G942-6989/92 $5.00+ 0.00 Copyright 0 1992Pergamon Press plc
VisionRes. Vol. 32, No. I, pp. 135-147,1992 Printed in Great Britain. All rights reserved
Perceived Direction of Moving Two-Dimensional Patterns Depends on Duration, Contrast and Eccentricity* CHRISTOPHER
YO,t HUGH
R. WILSONt
Received 30 May 1990; in revised form 3 October 1990; received for publication 18
June 1991
Type II two-dimensional motion is produced by superimposing two one-dimensional drifting cosine gratings with velocity vectors lying on the same side of the intersection-of-constraints (IOC) resultant. When type Dpatterns were constructed with components having the same spatialfrequency and contrast, perceived direction was found to be biased toward the vector sum direction at short durations and approached the direction predicted by IOC only after some time lag. This time lag was contrast dependent. At 5% contrast, the perceived direction after I set of presentation remained biased by more than 20”. Direction perception was also measured at 15” eccentricity. At this eccentricity the perceived direction of type II patterns was grossly biased away from the IOC prediction in the direction of the component vectors by an average of 25”. Motion
Intersection-of-constraints
Peripheral vision
INTRODUCTION The actual direction of a one-dimensional pattern moving across the receptive field (RF) of a neuron may be almost &90” away from the direction signaled by the neuron. This phenomenon is referred to as the aperture problem and was iirst studied by Wallach (1935, 1976). He demonstrated that the direction of a one-dimensional pattern moving behind an aperture depends on the aperture shape, but when another pattern at another orientation is superimposed on and drifted with the first one, the overall direction is unambiguous and is not affected by aperture shape. In 1982, Adelson and Movshon provided geometrical and psychophysical insight into the visual analysis of such two-dimensional pattern motion. Geometrically, they proposed that the resultant velocity is determined by the “intersection-ofconstraints” (IOC) or “velocity-space” construction. In the construction, components are treated as comprising a rigidly moving object. Local estimates of each component’s velocity will generate a host of physically possible motions bounded by its constraint line as shown in Fig. 1. As different components will likewise generate their own constraint lines, the predicted object motion is determined by the intersection of all the physically *Research first reported at the 1990 annual meeting of the Association for Research in Vision and Ophthalmology. TDepartment of Ophthalmology and Visual Science, University of Chicago, 939 E. 57th Street, Chicago, IL 60637, U.S.A. $Resultant refers to the resultant motion vector of the two-dimensional pattern defined by the IOC rule. When speaking of vector addition, the term “vector sum” will be employed.
MT topography
Oblique effect
possible interpretations generated by the components. Diagrammatically shown in Fig. l(a) is an object moving at speed P. The component speeds Cl and C2 of the component gratings comprising the object will be Cl = P cosa c2 = P cos/iI where a and /I denote the angles between the object velocity and the component velocities. The local estimates of speeds Cl and C2 will thus generate constraints depicted by the gray lines. As the components are assumed to comprise a rigid body, the global object velocity P must be consistent with both local readings; hence the resultantS is at the intersection of the constraint lines. This type of construction is different from a vector summation prediction in two respects. One is that as the angle between the two components increases, so does the resultant speed [the diameter of the circle in Fig. l(a) will increase]; vector summation would predict just the opposite. The other difference is that the vector produced by vector summation always lies between the two component vectors, but using the IOC, one can easily produce resultants that lie outside the boundaries of both components. In fact, any combination of vectors which lie on the circle in Fig. l(b) would yield the resultant vector indicated by the thick dark arrow. Ferrera and Wilson (1990) classified two-dimensional patterns into two groups: type I patterns [shown in Fig. l(a)] in which component vectors lie on both sides of the resultant vector (plaids), and type II patterns [shown in Fig. l(c)] in which the components are both located on 135
136
Type I (Plaids)
w
Type II: (Blobs) c
a P -.
side a fixed tolerable range in any of these dcm~ins, the catnponents are seen as independent entities traveling tra~sparen~~~ acmss each other in directions orthogonal
to their orientations. Therefore when the component vectors signaled by the first stage motion units come from essentially the same depth plane, they are selectively combined in the second stage to generate the resultant vector. This was the claim of’ Ad&on and colleagues for the case when both components are s~~~rnpos~* ~~b~uently~ Nakayama and Silverman (1988) showed that the second stage motion system is also capable of combining local velocity signals from VY b different spatial regions to reconstruct a global rigid t motion percept.. Welch (1989) ~rform~ speed discrimination ex~~rne~ts and showed that the ~sc~rn~~~ion thresholds of two-dimensional patterns reflected the discrimination thresholds at the component level. This further supports the two stage model by implying that L * the precision in the extraction of two-dimensional patvx tern speed is limited by noise at the component stage. FIG-E ‘I. Ve~tity-spaoe eangt~~aufor det~~ni~ resultant Mo~shon, Addson, Gizzi and Newsome jt9St Emotion. I% and vy denote the horizo?ltal and vertical components of ported that 40% of MT neurons were sensitive to only the m&m vtxtor. When the twa components cohere and move as a component directions when exposed to moving tworigid surface, the global velocity of the pattern is unique and is determined by the intersection of the constraint (gray) lines. Any dimensional grat,ings. Interestingly, another 25?;, were combination of vectors that lie an the circle (b) will generate the same found not to respond significantly to the component upward resultant pattern veotor. According to the dassikation by grating directions when the components were presented Ferrzra and Wilson (1%X& patterns ba6ng ~rn~n~ts located on alone but responded well to the pattern direction when both sides of the resultant are considenxi as type 1 [a) (previously both components were presented and to a one-dimenreferred to as plaids in Ferrtxa & Wilson, 1987), those having components located only on one side of the resultant are considered sional grating traveling in the pattern direction. The as type II (c) (previously referred to as blobs in Ferrera & Wilson, investigators hypothesized that the tuning properties of 1987). these pattern direction selective units were generated by highly nonlinear excitatory and inhibitory interactions one Side: af tk! 2x%&arrt ~~~~~~~~ -F&S ~~~~~~~~U~ was which characterize the second stage of the motion analybasx8 on p~yc~o~hy~~ca~ measureu?ents that have resis system. Furthermore, they suggested that these nonvealed three perceptual differences between these patlinear pattern selective neurons in MT received input terns: (1) the masking strength of a type I pattern is 2-4 from component direction selective neurons in VI and times more than that produced by either component MT and solved for the resultant two-dimensional patwhereas the masking strength of a type II pattern is tern direction by neura& im~lcmenting the KkT r&e. determined by the ~rnp~ne~~ nearest to the test (Ferrera. In this research, further evidence will be provided to & Wilson, 1987); (2) perceived direction of a type I show that motion processing takes place in two stages. pattern is consistent with the IOC prediction while the Type II patterns offer a more rigorous test of the IOC perceived direction of a type II pattern is biased toward rule than type I patterns because the predicted resultan% the components’ direction by about 7.5”; (3) direction lie outside the boundaries of either component vector. ~~rn~~~tion thresholds for type I