Vision Res. Vol. 35, No. 16, pp. 2277-2286, 1995
Pergamon
0042-6989(94)00315-7
Copyright © 1995 ElsevierScienceLtd
Printed in Great Britain. All rights reserved
0042-6989/95 $9.50 + 0.00
Effects of Luminance Contrast and Phase
Difference on Motion Assimilation for
Sinusoidal Gratings
YOSHIO OHTANI,* KEISUKE IDO,t YOSHIMICHI EJIMAt:~
Received 3 May 1994; in revised form 27 September 1994; in final form 6 December 1994
When a sinusoidal (test) grating is displaced horizontally by a phase angle of 180 deg in a two-frame
apparent motion display, the perceived direction of motion is ambiguous; the test grating appears to
move either to the left or to the right (or to both directions). On the other hand, when the test grating
is displaced by 180 deg synchronously with the inducing gratings which, presented above and below
the test grating, jump unambiguously in one direction (e.g. displaced by 90 deg), the test grating always
appears to move in the same direction as the inducing gratings (motion assimilation). In the present
study, the effects of luminance contrast and phase difference on motion assimilation were examined.
The proportion of perceived direction of motion (left or right) was measured as a function of phase
difference between the test grating in the first and the second frame. The magnitude of motion
assimilation was evaluated as the change in the phase difference for which the proportions of
observers' response were equal (50%) for both directions. The magnitude of motion assimilation
increased with increase in the contrast of the inducing gratings or with decrease in the contrast of the
test grating. Also, the magnitude increased as the phase difference of the inducing gratings departed
from 180 deg. Based on these results, a quantitative formulation between the magnitude of motion
assimilation, and the contrast and the phase difference of the stimulus gratings was derived. Further,
a model was proposed which explains the stimulus dependences of motion assimilation in terms of
response-integration among local motion detectors.
Motion assimilation
Luminance contrast Phase difference
INTRODUCTION
Perceived direction of motion of a visual stimulus is
influenced by the movement o f stimuli surrounding it.
Motion phenomenon showing such an influence has long
been known as "induced motion" or "motion contrast"
in which a physically stationary stimulus appears to
move in the opposite direction to the inducing stimuli
(Dunker, 1938; see Reinhardt-Rutland, 1988 for review).
In a variety of perceptual dimensions such as color,
brightness, and size, the human visual system manifests
two complementary properties of "contrast" and
"assimilation". Motion phenomenon showing an assimilation effect has recently been reported, in which a
physically non-moving (e.g. stationary or flickering)
stimulus appears to move in the same direction as the
inducing stimuli. This phenomenon, termed as "motion
Motion interaction Sinusoidal grating
capture" (Ramachandran, 1987), represents an integrative process in the human motion perception which
constitutes a complementary counterpart of a differential process underlying motion contrast (Braddick,
1993). Since the term "induced motion" essentially has
nothing to do with the direction of motion induced, and
"capture" is not an antonym for "contrast", we refer
to the two types of motion interactions as "motion
contrast" and "motion assimilation".
We recently found that strong motion assimilation
occurred with the stimulus configuration shown in
Fig. 1. A sinusoidal grating in the center field was
displaced horizontally in a two-frame apparent motion
display, while the gratings in the upper and the lower
fields were kept stationary. When the displacement of the
center grating between the two frames was near the
phase angle of 180 deg, the perceived direction of motion
was ambiguous; the center grating appeared to move
either to the left or to the right (or to both directions).
On the other hand, when the center grating was displaced by 180 deg synchronously with the inducing
gratings which moved unambiguously in one direction
(e.g. they were displaced by 90 deg), the center grating
*Department of Liberal Arts and Sciences, Faculty of Engineering,
Toyama Prefectural University, Kosugi-machi, Toyama 939-03,
Japan.
tDivision of Cognitive Science, Graduate School of Human and
Environmental Studies, Kyoto University, Yoshida-konoecho,
Sakyo-ku, Kyoto 606-01, Japan.
~To whom all correspondence should be addressed.
2277
2278
YOSHIO OHTANI et al.
~
o
¢o
t'o
-I-,s
Iq
12 °
~J
wl
FIGURE 1. Schematic representation of stimulus configuration.
The three fields, each of which subtended 12° by 3.Y~, were separated
by two horizontal black lines of 0.13 high, The test stimulus in the
center field and the inducing stimuli in the upper and the lower fields
were white-black vertical sinusoidal gratings of 1.1 c/deg. To facilitate
fixation, red squares of 0.13° was presented at the corners of an
imaginary square of 3.3° concentric with the center field.
always a p p e a r e d to m o v e in the same direction as the
inducing gratings.
W e find this o b s e r v a t i o n interesting because m o t i o n
c o n t r a s t , r a t h e r t h a n m o t i o n assimilation, has been
r e p o r t e d with a quite similar spatial c o n f i g u r a t i o n o f the
stimulus. Levi a n d Schor (1984) a n d R a y m o n d a n d
D a r c a n g e l o (1990) s h o w e d t h a t when the inducing
g r a t i n g s were drifted slowly in a m u l t i - f r a m e m o t i o n
display, the center g r a t i n g which was actually s t a t i o n a r y
a p p e a r e d to m o v e in the o p p o s i t e direction to the
inducing gratings. T h e similarity in the spatial configura t i o n allows us to e x a m i n e s y s t e m a t i c a l l y the effects o f
o t h e r stimulus p a r a m e t e r s on the i n d i v i d u a l types o f
m o t i o n interactions, t h e r e b y p r o m o t i n g the k n o w l e d g e
for the integrative a n d the differential processes in
*Threshold contrasts for the center and the peripheral gratings were
determined separately by a two-interval forced choice procedure
in conjunction with the method of constant stimuli. The duration
of the stimulus grating was 200 msec. The proportion of correct
responses for each contrast level was calculated based on 100 trials.
