although they may, of course, play a role in preventing it. Nonetheless, the obser-
vations of the cancellation experiments are consistent with the assumption that the observers change their frame of reference (as if they attempt to track the moving 3-c/deg grating) and then report the motion of the 1-c/deg grating relative to the moving frame of reference. In this explanation, the illusion is caused by a mismatch between the moving frame of reference and the position of the eyes; it occurs because the frame of reference begins to move in anticipation of a (tracking) eye movement. This notion is suggested
by the recent studies of Burr and Ross.'7 At longer durations the mismatch is removed either because the tracking movement takes place and the eyescatch up with the moving frame of reference or because the tracking movement does
not occur and the frame of reference is corrected. One difficulty with this explanation is that it provides no obvious explanation of the spatial-frequency selectivity of the phenomenon, that is, no explanation why the higher spatial frequency should be so much more effective in shifting the frame of reference than the lower. We have no supporting evidence for the moving-frame-of-reference con-
jecture. An alternative account of the phenomenon consistent with its spatial-frequency dependence is suggested by a second explanation. Temporal Frequency as a Function of Spatial Frequency
In the retinal image of a rigid (one-dimensional) object moving with constant velocity, the temporal frequency of each spatial-frequency component is given by the product of the object's velocity and the spatial frequency of the component. Thus velocity can be estimated either directly for any com-
ponent or indirectly from the slope of the line relating temporal frequency to spatial frequency (see Fig. 6). In a real object, for which the signal associated with any one component will be weak, we might even expect that the slope,
estimated from many spatial-frequency components, would provide a more reliable velocity estimate than any single component.
Velocity estimates based on local slope in the
temporal-frequency by spatial-frequency plane might lead to our illusory motion through misestimation of either spatial or temporal frequency, the latter being the more likely. First, note that in our stimuli there is a conflict: Because there are two different motions, the temporal frequencies do not fall on a constant-velocity
line in the temporal-frequen-
cy spatial-frequency plane. The system successfully resolves the two motions at long durations but fails with brief stimuli. It is possible that the illusory motion is seen at
Vol. 5, No. 10/October 1988/J. Opt. Soc. Am. A
1765
short durations because briefly presented stimuli have broad spectra that affect temporal-frequency estimates at each spatial frequency and consequently change the slope of the line from which velocity estimates may be made.
If the
misestimation were sufficient to cause the slope of the line to change sign, then we should expect reversed motion. Detailed consideration of the mechanisms available for estimating temporal frequencies"5 6"18-20 do not preclude this explanation. The complete answer to motion probably lies in the fact that motion, like color, is extracted by a finite number of systems. The stimulus for the illusory motion with brief stimuli results in the motion system's producing the motion analog of a metameric match. It is striking only in that the motion perceived is different in direction from that which actually occurs. The problem of inferring the set of mechanisms from which our brief stimuli and long-duration stimuli moving in the opposite direction produce the same responses, however, is not easy. Nevertheless, the suggestion
at least has clearly testable implications. SUMMARY (1)
A stimulus that is the sum of a moving sinusoidal
grating of 3 c/deg and a static 1-c/deg sinusoidal grating appears to move in the direction opposite that of the moving component if the stimulus duration is short. (2) The fact that direction-of-motion discrimination shows no dependence on the relative starting phase of the component stimuli allowsus to reject models of the low-level human motion system based on a simple gradient-based motion detector: Estimates of motion direction made by such a device show a strong dependence on phase; human observers do not.
(3) The stimulus duration below which our observers are unable to discriminate smooth from abrupt motion suggests that motion may be determined by mechanisms with temporal bandwidths of -10 Hz. This is the bandwidth of two of
the temporal channels estimated from flicker-frequency discrimination experiments' 7' 18 and from flicker-adaptation studies.' 9 (4)
The reversed motion can be canceled by moving the
initially static low spatial-frequency component in the same direction as the high spatial-frequency component. The temporal frequency required to cancel the motion is less if the two components are presented in different parts of the display and is negligible if the stimulus duration is long. (5) The temporal frequency required to cancel the reversed motion varies when the spatial frequencies of the two components are changed.
Only when the effect is at its
largest is the velocity of the canceling motion comparable with the velocity of the motion inducing the reversed motion. ACKNOWLEDGMENTS This research was supported in part by Medical Research Council project grant G82/19394N,Science and Engineering Research Council grant GR/D 87062 to A. M. Derrington, and the Addison Wheeler Fund. A. M. Derrington was an Addison Wheeler Fellow. We are grateful to D. R. Badcock, J. R. Bergen, and W.
G. B. Henning and A. M. Derrington
J. Opt. Soc. Am. A/Vol. 5, No. 10/October 1988
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Makous for their helpful criticism and discussion of aspects of this paper. G. B. Henning was on leave from the Department
of Ex-
perimental Psychology, University of Oxford, South Parks Road, Oxford, England.
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