patterns averaged t” When type XI patterns were constructed by srrperimposwhile those of type f1 patterns averaged 5.5” (Ferrera & ing two drifting cosine gratings of the same spatial Wilson, 1990).These percaFjtua1 differences between type frequency and contrast according to the IOC rule, I and type II patterns suggested that the underlying perceived direction was found to be biased in the neural circuitry for analyzing them is different (Ferrera vector sum direction at short presentation durations 6%Wilson, 1987, 1990). (K 90 msec) and approached the direction predicted by Adelson and ~o~sb~~ (1982) proposed that the TOC only after a time lag. This time lag was foirnd to be synthesis of ~~irn~nsi~~al pattern motion from onecontrast dependent. At 5% contrast, the perceived direcdimensional component motions is acl;omplished in tion after I set of presentation remained grossly biased two stages. Psychophysicslly, they showed that the combination of local component vector information is toward the vector sum direction. The type I “patterns used in this study were all symmetric, i.e. the componenr dependent on refative spatial frequency, velocity9 convectors are of the same speeds. Type I direction perceptrast and apparent depth of the twc~ c~~p~~en~= Outtion, unfke type II: motion, was found to be accurate at all durations and contrasts. *A simple way of remembering the distinction betwean type I and type In the second part of this paper, we ascerraiaed the II patterns is the following: typ I patterns have ant component on accuracy of type 1 and II pattern direction perception at each side of the IOC resultant, while type II patterns have NO components together on the same side of the ICX resultant. 15.‘ eccentricity in the upper. upper oblique temporaL
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positioned with a chin rest to maintain constant viewing distance. In fovea1 and peripheral direction matching experiments, 5 different stimulus configurations were used (Fig. 3). In Figure 3, component speeds are indicated by thin arrows and IOC resultant speeds are indicated by thick arrows. In a single experiment, the components in all 5 conditions had the same angular difference (22.3, 47.4 or 51.6”). Under conditions 1, 3 and 5 the two components drifted at the same speed, producing type I pattern motion which had resultants at -60, 0 and + 60” respectively (0” indicates upward motion, negative angles indicate leftward deviations from the upward direction and positive angles designate rightward deviations). In conditions 2 and 4, type II motions were produced with a resultant IOC direction that was directly upward and was equal to the direction of the type I pattern drifted in condition 3. The circular display window when positioned 38 in. from the viewer was 8” in dia and had a 4.8 x 4.8 min of arc dark fixation spot in the center. The subject fixated on the center and initiated pattern presentation by a button press. The duration of presentation remained constant throughout each experiment. A beep sounded after each presentation and a blank screen appeared for 0.2 set followed by the METHODS appearance of a 5.6” long pointer. The pointer could be Spatial patterns were generated on a Macintosh II rotated around the fixation point and the subject used microcomputer and displayed on an Apple high- the mouse to align the angle of the pointer to the resolution monochrome monitor (8 bits/pixel) with P4 perceived pattern direction. Once a match was made, the (white) phosphor and a 66.7 Hz frame rate. The mean subject pressed the mouse button for the computer to luminance was 66 cd/m2. Contrast was defined as record the match. A blank screen reappeared for 1 set, (L, - L,,)l(L& where L,, and Mean were the followed by the next presentation randomly selected maximum and mean luminances in the pattern. Subjects among the 5 conditions. Each pattern was presented 30 viewed the display through a circular aperture in a times in each experiment. Subjects were given practice on cardboard surround which was illuminated to approxiall tasks before actual data were collected. Each expermately the same hue and brightness as the screen. iment was repeated at least 3 times on different days for Pattern motion was achieved using the technique of each subject unless otherwise specified. Trials with differcolor table animation (Shoup, 1979; Sheets, 1988; Apple, ent durations of presentation were alternated. Table 1 1988; Knaster, 1988). A pixel map consisting of a lists all variations of the stimulus parameters used in linearized ramp of gray levels was first painted on the assessing fovea1 direction perception. screen. A cosine of the appropriate frequency was then Patterns used in cases 1, 2 and 3 have component scrolled through the color look-up table, transforming direction differences of 22.3, 47.4 and 51.6” respectively. the ramp into a drifting cosine grating. The look-up In cases l(c), (d), (e) and 3(a) and (b) the resultant speeds table was changed 67 times/set to create phase shifts of (P) of type I patterns were calculated to be equal to type the cosine pattern in successive frames that could be II pattern resultant speeds according to the IOC rule. In made almost arbitrarily small. Two-dimensional spatial cases l(a) and (b), the component speed of the type I patterns were created by drawing two one-dimensional ramps oriented at different angles on alternate horizontal pixel lines. We used type II patterns with component vector angular differences of 22.3, 47.4 and 51.6” which are shown in Fig. 2. Component and resultant speeds in Fig. 2 represented ratios rather than actual speeds. A total of twelve subjects participated in fovea1 and 1 2 3 4 5 peripheral direction matching experiments. In all experConditions iments subjects viewed the monitor monocularly. CY, IW, JC, PJ, JCH used their right eyes. HRW, VPF, HJ, FIGURE 3. Velocity-space construction of the five conditions used in direction matching experiment. The component vectors of the five YJZ, RB, RC and AS used their left eyes. JC, RB, JCH conditions all have the same angular difference. Conditions 1, 3 and and AS had no refractive error and the others wore 5 were type I patterns. Conditions 2 and 4 were type II. Thick arrows proper corrective eye glasses. All except CY, HRW and indicate IOC predicted resultant directions, thin arrows indicate VPF were naive. The subjects’ heads were comfortably component vector directions.
temporal, lower oblique temporal and lower visual fields (see Fig. 4). This was motivated by the results obtained from electrophysiological mappings of MT cortex. Maunsell and Van Essen (1987) and Maunsell (1988) showed that the macaque MT topographical organization has a representational bias in which the lower oblique temporal sector of the periphery is favored. Type I and II patterns in the peripheral direction matching experiments were calculated to move away from the fovea in the peripheral visual field sectors according to the IOC construction. This was based on Albright’s (1989) report that the preferred direction of MT neurons in the periphery (beyond 12” eccentricity) was biased toward representing foveofugal (away from fovea) directions. For type I patterns some evidence for an oblique effect was found, but direction perception was otherwise quite accurate. For type II patterns, however, large biases in the direction of the vector sum were found in all visual field quadrants, the average being 25”. Thus, the visual periphery is clearly deficient in the processing of type II patterns. In addition, these tests reflect some evidence of the topographical representation and directional bias found in area MT of macaques.
CHRISTOPHER
138
3
,22.3”,
YO and HUGH
R. WILSON
1
FIGURE 2. Type II patterns used in direction matching. The component vector angular differences in cases 1 (left), 2 (middle) and 3 (right) were 22.3,47.4 and 51.6” respectively. The component vector sum directions were 55.5,48.2 and 37.7” respectively. The velocity space construction is shown below each pattern. Numbers next to the arrows indicate the speed ratios of the components and the resultant pattern motion vector. Type I motion using these same spatial patterns will travel in a direction about 60” from the vertical.