The data were fitted by a Weibull function with a maximum
likelihood procedure (Watson, 1979), and the contrast at the
75% correct level was taken as the detection threshold. For the
center grating, the thresholds (in terms of the Micfielson contrast)
were 0.0063 for YO and 0.0081 for KI. For the peripheral gratings,
the thresholds were 0.0080 for YO and 0.010 for KI. Further,
to evaluate the possible effect of threshold elevation due to the
presence of the peripheral gratings, threshold contrast for the
center rating was measured with the contrast of the peripheral
gratings set at 16 times the threshold. The threshold contrast was
the same (0.0063 for YO), or only slightly elevated (0.0089 for KI)
as compared with the values obtained without the peripheral
gratings. As the threshold contrasts for the test grating in the center
field, we used the values obtained in the presence of the peripheral
gratings.
m o t i o n perception. A p r e l i m i n a r y s t u d y on the effect o f
d i s p l a y type ( t w o - f r a m e vs m u l t i - f r a m e display) has been
r e p o r t e d elsewhere (Ohtani, I d o & Ejima, 1994).
A n i m p o r t a n t aspect o f m o t i o n c o n t r a s t has been
r e p o r t e d by R a y m o n d a n d D a r c a n g e l o (1990). T h e y
showed that the m a g n i t u d e o f m o t i o n c o n t r a s t increased
with increasing the l u m i n a n c e c o n t r a s t o f the inducing
gratings over a wide range o f 2 . 5 - 6 0 % . Since this is
quite distinct f r o m the findings with o t h e r measures
(e.g. m o t i o n detection, m o t i o n aftereffect a n d velocity
d i s c r i m i n a t i o n ) that m o t i o n p e r c e p t i o n does not d e p e n d
on l u m i n a n c e c o n t r a s t a b o v e a b o u t 5 % (e.g. Keck,
Palella & Pantie, 1976; N a k a y a m a & Silverman, 1985;
M c K e e , Silverman & N a k a y a m a , 1986), it seems
w o r t h w h i l e to e x a m i n e w h e t h e r such effect o f l u m i n a n c e
c o n t r a s t is specific to m o t i o n c o n t r a s t or c o m m o n to
the two types o f m o t i o n interactions. R a y m o n d a n d
D a r c a n g e l o (1990) also f o u n d that the l u m i n a n c e contrast o f the test g r a t i n g h a d little effect on the m a g n i t u d e
o f m o t i o n contrast. I f the distinct effects o f l u m i n a n c e
c o n t r a s t o f the test a n d the inducing gratings are
o b t a i n e d for m o t i o n a s s i m i l a t i o n as well, they will be
an i m p o r t a n t source o f i n f o r m a t i o n in elucidating the
u n d e r l y i n g m e c h a n i s m s o f the m o t i o n interactions.
In the present experiments, the effects o f l u m i n a n c e
c o n t r a s t o f the test a n d the inducing gratings on m o t i o n
a s s i m i l a t i o n were e x a m i n e d systematically. The p r o p o r t i o n o f perceived d i r e c t i o n o f m o t i o n for the test
g r a t i n g was m e a s u r e d as a f u n c t i o n o f the phase difference between the gratings in the first a n d the second
frame with the l u m i n a n c e c o n t r a s t s o f the test a n d
the inducing gratings as p a r a m e t e r s . The m a g n i t u d e o f
m o t i o n a s s i m i l a t i o n was e v a l u a t e d q u a n t i t a t i v e l y as the
m a g n i t u d e o f lateral shift o f the empirical function.
F u r t h e r , the m a g n i t u d e o f m o t i o n a s s i m i l a t i o n was
m e a s u r e d as a function o f the phase difference o f the
inducing gratings. The results i n d i c a t e d that the m a g n i tude o f m o t i o n a s s i m i l a t i o n s h o w e d systematic dependences on the c o n t r a s t ratio o f the test a n d the inducing
gratings a n d the p h a s e difference o f the inducing
gratings. Based on these results, a q u a n t i t a t i v e f o r m u lation between the m a g n i t u d e o f m o t i o n assimilation,
a n d the c o n t r a s t a n d the p h a s e difference o f the stimulus
gratings was derived. F u r t h e r , a m o d e l was p r o p o s e d
which explains the stimulus d e p e n d e n c e s o f m o t i o n
a s s i m i l a t i o n in terms o f r e s p o n s e - i n t e g r a t i o n a m o n g
local m o t i o n detectors.
EXPERIMENTS
Methods
Stimuli and apparatus. The stimulus c o n f i g u r a t i o n is
s h o w n in Fig. 1. The three stimulus fields, each o f which
s u b t e n d e d 12 ° by 3.3 °, were s e p a r a t e d by two h o r i z o n t a l
b l a c k lines o f 0.13 ° high. T h e stimuli p r e s e n t e d in the
three fields were w h i t e - b l a c k vertical sinusoidal gratings.
The spatial frequency o f the g r a t i n g was 1.1 c/deg a n d
the l u m i n a n c e c o n t r a s t was varied between twice a n d
64 times the threshold.* The m e a n l u m i n a n c e o f the
EFFECTS
OF CONTRAST
AND
PHASE
DIFFERENCE
stimulus fields was 77 cd/m 2, and the background was
dark (0.7 cd/m2). To facilitate fixation, red squares of
0.13 ° (17 cd/m 2) were presented at the corners of an
imaginary square of 3.3 ° concentric with the center field.
The observers fixated at the center of the imaginary
square. The stimuli were generated using a Venus
graphics system (Neuroscientific; model 1020) which had
a 12-bit resolution for each of the R, G, and B channels,
and presented on a color C R T monitor (Mitsubishi
HL6615) at a frame rate of 90 Hz.
Procedure. An experimental session began after a
3 min dark adaptation and a 3 min light adaptation to
the uniform fields of 77 cd/m 2. In each trial, the grating
in the center field (termed the "test" hereafter) and the
gratings in the upper and the lower fields (termed the
"inducer") were presented for 200 msec, abruptly displaced horizontally with no inter-stimulus-interval, and
then presented further for 200 msec. The observers were
required to make a binary decision on the perceived
direction of motion (left or right) of the test by pressing
one of the two response keys.