MOVING TWO-DIMENSIONAL
139
PATTERNS
TABLE 1. Parameters for fovea1 direction matching experiment. Case 1 patterns all had a component vector angular difference of 22.3”, case 2 patterns had an angular difference of 47.4” and case 3 patterns had an angular difference of 51.6”. The third column indicates the size of the display window. The fourth column indicates the component spatial frequency. Cl, C2 and P represent component speeds and pattern speeds calculated by IGC (see Fig. 1) Type
1
Type 11 Speed@eg/=)
Speed(de+4 Case
l(a) l(b) l(c) l(d) l(e) 2(a) 2(b) 3(a) 3(b)
Angle (deg)
Size (deg)
22.3 22.3 22.3 22.3 22.3 47.4 47.4 51.6 51.6
8 8 8 2.7 8 8 8 8 2.7
SF (c/deg)
Cl
c2
P
Cl
1.5 1.5 1.5 4.5 1.5 1.0 1.0 1.0 3.0
1.33 5.33 3.93 1.31 1.31 2.00 8.00 4.32 1.44
1.33 5.33 3.93 1.31 1.31 2.00 8.00 4.32 1.44
1.36 5.43 4.00 1.33 1.33 2.18 8.74 4.80 1.60
1.33 5.33 1.33 0.44 0.44 0.25 1.00 0.40 0.13
patterns equaled the slower component of type II patterns, in cases 2(a) and (b), component speed of the type I patterns equaled the faster component of type II patterns. In all cases except l(d) and 3(b) (114 in., 2.7” display dia) the viewing distance was 38 in., producing a circular display dia of 8” and pixel size of 72 arc sec. Bold figures in Table 1 highlight the maximum and minimum speeds for type II patterns used in this study. Grating acuity was measured on CY, IW, HJ and JC in the upper (superior), upper oblique temporal, lower (inferior) oblique temporal and lower visual fields at 15” eccentricity. Oblique direction designates 45” above or below the horizontal meridian. Measurements were not made in the temporal visual field along the horizontal meridian due to the presence of the blind spot. The grating acuity experiment was conducted using a twoalternative forced-choice (2AFC) paradigm. Four grating sizes were used and each was repeated 40 times in random order. The subject’s task was to determine which temporal interval contained the vertical grating. Threshold was defined as the 75% correct level which was estimated by fitting the data with a Quick function (Quick, 1974) using a maximum likelihood estimation procedure. The peripheral direction matching experiment was performed with the patterns shown in cases 1 and 3 but viewed at a distance of 19 in. For these measurements, the circular display window was 16” in dia and was centered at 15” in the various visual field sectors. The spatial frequencies used were 0.75 and 0.5 c/deg and the pattern speeds were 8.0 and 9.6 deg/sec for case 1 and 3 type II patterns respectively. The visual field sectors are shown in Fig. 4 for a subject using the left eye. The white arrows indicated the direction of patterns in conditions 2, 3 and 4 calculated according to the IOC rule. In the upper oblique temporal, temporal and lower oblique visual sectors, the monitor was physically rotated to achieve the desired angle of pattern motions. In future discussions, the word temporal will be omitted when describing the oblique visual fields. Presentation duration was selected to be 1 set so that subjects could be
c2
P
2.67 4.00 10.7 16.08 2.67 4.00 0.88 1.33 0.88 1.33 2.00 2.50 8.00 10.00 4.00 4.80 1.33 1.60
given enough time to judge the equilibrium type II pattern direction. Subjects RB, IW, PJ, HJ were naive. IW, JC and PJ performed peripheral direction matching experiments before any fovea1 data were collected.
RESULTS Fovea1 2-D Motion Perception
Ferrera and Wilson (1990) found that perceived direction bias of type II patterns averaged 7.5” toward the mean component direction. Here we report that perceived type II pattern direction changes vividly during the course of a 1 set presentation. The shortest duration Ferrera tested was 200 msec. At even shorter durations of presentation, type II pattern direction was perceived to be in the component vector sum direction.
Upper Upper oblique
Lower oblique Lower
FIGURE 4. Visual field loci for peripheral direction matching. Measurements were made in the upper, upper oblique, temporal, lower oblique and lower visual field loci. The dimensions of the displays and the overlap in the tested visual field are also shown. Note that this figure only applies to a subject using the left eye. The dark circle in the temporal visual field along the horizontal meridian indicates the location of the blind spot.
140
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YO and HUGH
We have examined this novel phenomenon under the wide variety of conditions listed in Table 1. Typical raw data are shown in Fig. 5(a) and (b) obtained at two presentation durations (60 and 150 msec). The pointer directions that the subject chose are plotted on the x-axes. The number of times (frequency) the subject chose that pointed direction are plotted on the y-axes. 0” indicates upward direction, negative and positive directions indicate leftward and rightward deviations from the vertical respectively. Figure 5(a) shows data for type I patterns and (b) shows data for type II patterns. Top panels show results obtained in a single experiment with presentation duration set at 60 msec while bottom panels show results obtained in another experiment with presentation duration set at 150 msec. All types of patterns shown in Fig. 3 were presented randomly in each experiment with the component vector angle difference being the same. The three dark columns represent the matches for type I patterns in conditions 1, 3 and 5. The gray and light gray ones represent matches for type II patterns in conditions 2 and 4. Different column thicknesses in Fig. 5(b) are used to show the overlapping nature of the perceived directions but the actual bin size (a)
R. WILSON
is 10” for all conditions. Double headed arrows indicate predicted directions for these conditions using the IOC‘ rule. Typically, the direction match scatter is smallest for type I patterns moving upwards in condition 3: thu standard deviation averaged 1.5. in Fig. 5. The oblique& moving type I patterns in conditions 1 and 5 have larger scatters with standard deviations averaging about 4.6 ., thus showing the oblique effect. The type I1 patterns in conditions 2 and 4 have the largest scatter even though their IOC direction is vertically upwards. The standard deviation of perceived type II pattern direction averaged about 13.8”. At 60 msec presentation duration (3 frames), mean perceived type II pattern direction for subject CY deviated about 40” from the TOC‘predicted resultant direction. At 90 msec (6 frames), the distribution of perceived type II pattern directions shifted to a more vertical direction (not shown). At 150 msec (10 frames), the perceived direction of type II patterns was closer to the IOC predicted resultant direction, but continued to show a small bias towards the components‘ direction (Ferrera & Wilson, 1990). It was interesting that the perceived directions of type I patterns were always consistent with the IOC rule ( - 60 . 0 . i- 60”) at (b) 28
)
CY: 22.3”
Type II
20
20 c
$ 3 P I;
B
s
T! t.L IO
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-40.
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-90’
-40.
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20 G s s e IL IO
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-400 Direction match
+90' Direction
match
FIGURE 5. Raw data obtained from direction matching experiment. Perceived directions are plotted on the x-axes. The frequency which subject chose the pointer direction are plotted on the y-axes using bins IO” wide. Top panels in (a) and (b) indicate results obtained in one experiment with presentation duration set at 60 msec. Bottom panels in (a) and (b) indicate results obtained in another experiment with presentation duration set at 15Omsec. Double headed arrows indicate IOC predicted resultant directions. Type I motion (conditions 1, 3, 5 from Fig. 3) data indicated by solid columns were duration independent and were veridical at 60 msec. Type II motion (conditions 2 and 4 from Fig. 3) data indicated by gray and light gray columns were duration dependent. Different column widths in (b) were used to show the overlapping nature of perceived directions.