The direction and the magnitude of the displacement
was defined as the phase difference between the gratings
in the first and the second frame, with a rightward
displacement expressed as a positive value. For the test,
the phase difference (tkt) was varied from 90 to 270 deg
in 10 deg steps. For the inducer, the phase difference (qS~)
was either 90 or 270 deg in the first three experiments,
while it was varied between 90 and 270 deg in the fourth
experiment. The inducer with q~i--90 deg appeared to
move unambiguously to the right, and that with
q~i = 270 deg did to the left. For both the test and the
inducer, the phase difference and the phase of the grating
in the first frame (relative to the center of the stimulus
field) were randomized independently across trials. Each
session consisted of I0 trials for each phase difference of
the test and the inducer. The luminance contrasts of the
test and the inducer were varied between sessions.
Observers. Two of the authors (YO, KI) participated
in all the experiments. Another observer (NI) naive to
the purpose of the present study took part in the third
experiment. YO and N I were emmetropic; K I was
myopic with his acuity corrected with contact lenses. The
observer sat in a darkened room and viewed the stimulus
with his right eye at a distance of 67 cm.
Results
Experiment 1: effect of luminance contrast of the
inducer. The proportion of "right" responses (Pr)
vs phase-difference [sin(tht)] functions for the test of
8 times the threshold contrast were obtained for the
inducers varying in contrast from twice to 64 times the
threshold. Figure 2 represents examples of the Pr vs
phase-difference functions for the test with the inducer
of 16 times the threshold. The upper and the lower
panels are for YO and KI, respectively. In each panel,
open circles are for the test with the inducer of 90 deg
phase difference (referred to as the "rightward-moving
inducer"), and filled circles are for the test with the
inducer of 270deg phase difference (the "leftwardVR 35/16~C
ON MOTION
ASSIMILATION
2279
YO
1.00
/
0.75
~,
/
0.25
III
p
/
/"
/
o
~"
/"
o.oo
/
•
-" • ~ " ~ -
m/---I~l-
d:l
~t~
"12
,
[ --(3--- rightward-moving inducer]
+
leftward-moving inducer i
-- R- - without inducer
J
KI
1.00
e.~
0.75
0.50
0.25
o.oo
:.g_~m~
-1
leftward t:S
_
-0.5
•
~ /
0
sin(~t)
,
0,5
1
~, rightward
FIGURE 2. The proportion of "right" responses vs sin(q~t) functions
for the test 8 times the threshold with the inducer of 16 times the
threshold. The upper panel for YO, and the lower for KI. Open circles
are for the test with the rightward-movinginducer, and solid circles are
for the leftward-movinginducer. Solid squares are for the test without
the inducer. Each data point is based on at least 20 trials. Solid and
broken curves represent the functions fitted by equation (1).
moving inducer"). The data for the test without the
inducer (solid squares) are shown for comparison. Solid
and broken curves represent the best-fitting functions
obtained by using equation (1) (see overleaf). Each data
point is based on at least 20 trials.
The three functions in the figure show a c o m m o n
S-shaped characteristic, but their positions along the
horizontal axis vary widely depending on the presence
and the direction of motion of the inducer. For the test
with the rightward-moving inducer, the Pr VS phasedifference function shifts to the left relative to that
obtained without the inducer. For the test with the
leftward-moving inducer, the function shifts to the right.
Since these shifts imply that the test is more likely to
move in the same direction as the inducer, it is clear that
motion assimilation occurs with the present stimulus
condition.
For the examples shown, the magnitude of motion
assimilation is quite large. Consider Pr for the test
with sin(~bt)= 0. Without the inducer, Pr is about 0.5,
indicating that the perceived direction of motion is
ambiguous. On the other hand, Pr is 1.0 for the test
with the rightward-moving inducer, and 0 for the test
with the leftward-moving inducer. This indicates that
the perceived direction of motion of the test becomes
2280
YOSHIO
OHTANI
completely unambiguous due to the presence of the
inducer.
To quantify the effect of contrast of the inducer, we
fitted the data for each contrast level with a logistic
function and estimated the values of the two parameters
and fl:
P~ =
1
(1)
1 + exp{ --~ • [sin(~bi) - fl]}
where ~ and fl represent the slope and the uncertainty
point [sin(~bt) at which P~ = 0.5] of the Pr VS phasedifference function, respectively. The values of ~ and fl
were estimated by using a maximum likelihood procedure (Watson, 1979). As exemplified in Fig. 2, the fit
of equation (1) to the data was good; goodness-of-fit
proved to be statistically satisfactory (Z 2 test; P < 0.05)
for all the conditions of the contrast and the phase
difference of the inducer.
The uncertainty point and the slope of the function
for the two observers are plotted in Fig. 3 as a function
of contrast of the inducer expressed as multiples of the
threshold contrast. Open symbols are for the test
1.00
e~
(a)
0.50
~
0.00
,...,
-11.50
"-"~ ~
±
L}..-- "--Cq
-1.00
tO
100
Contrast of inducer ( × threshold)
--m
25.00
YO; rightward-moving inducer
YO; leftward-moving inducer
- KI; rightward-moving inducer
- KI; leftward-moving inducer
-(b)
20.00
/
/?\
15.00
/
~D
Q
10.00
5.00
0.0{I
. . . . . .
~.m
i
i
......
10
i
100
Contrast of inducer ( × threshold)
F I G U R E 3. The uncertainty point (fl) and the slope (~) of the P~
vs sin(~bt) function as a function of contrast of the inducer expressed
as multiple of the threshold. The contrast of the test is 8 times the
threshold. (a) The uncertainty point, (b) the slope. Open symbols are
for the test with the rightward-moving inducer, and solid symbols are
for the test with the leftward-moving inducer. Circles are for observer
YO and squares are for KI. The arrow on the abscissa indicates the
point at which the contrast of the inducer matches with that of the test.
et al.
with the rightward-moving inducer, and solid symbols
are for the test with the leftward-moving inducer. The
arrow on the abscissa indicates the point at which the
contrast of the inducer matches with that of the test.