MOVING TWO-DIMENSIONAL
the shortest presentation duration even though the pattern speed was calculated to be the same as that of the type II patterns [case l(c)]. To show the duration dependence of perceived direction of type II patterns and the duration independent nature of type I pattern perception more succinctly, the data are presented in another format in the following figures. The perceived directions of the five patterns are plotted on the y-axis and the duration of presentation is plotted on the x-axis in Fig. 6. Symbols for type II data points have been shifted laterally by 2 msec to avoid overlap. It can be seen that perceived type I motion is constant with respect to time but perceived type II motion is not. At 60 msec, the perceived type II pattern directions for both subjects deviated from the IOC prediction by about 55” which happened to be the vector
. rl
sum direction (55.5”) of type II patterns with component direction difference of 22.3” (case 1). Speed variations
The perceived direction change was next investigated with different pattern speeds. Perceived directions are plotted on the y-axis and presentation duration is plotted on the x-axis in Fig. 7 as in the previous figure. Data obtained with different speeds have been plotted on each graph to facilitate the comparison of perceived direction as a function of pattern speed. Type I pattern direction matching data are not shown because they are veridical and duration independent for all subjects. For subject CY:22.3’
Type II;
90 60 -
KXCond.1 Condition1 Condition2 Condition3 Condition4 Condnion 5 IOCCond.5
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141
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’
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Type If; 1.33-4O/sec
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40
1.33% ICOnd.2) 1.33'/S(COPd.4)
-30 -
60 -
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I=
16Vsec Icond.2) IWsec (cond.4) 4%ec ICOnd.21 4vSec(cofhl.4)
30 -
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--t e ....Q... ....*...
100
HJ:47.4*
’
60-
90
30 -
60
o-
30
150
200
Type If;
2.5-10°/sec
250
---t
10vsec (cond.2)
e
lOVwc(cond.4)
300
-30 -60 -
--40
60
60
100
Duration
120
140
160
(msec)
FIGURE 6. Perceived direction as a function of presentation duration. Perceived directions for the five conditions are plotted on the y-axis, duration is plotted on the x-axis. Dashed dotted line indicates predicted IOC direction for type I motion in condition 1 and dashed line indicates predicted IOC direction for type I motion in condition 5. Solid circles, solid squares and solid triangles indicate the perceived directions of type I motion in conditions 1, 3 and 5 respectively. Open circles and open triangles connected by heavy black lines indicate the perceived directions of type II motion in conditions 2 and 4 respectively. Error bars indicate standard deviations. For both subjects, type I motion was veridical at the shortest presentation durations. Type II pattern motion required a distinct time lag before approximating IOC pedicted resultant direction. At 60 msec, both subjects perceived type II patterns to move in its vector sum direction (55.5’).
2.5%~
-60
(mnd.2)
2.S0/sec (wnd.4) -90 40
60
60
100 Duration
120
140
i0
(msec)
FIGURE 7. The effect of speed on perceived direction of type II patterns. There is a 1Zfold difference in speed for CY, 3-fold difference for JCH, and a 4-fold difference for JH. Perceived directions are plotted on the y-axis, presentation duration is plotted on the x-axis. Solid lines connecting dark symbols indicate patterns drifted at the faster speed. Dotted line connecting open symbols indicate patterns drifted at a slower speed. Dashed lines connecting square symbols indicate patterns drifted at the slowest speed. Top left graph show that speed variation has little effect on perceived motion for CY. For subjects JCH and HJ, the faster 22.3 and 47.4” type II patterns converged quicker. Therefore increasing speed tend to increase rate of convergence.
142
CHRISTOPHER
YO
CY, a 12-fold difference in type II pattern speed did not produce any conspicuous difference in the duration needed to achieve IOC resultant direction even though the mean bias at 60 msec of the 1.33 deg/sec pattern was significantly larger (P < 0.0005) than that of the 16 deg/sec patterns. For subject JCH, a 3-fold difference in speed produced about 2-fold difference in the total duration needed to perceive a direction close to the IOC prediction, i.e. the duration in the slower case [l(e)] was 300 msec and in the faster case [ 1(c)] was about 150 msec. Comparing the 47.4” type II patterns traveling at 2.5 deg/sec [case 2(a)] to those traveling at 10 deg/sec [case 2(b)], HJ showed a 2-fold difference in the time delay, i.e. the perceived biases in the slower case [2(a)] at 90 and 150 msec corresponded to the perceived biases in the faster case [2(b)] at 45 and 75 msec respectively. For subject CY, the magnitude of the direction biases in case 2(a) failed to differ significantly from those in case 2(b) at the 0.1 level (data not shown) at 90 and 150 msec (by ANOVA). These results show that the duration required for perceived direction to converge toward IOC prediction is not consistently affected by speed and therefore not related to distance traveled when presentation duration exceeds 60 msec. At short presentation durations (660 msec), all type II patterns have a large bias. To show that with presentation durations exceeding 60msec, perceived direction bias for type II pattern is not due to the limited distance traveled, the pattern was presented at different durations while keeping the distances traveled by the components constant. If direction bias was due to distance, then it would appear to move in the same direction for any presentation duration. In Fig. 8, we show that perceived directions of the 5 conditions (refer to Fig. 3) for two subjects with type II patterns which had a component angular difference of 22.3 and 51.6” [case l(d), 3(a) and (b)]. The component spatial frequencies under cases l(d), 3(a) and (b) were 4.5, 1.Oand 3.0 c/deg respectively (Table 1). Most importantly, notice the perceived directions of the type II patterns indicated by open symbols that are connected by heavy black lines. The presentations at longer durations utilized the same phase shifts in creating the motion perception at 90 msec [case l(d)] and 60 msec [cases 3(a) and (b)], but each frame has been presented multiple times (double, triple and quadruple times). These results show that the critical variable in altering perceived direction is duration rather than distance traveled. With long enough presentation duration, even though the speed is slower, the perceived direction of type II patterns will approximate IOC rule predictions. Taken together, all the above results indicate that the perceived direction bias for type II patterns is not due to distance traveled. It depends on presentation duration and therefore is consistent with the notion that additional slower neural processes are required for accurate type II motion processing. On the other hand, type I motion processing is almost instantaneous as its perceived direction is accurate with short presentation durations (d 90 msec).
and HUGH
R. WILSON
.._._..,.. +
101 -)* --)_____
10CCOGd.l Condition Condition Condition Condition Condition IOC Cond
CY:22.3”,
1
2 3 4 5 5
4.5
cpd -
90 . 6 -w
60
frames e-m__
120
80
______
l
t
160
200
240
CY:51.6”, 90
I
4
280
320
360
400
3cpd
frames
40
80
120
160
HJ:51.6”,
200
240
2
0
1 cpd
90,
30
4
-
frames
4 o-
-30 -
-60
-
40
60
80
100
120
Duration
140
160
180
1
200
(msec)
FIGURE 8. Perceived directions at different durations with constant distance traveled. Symbol designations are the same as those in Fig. 6. CY was tested with patterns in cases l(d) (22.3”, 4.5 c/deg) and 3(b) (51.6”, 3 c/deg), HJ was tested with patterns in case 3(a) (51.6-. 1 c/deg). With multiple presentations of the same four (60 msec) or six (90 msec) initial phase shifts, perceived directions for type II patterns changed by more than 30” to approximate IOC predicted direction for both subjects. If perceived direction change was due to distance traveled, it would not have occurred. Therefore, perceived direction change for type II patterns is due to duration and not due to distance traveled.