Figure 3(a) shows that, except for the lowest contrast,
the uncertainty point is negative for the test with the
rightward-moving inducer and positive for the test with
the leftward-moving inducer, indicating the occurrence
of motion assimilation. The absolute value of the uncertainty point is around 0 at the lowest contrast of the
inducer, increases linearly with increasing the contrast
up to 16 times the threshold, and asymptotes for the
higher contrasts. This indicates that, within a certain
range, the magnitude of motion assimilation increases
with increase in the contrast of the inducer. Figure 3(b)
shows that the slope tends to increase with increasing
the contrast of the inducer, although some of the data
for KI (for the tests with the rightward-moving inducer
of 16 and 64 times the threshold) deviate from this
tendency.
To evaluate the reliability of these results, an
additional experiment was executed for observer KI,
in which the Pr VS phase-difference functions were
measured in five sessions (10 trials/data-point for each
function), and the variation of the parameter values
estimated for each function was calculated. For both
the highest and the lowest contrasts of the inducer
(twice and 64 times the threshold), standard deviation
of the uncertainty point was very small (less than 0.06).
It is unlikely that the change in the uncertainty point
described above is simply ascribed to experimental
errors. On the other hand, standard deviation of the
slope ranged from 1.6 up to 7.7. Given the large
variation of the slope values from session to session,
it seems difficult to draw a definite conclusion on the
slope-dependence on the contrast of the inducer. In the
following experiments (except for Experiment 5), we are
mainly concerned with change in the uncertainty point.
Experiment 2: effect of luminance contrast of the test.
The Pr vs phase-difference functions were obtained for
the tests varying in contrast from twice to 64 times the
threshold. The contrast of the inducer was kept at 16
times the threshold. The data for each contrast of the test
were fitted with equation (1). In the fitting procedure,
we used the data for the contrast of 2.8 (KI) or 4.0 (YO)
to 64 times the threshold. For the lower contrasts
(twice and 2.8 times the threshold for YO and twice the
threshold for KI), the test was "completely assimilated";
over the whole range of phase difference, Pr was 1.0
for the test with the rightward-moving inducer, and Pr
was 0 for the test with the leftward-moving inducer.
For these contrasts, fitting with equation (l) was not
appropriate.
Figure 4(a) shows the uncertainty point and Fig. 4(b)
the slope as a function of contrast of the test expressed
as multiples of the threshold contrast. The data for the
test of 8 times the threshold (with the inducer of 16 times
the threshold) are replotted from Fig. 3. The arrow on
the abscissa indicates the point at which the contrast of
the test matches with that of the inducer,
EFFECTS OF CONTRAST AND PHASE DIFFERENCE ON MOTION ASSIMILATION
1.011
"---"
_(a)
0.50
O
~
0.00
o
-0.50
-1.00
10
Contrast of test ( × threshold)
25.00
---O---+
---II -
100
YO; rightward-moving
YO; leftward-moving
KI; rightward-moving
KI; leftward-moving
inducer
inducer
inducer
inducer
For the three observers, the absolute value of the
uncertainty point is plotted as a function of log of the
contrast ratio in Fig. 5. Since the previous two experiments did not reveal any systematic effect o f the type
of the inducer (rightward- or leftward-moving) on the
magnitude of motion assimilation, the averages of the
absolute values for the tests with the two types are shown
in the figure. For YO and KI, some of the points are
based on the data shown in Figs 3 and 4. The results
indicate that the data points for the different contrasts
o f the test are approximately aligned linearly except for
NI's data for the lowest ratio o f 0.25. Thus, one may say
that the magnitude of motion assimilation depends
primarily on the relative contrast between the test and
the inducer.
Experiment 4: effect of phase difference of the inducer.
In Experiments 1-3, the phase difference of the inducer
was fixed at either 90 deg or 270 deg. Since the motion
signal of the inducer is contributed by the phase difference as well as by the contrast, it is likely that the
magnitude o f motion assimilation depends on the phase
difference of the inducer. This is examined quantitatively
in Experiment 4.
-(b)
20.00
15.00
0
2281
10.0o
5.00
0.00
,
,
,
,
,
,I,I
i
. . . . . . .
10
1.00
i
[]
100
Contrast of test ( × threshold)
0.75
F I G U R E 4. The uncertainty point and the slope of the Pr vs sin(~bt)
function as a function of contrast of the test. The contrast of the
inducer is 16 times the threshold. The arrow on the abscissa indicates
the point at which the contrast of the test matches with that of the
inducer. The other graphic conventions are the same as in Fig. 3.
0.50
The absolute value of the uncertainty point decreases
linearly with increase in the contrast o f the test up to the
highest value o f 64 times the threshold. This indicates
that the magnitude o f motion assimilation decreases
with increase in the contrast of the test, conforming to
the results previously reported for colored stimuli
(Ramachandran, 1987; Murakami & Shimojo, 1993).
The effective range of contrast of the test appears to be
wider than that of the inducer (up to 16 times the
threshold; Fig. 3).
Experiment 3: effect of relative contrast between the
test and the inducer. The two experiments described
above showed that the magnitude o f motion assimilation increased with increasing the contrast of the
inducer or with decreasing the contrast of the test.
These patterns of results led to a hypothesis that the
magnitude o f motion assimilation is determined by
the relative contrast between the test and the inducer,
rather than by their contrasts per se. To test this
hypothesis, the Pr vs phase-difference functions were
obtained for a range of contrast ratio [(the contrast of
the inducer)/(the contrast o f the test); the contrasts in
threshold units] from 0.25 to 4. In this experiment,
additional data were collected from a naive observer
(NI).
YO
~0
D
0
•
x7
Contl"ast
0
•
•
0.25
(x
0
of test
threshold)
2.0
4.0
5.6
nO
0
@
16
22
32
64
~
~
0.00
. . . . . . . . .
1.00
L . . . . . . .