Spatial frequency
variations
Spatial frequency was tripled by increasing the monitor viewing distance 3-fold. By this maneuver, the window size was reduced by 3 times but a constant number of nodes and antinodes for the two-dimensional patterns was displayed. The effect on perceived direction was performed on four subjects. In some cases, the effect of spatial frequency differences was examined with temIDora1 freauencv I , being constant while in others. the
MOVING TWO-DIMENSIONAL
pattern resultant speed was held constant. A 3-fold differences in spatial frequency (1 vs 3 c/deg 51.6” patterns; 1.5 vs 4.5 c/deg 22.3” patterns) did not produce any conspicuous difference in the overall time course for type II patterns to approach IOC predicted direction. Mean direction biases between patterns having a 3-fold difference in spatial frequency measured at different time intervals did not show significant differences by the post hoc Tukey HSD test at the 0.05 level (Wirier, 1971). For all subjects under all spatial frequency conditions, type I pattern direction perception was accurate and duration independent. Further details are available elsewhere (Yo, 1990). Contrast
143
PATTERNS 60
CY: 22.3”; case Ic
ob
I
I
1
I
,I
1000
100
1
60
YJZ
: 22.3’
; case Ic
variations
If one temporally modulates the type II pattern contrast using a Gaussian envelope, the perceptual direction change near the beginning and end of the presentation is apparent. When the contrast gradually increased at the beginning of the presentation, the perceived direction changed from the component vector sum direction to the predicted IOC resultant direction. When the contrast decreased after the peak of the Gaussian, the perceived direction deflected back to the component vector sum direction. To quantify this observation, we measured the perceived direction of two-dimensional patterns as a function of contrast. As contrast variations of 5-100% had no effect on type I pattern direction perception, their perceived directions will not be shown in the following figure. Figure 9 contains semilog plots of direction bias vs duration at different contrasts for three subjects. Type II pattern bias represented averaged magnitudes obtained under conditions 2 and 4 (refer to Fig. 3). All subjects under all conditions showed a marked lengthening of the time course with decreasing contrast; and at 5-10% contrast, a substantial bias was observed even after 1 set of presentation. The direction matches at 5 and 100% contrasts for subject YJZ were only performed once. Experienced subject CY noticed that 47.4” [case 2(b)] type II patterns cohered at 50 and 100% contrast, but were incoherent when contrast was reduced to 5%. For experienced subject HRW, the average bias for 51.6” [case 3(a)] type II patterns with 1 set of presentations at 5% contrast was 15”; and he noticed the patterns being incoherent during some of the trials. Judging from HJ’s large perceived directional bias (about 36”) after 1 set of presentation in case 3(a) at 5 and 10% contrast, the type II motions could have been incoherent, as his direction match was close to the direction of the faster component (33.6” from the vertical). Thus, it is apparent that the neural units processing type II motion have higher thresholds than those mediating type I motion.
oh,
,,I
J 100
1000
6Oi-
I
j case 30
HJ:51.6O
100
1000
Duration
(msec)
FIGURE 9. Contrast dependence of type II motion perception in the fovea. Direction bias on the y-axis represents the average magnitude of bias found in conditions 2 and 4. The vector sum directions of case l(c) and 3(a) type II motions are 55.5 and 37.7” from the vertical respectively whereas the directions of the faster component are 48.2 and 33.6” from the vertical. Data points for JH when tested with 5 and 10% contrast case 3(a) patterns were close to the direction of the faster component indicating that the type II pattern might have been incoherent at these contrasts.
51.6OType
IT ; duration - 1 set I
-A- PJ:LO -0.cy:u
0.1
1
Contrast
Peripheral
2-D Motion
Perception
Scaling
Grating acuity was first measured at 15” eccentricity in the lower, lower oblique, upper oblique and the upper
FIGURE 10. Contrast dependence of type II motion perception in the periphery. Direction bias on the y-axis represents the average magnitude of bias obtained in conditions 2 and 4. Triangular and circular symbols indicate measurements made on subjects PJ and CY respectively. Solid and open symbols indicate measurements made in the lower oblique and upper visual sectors respectively.
144
CHRISTOPHER Combined
across
subjects
YO and HUGH R. WILSON
22.3” Combined
50
acrass
subjects
22.3”
.,.,.,.,.,1..,.....1~,.,.,.~.~~.........~....,.,.~~......~.~.
:j -G 0 z
40
---
5
Vector Sum (55.57
-'.a- FasterComp(48.2')
s 30
s '3 820 .s
L-dn
L-up
LO
LO-dn
Temp
UO
U
0
L-dn Combined
across
subjects
L-up
LO
LO-dn
Temp
UO
subjects
51.6”
U
51.6’ Combined
across
“h-GzTl
L-dn
L-up
LO
LO-dn
Temp
UO
U
FIGURE 11. Average peripheral direction error for type I and II patterns. Top panel compares average magnitude of perceived direction error for type I and II patterns with component vector angular diierence of 22.3”. Lower panel compares average magnitude of perceived direction error for type I and II patterns with component vector angular difference of 51.6”. L-dn refers to downward moving patterns presented in the lower visual field. L-up refers to upward moving patterns in the lower visual field. LO refers to foveofugally moving patterns in the lower oblique quadrant. LO-dn refers to vertically downward moving patterns presented in the LO quadrant. Temp, UO and U refer to the temporal visual field, the upper oblique sector and the upper visual field respectively. Perceived direction error ascertained with type II patterns showed a directional anisotropy in both L and LO visual fields in that perceived direction error was lower in the foveofugal directions. Also shown are the predicted errors if type II direction was judged according to the vector sum addition rule and according to the faster moving component vector indicated by the dashed and dashed-dotted lines respectively.
visual fields. It was not performed in the temporal visual field along the horizontal meridian due to the interference of the blind spot. Data for four subjects did not show significant difference (P > 0.15) in visual acuity ascertained in the four peripheral locations. Grating acuity averaged 7 times lower than fovea1 acuity. Peripheral direction matching experiments were performed at a distance 6 times closer than those in cases l(d) and 3(b). As we were concerned about maintaining a large enough display size and yet not placing the monitor too close to the subject’s eye, a scaling of 6 times the fovea1 distance provided a satisfactory compromise.
L-dn
L-up
LO
LO-dn
Temp
UO
U
FIGURE 12. Combined standard deviation of peripheral direction match across subjects. x-axis notation is explained in the legend of the previous figure. In both cases, type I pattern direction standard deviation was greatest in the LO and UO visual field loci. Standard deviation of perceived directions for type II patterns were greater than type I patterns in all the visual field locations.
Contrast
variations
Fovea1 data indicated that type II motion perception was contrast dependent. Pilot experiments in the periphery were performed in the upper and lower oblique visual field loci at three different contrasts with patterns drifting away from the fovea. Direction bias (y-axis) is defined as the difference (in deg) between the pattern direction calculated by the IOC rule and the subject’s orientation match using a rotating pointer displayed on the computer monitor after 1 see of pattern presentation (see Methods). Results from two subjects tested with 51.6” type II patterns are shown in Fig. IO. Direction bias was larger in the upper visual sector compared to the lower oblique visual sector at all three contrasts. The bias was smaller for higher contrast but tended to level off beyond 20% contrast. In subsequent direction matching experiments performed in the other visual field locations, a 20% pattern contrast was therefore used. Peripheral
type I motion perception
The top panels in Figs 11 and 12 compare type I and II motion data collected using patterns with 22.3”
MOVING TWO-DIMENSIONAL TABLE 2. Student’s t-test for data measured with 22.3” type II patterns Error LO < L-dn
CY
HJ
IW
PJ
JC
RB
yes
yes
no
no
no
no
yes
yes
yes
no
P < 0.05P < 0.01 L-dn < U
yes
yes
P < 0.01 P
VisionRes. Vol. 32, No. I, pp. 135-147,1992 Printed in Great Britain. All rights reserved
Perceived Direction of Moving Two-Dimensional Patterns Depends on Duration, Contrast and Eccentricity* CHRISTOPHER
YO,t HUGH
R. WILSONt
Received 30 May 1990; in revised form 3 October 1990; received for publication 18
June 1991
Type II two-dimensional motion is produced by superimposing two one-dimensional drifting cosine gratings with velocity vectors lying on the same side of the intersection-of-constraints (IOC) resultant. When type Dpatterns were constructed with components having the same spatialfrequency and contrast, perceived direction was found to be biased toward the vector sum direction at short durations and approached the direction predicted by IOC only after some time lag. This time lag was contrast dependent. At 5% contrast, the perceived direction after I set of presentation remained biased by more than 20”. Direction perception was also measured at 15” eccentricity. At this eccentricity the perceived direction of type II patterns was grossly biased away from the IOC prediction in the direction of the component vectors by an average of 25”. Motion
Intersection-of-constraints
Peripheral vision
INTRODUCTION The actual direction of a one-dimensional pattern moving across the receptive field (RF) of a neuron may be almost &90” away from the direction signaled by the neuron. This phenomenon is referred to as the aperture problem and was iirst studied by Wallach (1935, 1976). He demonstrated that the direction of a one-dimensional pattern moving behind an aperture depends on the aperture shape, but when another pattern at another orientation is superimposed on and drifted with the first one, the overall direction is unambiguous and is not affected by aperture shape. In 1982, Adelson and Movshon provided geometrical and psychophysical insight into the visual analysis of such two-dimensional pattern motion. Geometrically, they proposed that the resultant velocity is determined by the “intersection-ofconstraints” (IOC) or “velocity-space” construction. In the construction, components are treated as comprising a rigidly moving object. Local estimates of each component’s velocity will generate a host of physically possible motions bounded by its constraint line as shown in Fig. 1. As different components will likewise generate their own constraint lines, the predicted object motion is determined by the intersection of all the physically *Research first reported at the 1990 annual meeting of the Association for Research in Vision and Ophthalmology. TDepartment of Ophthalmology and Visual Science, University of Chicago, 939 E. 57th Street, Chicago, IL 60637, U.S.A. $Resultant refers to the resultant motion vector of the two-dimensional pattern defined by the IOC rule. When speaking of vector addition, the term “vector sum” will be employed.
MT topography
Oblique effect
possible interpretations generated by the components. Diagrammatically shown in Fig. l(a) is an object moving at speed P. The component speeds Cl and C2 of the component gratings comprising the object will be Cl = P cosa c2 = P cos/iI where a and /I denote the angles between the object velocity and the component velocities. The local estimates of speeds Cl and C2 will thus generate constraints depicted by the gray lines. As the components are assumed to comprise a rigid body, the global object velocity P must be consistent with both local readings; hence the resultantS is at the intersection of the constraint lines. This type of construction is different from a vector summation prediction in two respects. One is that as the angle between the two components increases, so does the resultant speed [the diameter of the circle in Fig. l(a) will increase]; vector summation would predict just the opposite. The other difference is that the vector produced by vector summation always lies between the two component vectors, but using the IOC, one can easily produce resultants that lie outside the boundaries of both components. In fact, any combination of vectors which lie on the circle in Fig. l(b) would yield the resultant vector indicated by the thick dark arrow. Ferrera and Wilson (1990) classified two-dimensional patterns into two groups: type I patterns [shown in Fig. l(a)] in which component vectors lie on both sides of the resultant vector (plaids), and type II patterns [shown in Fig. l(c)] in which the components are both located on 135
136
Type I (Plaids)
w
Type II: (Blobs) c
a P -.
side a fixed tolerable range in any of these dcm~ins, the catnponents are seen as independent entities traveling tra~sparen~~~ acmss each other in directions orthogonal
to their orientations. Therefore when the component vectors signaled by the first stage motion units come from essentially the same depth plane, they are selectively combined in the second stage to generate the resultant vector. This was the claim of’ Ad&on and colleagues for the case when both components are s~~~rnpos~* ~~b~uently~ Nakayama and Silverman (1988) showed that the second stage motion system is also capable of combining local velocity signals from VY b different spatial regions to reconstruct a global rigid t motion percept.. Welch (1989) ~rform~ speed discrimination ex~~rne~ts and showed that the ~sc~rn~~~ion thresholds of two-dimensional patterns reflected the discrimination thresholds at the component level. This further supports the two stage model by implying that L * the precision in the extraction of two-dimensional patvx tern speed is limited by noise at the component stage. FIG-E ‘I. Ve~tity-spaoe eangt~~aufor det~~ni~ resultant Mo~shon, Addson, Gizzi and Newsome jt9St Emotion. I% and vy denote the horizo?ltal and vertical components of ported that 40% of MT neurons were sensitive to only the m&m vtxtor. When the twa components cohere and move as a component directions when exposed to moving tworigid surface, the global velocity of the pattern is unique and is determined by the intersection of the constraint (gray) lines. Any dimensional grat,ings. Interestingly, another 25?;, were combination of vectors that lie an the circle (b) will generate the same found not to respond significantly to the component upward resultant pattern veotor. According to the dassikation by grating directions when the components were presented Ferrzra and Wilson (1%X& patterns ba6ng ~rn~n~ts located on alone but responded well to the pattern direction when both sides of the resultant are considenxi as type 1 [a) (previously both components were presented and to a one-dimenreferred to as plaids in Ferrtxa & Wilson, 1987), those having components located only on one side of the resultant are considered sional grating traveling in the pattern direction. The as type II (c) (previously referred to as blobs in Ferrera & Wilson, investigators hypothesized that the tuning properties of 1987). these pattern direction selective units were generated by highly nonlinear excitatory and inhibitory interactions one Side: af tk! 2x%&arrt ~~~~~~~~ -F&S ~~~~~~~~U~ was which characterize the second stage of the motion analybasx8 on p~yc~o~hy~~ca~ measureu?ents that have resis system. Furthermore, they suggested that these nonvealed three perceptual differences between these patlinear pattern selective neurons in MT