,
,
t
KI
[]
0.75
O
e~
0
~g
0.50
0
A
[] •
0
•
0
ContTast
(x
oa
0.25
•0
8
o
[]
•
0
0.00
,
1.00
,
,
,
,
,
,
,
,
i
,
,
,
,
of test
threshold)
.1/4
16
~ 32
4.0
5.6
8.0
,
,
,
,
,
of
test
i
NI
0.75
[]
0.50
0
Contrast
(×
0.25
0.00
0
,
-1.0
threshold)
0
A
,
,
,
V
,
,
,
,
,
t
0.0
,
,
. . . . . . .
i
1.0
L o g contrast ratio
[Log (Contrast of inducer / Contrast of test)]
F I G U R E 5. Absolute value of the uncertainty point as a function of
log of the contrast ratio [log (the contrast of the inducer/the contrast
of the test); the contrasts in threshold units]. Each data point shown
is the average of the absolute values for the test with the rightwardmoving inducer and that for the leftward-moving inducer. For YO and
KI, some of the points are based on the data shown in Figs 3 and 4.
2282
YOSHIO O H T A N I et al.
The P~ vs phase-difference functions were obtained for
three pairs of the phase difference of the inducer. The
phase values for each pair were either (150, 210deg),
(160, 200 deg), or (170, 190 deg). The different pairs were
used in separate sessions, and at least two sessions were
executed for each pair. The contrasts of the test and the
inducer were 8 times the threshold.
Figure 6 shows the uncertainty point and the slope as
a function of the phase difference of the inducer [sin(qS~)].
The data for sin(~b)= 1 (q~i = 90 deg) and sin(q~i)= --1
(qS, = 270 deg) are replotted from Fig. 3.
The uncertainty point shows a clear dependence on
the phase difference of the inducer. For the sin(qSi)
around 0 (i.e. q5i = 170 deg or 190 deg), the uncertainty
point is nearly 0. As the absolute value of sin(qS~)
increases, the uncertainty point increases for sin(qS~) < 0
and decreases for sin(q~i) > 0. This relation may be well
described by the solid and the broken lines shown in the
figure (see Discussion for details). Since the perceived
direction of motion of the inducer becomes unambiguous as the absolute value of sin(qS~) becomes apart from
0, the magnitude of motion assimilation may covary
with the strength of motion signal of the inducer.
Experiment 5: effect o f luminance contrast on direction
discrimination without inducing stimuli. Experiments 1
and 2 showed that the magnitude of motion assimilation
depended on the luminance contrast up to 16 (for the
(a)
1.00
.=.
(a)
0.50
O
e~
0.0o
-0.50
-1.00
.
.
.
.
J llll
J
i
i
i llll
10
100
Stimulus contrast ( × threshold)
YO; center field
+
YO; upper/lower fields
]
15.00
--i
- KI; center I]eld
- KI; upper/lower fields
- (b)
10.00
O
5.00
0.00
i
i
i
i
i i~ll
i
. . . . . . .
10
i
100
Stimulus contrast (× threshold)
F I G U R E 7. The uncertainty point and the slope of the Pr vs sin(~t)
function as a function of contrast of the stimulus grating(s) presented
either in the center field or in the upper and the lower fields. Open
symbols are for the grating in the center field, and solid symbols are
for the gratings in the upper and the lower fields. The other graphic
conventions are the same as in Fig. 3.
e~
-fi
1.00
0.50
0.00
-0.50
-1.00
15.00
I
I
-1
-0.5
I
0
sin(d~i)
I
I
0.5
1
(b)
10.00
5.00
I--
0.00
---IN
I
I
I
I
I
-1
-0.5
0
0.5
1
sin(~i)
F I G U R E 6. The uncertainty point and the slope of the Pr vs sin(tht)
function as a function of sine of the phase difference of the inducer
[sin(~i)]. The data for sin(~bi)= +1 are replotted from Fig. 3. Solid
and broken lines represent the functions fitted by equation (2) (see
Discussion).
inducer) or 64 (for the test) times the threshold contrast.
Taking into account that the threshold contrasts for
the two observers were around 1% (see footnote on
p. 2278), the effective range of luminance contrast
extends up to about 16 or 64%. Raymond and Darcangelo (1990) found that the magnitude of motion contrast
increases with increasing the luminance contrast of the
inducer from 2.5% up to as high as 60%. They pointed
out that the effective range of luminance contrast is quite
different from the results with other measures (e.g.
motion detection, motion aftereffect, directionallyspecific adaptation, and velocity discrimination) which
indicate that motion perception does not depend on
luminance contrast above about 5% (Keck, Palella &
Pantle, 1976; Pantle, Lehmkuhle & Caudill, 1978;
Sekuler et al., 1978; N a k a y a m a & Silver•an, 1985;
Johnston & Wright, 1985; McKee et al., 1986; Boulton
& Hess, 1990).
To directly compare the effective range of luminance
contrast for motion assimilation with that for direction
discrimination without the inducing stimuli, the Pr vs
phase-difference functions were collected for the gratings
presented either in the center field or in the upper and
the lower fields. The luminance contrast was varied from
EFFECTS OF CONTRAST AND PHASE DIFFERENCE ON MOTION ASSIMILATION
2283
TABLE 1. The estimated values of k, rn, and n in equation (2) to fit the results of
Experiments 1, 2, and 4
YO
Ct, t~i constant, C~ varied
KI
k
m
n
-0.717a/-0.704 b
-0.506
0.051
-0.728~/--0.847 b
-0.494
-0.093
Ci, q~ constant, Ct varied
(Experiment 2)
k
m
n
--0.494a/--0.627 b
--0.536
0.046
--0.454a/--0.573 b
--0.528
--0.105
Ct, Ci constant, q~i varied
(Experiment 4)
k
m
n
NA
-0.604
0.048
NA
-0.647
-0.128
(Experiment I)
aFor the test with the rightward-moving inducer.
bFor the test with the leftward-moving inducer.
NA: not available.
twice to 64 times the t h r e s h o l d with the r e m a i n i n g field(s)
kept uniform.