received input terns: (1) the masking strength of a type I pattern is 2-4 from component direction selective neurons in VI and times more than that produced by either component MT and solved for the resultant two-dimensional patwhereas the masking strength of a type II pattern is tern direction by neura& im~lcmenting the KkT r&e. determined by the ~rnp~ne~~ nearest to the test (Ferrera. In this research, further evidence will be provided to & Wilson, 1987); (2) perceived direction of a type I show that motion processing takes place in two stages. pattern is consistent with the IOC prediction while the Type II patterns offer a more rigorous test of the IOC perceived direction of a type II pattern is biased toward rule than type I patterns because the predicted resultan% the components’ direction by about 7.5”; (3) direction lie outside the boundaries of either component vector. ~~rn~~~tion thresholds for type I patterns averaged t” When type XI patterns were constructed by srrperimposwhile those of type f1 patterns averaged 5.5” (Ferrera & ing two drifting cosine gratings of the same spatial Wilson, 1990).These percaFjtua1 differences between type frequency and contrast according to the IOC rule, I and type II patterns suggested that the underlying perceived direction was found to be biased in the neural circuitry for analyzing them is different (Ferrera vector sum direction at short presentation durations 6%Wilson, 1987, 1990). (K 90 msec) and approached the direction predicted by Adelson and ~o~sb~~ (1982) proposed that the TOC only after a time lag. This time lag was foirnd to be synthesis of ~~irn~nsi~~al pattern motion from onecontrast dependent. At 5% contrast, the perceived direcdimensional component motions is acl;omplished in tion after I set of presentation remained grossly biased two stages. Psychophysicslly, they showed that the combination of local component vector information is toward the vector sum direction. The type I “patterns used in this study were all symmetric, i.e. the componenr dependent on refative spatial frequency, velocity9 convectors are of the same speeds. Type I direction perceptrast and apparent depth of the twc~ c~~p~~en~= Outtion, unfke type II: motion, was found to be accurate at all durations and contrasts. *A simple way of remembering the distinction betwean type I and type In the second part of this paper, we ascerraiaed the II patterns is the following: typ I patterns have ant component on accuracy of type 1 and II pattern direction perception at each side of the IOC resultant, while type II patterns have NO components together on the same side of the ICX resultant. 15.‘ eccentricity in the upper. upper oblique temporaL
MOVING TWO-DIMENSIONAL
PATTERNS
137
positioned with a chin rest to maintain constant viewing distance. In fovea1 and peripheral direction matching experiments, 5 different stimulus configurations were used (Fig. 3). In Figure 3, component speeds are indicated by thin arrows and IOC resultant speeds are indicated by thick arrows. In a single experiment, the components in all 5 conditions had the same angular difference (22.3, 47.4 or 51.6”). Under conditions 1, 3 and 5 the two components drifted at the same speed, producing type I pattern motion which had resultants at -60, 0 and + 60” respectively (0” indicates upward motion, negative angles indicate leftward deviations from the upward direction and positive angles designate rightward deviations). In conditions 2 and 4, type II motions were produced with a resultant IOC direction that was directly upward and was equal to the direction of the type I pattern drifted in condition 3. The circular display window when positioned 38 in. from the viewer was 8” in dia and had a 4.8 x 4.8 min of arc dark fixation spot in the center. The subject fixated on the center and initiated pattern presentation by a button press. The duration of presentation remained constant throughout each experiment. A beep sounded after each presentation and a blank screen appeared for 0.2 set followed by the METHODS appearance of a 5.6” long pointer. The pointer could be Spatial patterns were generated on a Macintosh II rotated around the fixation point and the subject used microcomputer and displayed on an Apple high- the mouse to align the angle of the pointer to the resolution monochrome monitor (8 bits/pixel) with P4 perceived pattern direction. Once a match was made, the (white) phosphor and a 66.7 Hz frame rate. The mean subject pressed the mouse button for the computer to luminance was 66 cd/m2. Contrast was defined as record the match. A blank screen reappeared for 1 set, (L, - L,,)l(L& where L,, and Mean were the followed by the next presentation randomly selected maximum and mean luminances in the pattern. Subjects among the 5 conditions. Each pattern was presented 30 viewed the display through a circular aperture in a times in each experiment. Subjects were given practice on cardboard surround which was illuminated to approxiall tasks before actual data were collected. Each expermately the same hue and brightness as the screen. iment was repeated at least 3 times on different days for Pattern motion was achieved using the technique of each subject unless otherwise specified. Trials with differcolor table animation (Shoup, 1979; Sheets, 1988; Apple, ent durations of presentation were alternated. Table 1 1988; Knaster, 1988). A pixel map consisting of a lists all variations of the stimulus parameters used in linearized ramp of gray levels was first painted on the assessing fovea1 direction perception. screen. A cosine of the appropriate frequency was then Patterns used in cases 1, 2 and 3 have component scrolled through the color look-up table, transforming direction differences of 22.3, 47.4 and 51.6” respectively. the ramp into a drifting cosine grating. The look-up In cases l(c), (d), (e) and 3(a) and (b) the resultant speeds table was changed 67 times/set to create phase shifts of (P) of type I patterns were calculated to be equal to type the cosine pattern in successive frames that could be II pattern resultant speeds according to the IOC rule. In made almost arbitrarily small. Two-dimensional spatial cases l(a) and (b), the component speed of the type I patterns were created by drawing two one-dimensional ramps oriented at different angles on alternate horizontal pixel lines. We used type II patterns with component vector angular differences of 22.3, 47.4 and 51.6” which are shown in Fig. 2. Component and resultant speeds in Fig. 2 represented ratios rather than actual speeds. A total of twelve subjects participated in fovea1 and 1 2 3 4 5 peripheral direction matching experiments. In all experConditions iments subjects viewed the monitor monocularly. CY, IW, JC, PJ, JCH used their right eyes. HRW, VPF, HJ, FIGURE 3. Velocity-space construction of the five conditions used in direction matching experiment. The component vectors of the five YJZ, RB, RC and AS used their left eyes. JC, RB, JCH conditions all have the same angular difference. Conditions 1, 3 and and AS had no refractive error and the others wore 5 were type I patterns. Conditions 2 and 4 were type II. Thick arrows proper corrective eye glasses. All except CY, HRW and indicate IOC predicted resultant directions, thin arrows indicate VPF were naive. The subjects’ heads were comfortably component vector directions.
temporal, lower oblique temporal and lower visual fields (see Fig. 4). This was motivated by the results obtained from electrophysiological mappings of MT cortex. Maunsell and Van Essen (1987) and Maunsell (1988) showed that the macaque MT topographical organization has a representational bias in which the lower oblique temporal sector of the periphery is favored. Type I and II patterns in the peripheral direction matching experiments were calculated to move away from the fovea in the peripheral visual field sectors according to the IOC construction. This was based on Albright’s (1989) report that the preferred direction of MT neurons in the periphery (beyond 12” eccentricity) was biased toward representing foveofugal (away from fovea) directions. For type I patterns some evidence for an oblique effect was found, but direction perception was otherwise quite accurate. For type II patterns, however, large biases in the direction of the vector sum were found in all visual field quadrants, the average being 25”. Thus, the visual periphery is clearly deficient in the processing of type II patterns. In addition, these tests reflect some evidence of the topographical representation and directional bias found in area MT of macaques.