F i g u r e 7(a) shows t h a t the u n c e r t a i n t y p o i n t is n e a r l y
c o n s t a n t a r o u n d 0 for all the c o n t r a s t levels. T h e slope
[Fig. 7(b)] increases linearly as the c o n t r a s t increases up
to 4 o r 5.6 times the t h r e s h o l d , a n d a s y m p t o t e s for the
higher c o n t r a s t s . These results indicate that, for the
d i r e c t i o n d i s c r i m i n a t i o n w i t h o u t the i n d u c i n g stimuli,
the Pr vs phase-difference function is a l m o s t i n v a r i a n t
with the c o n t r a s t b e y o n d as low as 4 - 5 % . This is in
a g r e e m e n t with the n o t i o n t h a t the effective r a n g e o f
l u m i n a n c e c o n t r a s t is w i d e r for m o t i o n a s s i m i l a t i o n t h a n
for the d i r e c t i o n d i s c r i m i n a t i o n w i t h o u t the inducing
stimuli.
DISCUSSION
Formulation
assimilation
of
the
stimulus
dependences
of
motion
T h e p r e s e n t e x p e r i m e n t s s h o w e d t h a t the m a g n i t u d e
o f m o t i o n a s s i m i l a t i o n , defined as the c h a n g e in the
u n c e r t a i n t y p o i n t o f the Pr VS phase-difference function,
varied s y s t e m a t i c a l l y with c h a n g e in the l u m i n a n c e contrast o f the test a n d the i n d u c e r as well as with c h a n g e
in the p h a s e difference o f the inducer. M o r e specifically,
the p r e s e n t results are s u m m a r i z e d as follows.
(1) W h e n the p h a s e difference o f the i n d u c e r (qSi)
is fixed at 9 0 d e g o r 2 7 0 d e g [i.e. sin(q~i)= _+1], the
u n c e r t a i n t y p o i n t m a y be d e s c r i b e d by a linear function
tFor the first two sets, the actual equation used was
fl = k * log(fi/ft) + rn + n
for the test with the rightward-moving inducer [i.e. sin(~bi)= 1;
qSj= 90 deg], and
fl = --k * log(Ci/Ct) -- m + n
for the test with the leftward-moving inducer [i.e. sin(q~i)=- 1;
4~i= 270 deg]. For the data with each type of the inducer, the values
of m and n were not demarcated, but only their sum (rn + n) or
difference ( - m + n) was estimated. We obtained the values of m
and n by solving the two equations including the two parameters
[i.e. m + n = p and - m +n =p'; p and p' are the constants
estimated]. For the third set, the actual equation was
fl = m * sin(~bi)+ n.
o f log o f the c o n t r a s t ratio o f the i n d u c e r to the test [i.e.
log(Ci/Ct); C is for the c o n t r a s t in t h r e s h o l d units, " i "
for the inducer a n d " t " for the test]. The linear relation
h o l d s up to the c o n t r a s t o f the inducer 16 times the
t h r e s h o l d a n d u p to the c o n t r a s t o f the test 64 times the
threshold.
(2) W h e n the c o n t r a s t ratio is fixed at 1 [i.e.
log(C~/Ct) = 0], the u n c e r t a i n t y p o i n t m a y be a linear
function o f sin(~bi).
It is t e m p t i n g to s u p p o s e t h a t these p a t t e r n s o f results
m a y be d e s c r i b e d by a single e q u a t i o n . O n e possible
f o r m u l a t i o n w o u l d be:
fl = [k * l o g ( C i / C t ) + m] t sin(~bi) + n
(2)
where k, m, a n d n are constants. T o e v a l u a t e the validity
o f this f o r m u l a t i o n , we fitted the three sets o f d a t a
(i.e. the d a t a in the linear p o r t i o n in Fig. 3, a n d the
d a t a in Figs 4 a n d 6) i n d e p e n d e n t l y by using e q u a t i o n
(2). F o r each o b s e r v e r (YO, K I ) , the best fitting functions for the first two sets are s h o w n in Fig. 8 t o g e t h e r
with the d a t a p l o t t e d as a f u n c t i o n o f log(C~/Ct).
T h e best fitting functions for the third set are shown in
Fig. 6. As can be seen f r o m the two figures, the fits o f
e q u a t i o n (2) to the d a t a are quite g o o d .
T h e e s t i m a t e d values o f k, m, a n d n o b t a i n e d by a
m e t h o d o f least s q u a r e are given in T a b l e 1.'~ F o r each
observer, the a b s o l u t e values o f k are 1.1-1.6 times larger
for the d a t a o b t a i n e d for the c o n s t a n t Ct with v a r y i n g C~
( E x p e r i m e n t 1) t h a n for those o b t a i n e d for the c o n s t a n t
Ci with v a r y i n g Ct ( E x p e r i m e n t 2). T h e values o f m a n d
n v a r y by a f a c t o r o f 1.1-1.4 a m o n g the three d a t a sets.
These v a r i a t i o n s a p p e a r to be s o m e w h a t larger t h a n
one m i g h t expect, a n d suggest t h a t the present results
m a y be also c o n t r i b u t e d by some factor(s) o t h e r t h a n the
c o n t r a s t r a t i o a n d the p h a s e difference o f the i n d u c e r
i n c o r p o r a t e d in e q u a t i o n (2). But at least to a first
a p p r o x i m a t i o n , e q u a t i o n (2) m a y serve as one unified
f o r m u l a t i o n o f m o t i o n a s s i m i l a t i o n o b t a i n e d u n d e r the
v a r i o u s conditions.
R e s p o n s e integration o f local m o t i o n detectors
underlying m e c h a n i s m o f m o t i o n assimilation
as an
In this section, we discuss h o w the present results
m a y be e x p l a i n e d in terms o f the i n t e r a c t i o n a m o n g
2284
YOSHIO OHTANI et al.
local m o t i o n detectors. To facilitate the discussion,
a schematic model is presented in Fig. 9, which gives
an outline o f one possible mechanism underlying
the stimulus dependences o f m o t i o n assimilation.
Figure 9(a) represents the case for the test with the
rightward-moving inducer, but the same line o f
a r g u m e n t holds for the test with the leftward-moving
inducer.
According to the model, the response o f the local
m o t i o n detector is described a s f ( C ) * sin(qS), w h e r e f ( C )
is the detector's contrast response function which is
m o n o t o n i c a l l y increasing with C (cf. van Santen &
Sperling, 1985; N a k a y a m a & Silverman, 1985). The
detectors' responses are integrated over a relatively large
region o f the stimulus field. The integrated response (IR)
for the test is:
I R ~--f(Ct)
*
sin(qSt) + g * f ( C i ) * sin(qSi)
where the factor g represents the effectiveness o f the
inducer-generated response in the sum-up operation.
Figure 9(b) visualizes the effect o f the inducer on the I R
v s sin(q~t) function for a positive value o f g. N o t e that
the upward shift o f the I R function is accompanied by
the leftward shift o f the "uncertainty p o i n t " at which
IR =0.
The contrast-dependent c o m p o n e n t o f the integrated
response is compensated for by normalizing, or dividing,
I R by the contrast-response o f the visual system which
is independent o f stimulus motion. The o u t p u t o f the
normalization process is:
- I R- -
h(G, C)
h(C, Ca)
where h(C,, C~) is a normalization factor. A similar
notion o f contrast normalization has been proposed
for speed perception by Stone and T h o m p s o n (1992).
They suggest that the normalization factor m a y be an
"average contrast" over the whole stimulus field. As
shown in equation (3) below, the specific form o f h is not
critical in this discussion.
The normalized signal is then perturbed by an internal
noise [prescribed by a normal distribution; N(0, a2)] and
fed into a threshold device which generates a binary
response (i.e. left or right) for the direction o f stimulus
motion. Since the uncertainty point o f the Pr vs phasedifference function predicted by the model is not
affected by the noise, it is obtained by letting I R = 0 in
the above equation and solving the equation for sin(~b 0.
The theoretical value o f the uncertainty point (flth) is:
f(Ci)
fl,h = - g * - -
f(c,)
* sin(qSi).
(b)
YO (Ci constant, Ct varied; Expt. 2)
0.50
<~-- r ightward-moving i n d u ~
leftward-moving inducer ]
0,00
-0.50
.2
-1.00
O
KI (Ct constant, Ci varied; Expt. 1)
1.00
[] (Ci constant, Ct varied; Expt. 2)
IB..~ o
%
0.50
X
/O
J
0.00
----0 - rightward-moving inducer
- eflward-mov ng nduoer
,4
-0.50
C7--..9"'".(3
O....~ 3
-1.00
. . . .
-1
i
-0.5
. . . .
i
0
. . . .
i
0.5
. . . .
i
1
(3)
To c o m p a r e the stimulus dependences o f J~th with
those o f fl empirically obtained, consider first the case in
which the phase difference o f the inducer is fixed at 90
or 270 deg. W h e n the contrast o f the test is constant, the
absolute value o f fl~h increases with increasing the contrast o f the inducer; when the contrast o f the inducer is
(a)
YO (c t constant, c i varied; Expt. 1)
1.00
f ( C t ) * sin(qS0 + g , f ( C i ) * sin(~i)
h(c~, G)
. . . .
-1
t
. . . .
-0.5
i
0
. . . .
i
0.5
. . . .
J
1
Log contrast ratio [Log (Ci/Ct) ]
FIGURE 8. The uncertainty point as a function of log of the contrast ratio replotted by using the data shown in Figs 3 and 4.
(a) The data obtained in Experiment 1. (b) The data obtained in Experiment 2. Open and solid symbols represent the data
for the test with the rightward-moving inducer and those with the leftward-moving inducer, respectively. Solid and dashed lines
represent the functions fitted by equation (2) (see Discussion).
EFFECTS OF CONTRASTAND PHASEDIFFERENCEON MOTIONASSIMILATION
(a)
Local motion
detector
Inducer
phase
Test
Integration
Contrast
process normalization
Threshold
device
i
2285
Pr vs phase-difference
function
with
o~ I rightward-moving
induce~_..~
phase ~ / ' ~ " - - - ' ~ } * s i n ( ¢ i ~ i
i
~
}~
I
r-0.s
I .......................................
i
! . . . . . . . . . . . . . . . . . . . . . . , ino,se
........ /,'-. . . . . ~ inducer
',
?~
......./i
0 sin@t
h(C t, C i)
(b)
IR vs phase-difference function
(I]
with rightward-
~
4
movinginducer
"l).~.j "~ withoutinducer
0
sin@t
FIGURE 9. A schematicmodel which explainsthe stimulus dependencesof motion assimilation in terms of response integration
among local motion detectors. See text for details.
constant, the absolute value of flth decreases with increasing the contrast o f the test. Consider next the case in
which the contrasts of the test and the inducer are fixed
while the phase difference of the inducer is varied. In this
case, /~th is a linearly decreasing function of sin(4~i). All
these predictions conform well to the results obtained in
the present experiments.
An additional favorable feature of the model is
that it predicts the slope invariance [above the very
low contrasts; Fig. 7(b)] o f the P, vs phase-difference
function in the absence of the inducer, without
requiring a rapid contrast-saturation of the local
motion detector. The slope is formally expressed as
[l/(o'~,,/~)]*f(Ct)/h(Ct,
Ci) , where C i = 0 for the
case under discussion. This implies that if the ratio
f(Ct)/h(Ct, Ci) becomes constant (i.e. if the contrast
normalization operates effectively) above the very low
contrasts, the slope becomes saturated even if f(C~)
per se increases over a wide range of contrast. Thus, the
model may explain the difference between the effective
range o f contrast for motion assimilation (evaluated as
the change in the uncertainty point) and that for the
direction discrimination without the inducer (evaluated
as the change in the slope).
The present model is intended simply to show that the
stimulus dependences of motion assimilation may be
well explained, at least qualitatively, by assuming the
response-integration among the local motion detectors.
So the model, as it is, does not explain some aspects
of our results. First, the model merely states that
the magnitude of motion assimilation is a function
of f(Ci)/f(C~) without prescribing the specific form
empirically obtained [equation (2)]. But this is not a
critical problem since the model does not preclude the
possibility that the magnitude of motion assimilation
may be "approximated" by a function of log(C~/C,).
Second, the model does not explain that the magnitude
of motion assimilation became saturated for the higher
contrasts of the inducer [Fig. 3(a)]. Since such contrastsaturation was not obtained by varying the contrast
of the test [Fig. 4(a)], the factor g in the model should
be elaborated so as to incorporate a saturation characteristic which is specific to the inducer-generated
response. In spite that there remain some aspects of the
results to be explained, the present model offers a useful
framework which allows us to explore further the
interaction among local cues in the human motion
processing.
Motion assimilation and motion contrast
Levi and Schor (1984) and Raymond and Darcangelo
(1990) obtained motion contrast with the spatial
configuration of the stimulus almost identical with ours.
In the model described above, motion contrast may be
explained by postulating that the factor g has a negative
value depending on the stimulus parameters. For a
negative value of g, the IR function shown in Fig. 9(b)
shifts downward when the test is accompanied by
the rightward-moving inducer. This gives rise to the
rightward, as opposed to the leftward, shift of the Pr vs
phase-difference function indicating the occurrence of
motion contrast.
YOSHIO OHTAN1 et al.
2286
To elaborate this line o f argument further, there are
at least two questions to be answered. The first is how
and why the value of g may become positive or negative
depending on the stimulus parameters. Since the two
types of motion interactions occur with a quite similar
spatial configuration and over nearly the same range of
the luminance contrast, one might suppose that change
in the sign of g may be ascribed mainly to the difference
in the stimulus temporal parameters. Levi and Schor
(1984) and R a y m o n d and Darcangelo (1990) used a
multi-frame motion display, in which the stimulus
gratings moved slowly and continuously, while we used
a two-frame motion display, in which the stimulus
gratings were displaced abruptly. We are currently investigating the effects of stimulus temporal parameters on
the two types of motion interactions.
The second question is why motion contrast depends
on the luminance contrast of the inducer but not on that
o f the test ( R a y m o n d & Darcangelo, 1990), whereas
motion assimilation depends on both. If, as suggested by
Raymond and Darcangelo (1990), motion contrast is
contributed by the higher-order processing based on the
figure-ground segregation, a generic model for the
two types of motion interactions should include at least
two levels (or components) of processing at which the
stimulus contrasts have different effects.
REFERENCES
Boulton, J. C. & Hess, R. F. (1990). Luminance contrast and motion
detection. Vision Research, 30, 175 179,
Braddick, O. (1993). Segmentation versus integration in visual motion
processing. Trends in Neurosciences, 16, 263 268.
Dunker, K. (1938). Uber induzierte Bewegung (Ein Beitrag zur Theorie
optisch wahrgenommener Bewegung). In Ellis, W. D. (Ed. &
Trans.), Source book of Gestalt psychology (pp. 161 172), London:
Routledge & Kegan Paul. [Reprinted from Psychologisehe
Forschung, 12, 180 259 (1929)]
Johnston, A. & Wright, M. J. (1985). Lower thresholds of motion for
gratings as a function of eccentricity and contrast. Vision Research,
25, 179 185.
Keck, M. J., Palella, T. D. & Pantle, A. (1976). Motion aftereffect as
a function of the contrast of sinusoidal gratings. Vision Research, 16,
187 191.
Levi, D. M. & Schor, C. M. (1984). Spatial and velocity tuning
of processes underlying induced motion. Vision Research, 24,
1189 1196.
McKee, S. P., Silverman, G. H. & Nakayama, K. (1986). Precise
velocity discrimination despite random variations in temporal
frequency and contrast. Vision Research, 26, 609 619.
Murakami, I. & Shimojo, S. (1993). Motion capture changes to
induced motion at higher luminance contrasts, smaller eccentricities,
and larger inducer sizes. Vision Research, 33, 2091-2107.
Nakayama, K. & Silverman, G. H. (1985). Detection and discrimination of sinusoidal grating displacements. Journal o[" the Optical
Society of America A, 2, 267 274.
Ohtani, Y., Ido, K. & Ejima, Y. (1994). Effects of temporal parameters
of stimulus on motion contrast and motion assimilation. Proceedings
~[ the Tenth Annual Meeting o[' the International SocieO~ Jor
Psyehoph.vsies, pp. 173 178.
Pantie, A., Lehmkuhle, S. & Caudilk M. ([978). On the capacity of
directionally selective mechanisms to encode different dimensions of
moving stimuli. Perception, 7, 261 267.
Ramachandran, V. S. (1987). Interaction between colour and motion
in human vision. Nature, London 328, 645 647.
Raymond, J. E. & Darcangelo, S. M. (1990). The effecl of local
luminance contrast on induced motion. Vision Research, 30,
751 756.
Reinhardt-Rutland, A. H. (1988). Induced movement in the visual
modality: An overview. Psychological Bulletin, 103, 57 71.
van Santen, J. P. H. & Sperling, G. (1985). Elaborated Reichardt
detectors. Journal o f the Optical SocieO, of America A, 2, 300 321.
Sekuler, R., Pantle, A. & Levinson, E. (1978). Physiological basis of
motion perception. In Held, R., Leibowitz, H. W. & Teuber, H. L.
(Eds), Handbook of sensory physiolof,,y (Vol. VIII, pp. 67 96). Berlin:
Springer.
Stone, L. S. & Thompson, P. (1992). Human speed perception is
contrast dependent. Vision Research, 32, 1535 1549.
Watson, A. B. (1979). Probability summation over time. Vision
Research, 19, 515-522.
Acknowledgements--Y. Ohtani was supported by Grant in Aid for
Scientific Research (No. 06212220) from the Ministry of Education.
K. ldo was supported by Fellowships of the Japan Society for the
Promotion of Science for Japanese Junior Scientists. Y. Ejima was
supported by Grant in Aid for Scientific Research (Nos 05267224 and
04236105) from the Ministry of Education.