CHRISTOPHER
138
3
,22.3”,
YO and HUGH
R. WILSON
1
FIGURE 2. Type II patterns used in direction matching. The component vector angular differences in cases 1 (left), 2 (middle) and 3 (right) were 22.3,47.4 and 51.6” respectively. The component vector sum directions were 55.5,48.2 and 37.7” respectively. The velocity space construction is shown below each pattern. Numbers next to the arrows indicate the speed ratios of the components and the resultant pattern motion vector. Type I motion using these same spatial patterns will travel in a direction about 60” from the vertical.
MOVING TWO-DIMENSIONAL
139
PATTERNS
TABLE 1. Parameters for fovea1 direction matching experiment. Case 1 patterns all had a component vector angular difference of 22.3”, case 2 patterns had an angular difference of 47.4” and case 3 patterns had an angular difference of 51.6”. The third column indicates the size of the display window. The fourth column indicates the component spatial frequency. Cl, C2 and P represent component speeds and pattern speeds calculated by IGC (see Fig. 1) Type
1
Type 11 Speed@eg/=)
Speed(de+4 Case
l(a) l(b) l(c) l(d) l(e) 2(a) 2(b) 3(a) 3(b)
Angle (deg)
Size (deg)
22.3 22.3 22.3 22.3 22.3 47.4 47.4 51.6 51.6
8 8 8 2.7 8 8 8 8 2.7
SF (c/deg)
Cl
c2
P
Cl
1.5 1.5 1.5 4.5 1.5 1.0 1.0 1.0 3.0
1.33 5.33 3.93 1.31 1.31 2.00 8.00 4.32 1.44
1.33 5.33 3.93 1.31 1.31 2.00 8.00 4.32 1.44
1.36 5.43 4.00 1.33 1.33 2.18 8.74 4.80 1.60
1.33 5.33 1.33 0.44 0.44 0.25 1.00 0.40 0.13
patterns equaled the slower component of type II patterns, in cases 2(a) and (b), component speed of the type I patterns equaled the faster component of type II patterns. In all cases except l(d) and 3(b) (114 in., 2.7” display dia) the viewing distance was 38 in., producing a circular display dia of 8” and pixel size of 72 arc sec. Bold figures in Table 1 highlight the maximum and minimum speeds for type II patterns used in this study. Grating acuity was measured on CY, IW, HJ and JC in the upper (superior), upper oblique temporal, lower (inferior) oblique temporal and lower visual fields at 15” eccentricity. Oblique direction designates 45” above or below the horizontal meridian. Measurements were not made in the temporal visual field along the horizontal meridian due to the presence of the blind spot. The grating acuity experiment was conducted using a twoalternative forced-choice (2AFC) paradigm. Four grating sizes were used and each was repeated 40 times in random order. The subject’s task was to determine which temporal interval contained the vertical grating. Threshold was defined as the 75% correct level which was estimated by fitting the data with a Quick function (Quick, 1974) using a maximum likelihood estimation procedure. The peripheral direction matching experiment was performed with the patterns shown in cases 1 and 3 but viewed at a distance of 19 in. For these measurements, the circular display window was 16” in dia and was centered at 15” in the various visual field sectors. The spatial frequencies used were 0.75 and 0.5 c/deg and the pattern speeds were 8.0 and 9.6 deg/sec for case 1 and 3 type II patterns respectively. The visual field sectors are shown in Fig. 4 for a subject using the left eye. The white arrows indicated the direction of patterns in conditions 2, 3 and 4 calculated according to the IOC rule. In the upper oblique temporal, temporal and lower oblique visual sectors, the monitor was physically rotated to achieve the desired angle of pattern motions. In future discussions, the word temporal will be omitted when describing the oblique visual fields. Presentation duration was selected to be 1 set so that subjects could be
c2
P
2.67 4.00 10.7 16.08 2.67 4.00 0.88 1.33 0.88 1.33 2.00 2.50 8.00 10.00 4.00 4.80 1.33 1.60
given enough time to judge the equilibrium type II pattern direction. Subjects RB, IW, PJ, HJ were naive. IW, JC and PJ performed peripheral direction matching experiments before any fovea1 data were collected.
RESULTS Fovea1 2-D Motion Perception
Ferrera and Wilson (1990) found that perceived direction bias of type II patterns averaged 7.5” toward the mean component direction. Here we report that perceived type II pattern direction changes vividly during the course of a 1 set presentation. The shortest duration Ferrera tested was 200 msec. At even shorter durations of presentation, type II pattern direction was perceived to be in the component vector sum direction.
Upper Upper oblique
Lower oblique Lower
FIGURE 4. Visual field loci for peripheral direction matching. Measurements were made in the upper, upper oblique, temporal, lower oblique and lower visual field loci. The dimensions of the displays and the overlap in the tested visual field are also shown. Note that this figure only applies to a subject using the left eye. The dark circle in the temporal visual field along the horizontal meridian indicates the location of the blind spot.
140
CHRISTOPHER
YO and HUGH
We have examined this novel phenomenon under the wide variety of conditions listed in Table 1. Typical raw data are shown in Fig. 5(a) and (b) obtained at two presentation durations (60 and 150 msec). The pointer directions that the subject chose are plotted on the x-axes. The number of times (frequency) the subject chose that pointed direction are plotted on the y-axes. 0” indicates upward direction, negative and positive directions indicate leftward and rightward deviations from the vertical respectively. Figure 5(a) shows data for type I patterns and (b) shows data for type II patterns. Top panels show results obtained in a single experiment with presentation duration set at 60 msec while bottom panels show results obtained in another experiment with presentation duration set at 150 msec. All types of patterns shown in Fig. 3 were presented randomly in each experiment with the component vector angle difference being the same. The three dark columns represent the matches for type I patterns in conditions 1, 3 and 5. The gray and light gray ones represent matches for type II patterns in conditions 2 and 4. Different column thicknesses in Fig. 5(b) are used to show the overlapping nature of the perceived directions but the actual bin size (a)
R. WILSON
is 10” for all conditions. Double headed arrows indicate predicted directions for these conditions using the IOC‘ rule. Typically, the direction match scatter is smallest for type I patterns moving upwards in condition 3: thu standard deviation averaged 1.5. in Fig. 5. The oblique& moving type I patterns in conditions 1 and 5 have larger scatters with standard deviations averaging about 4.6 ., thus showing the oblique effect. The type I1 patterns in conditions 2 and 4 have the largest scatter even though their IOC direction is vertically upwards. The standard deviation of perceived type II pattern direction averaged about 13.8”. At 60 msec presentation duration (3 frames), mean perceived type II pattern direction for subject CY deviated about 40” from the TOC‘predicted resultant direction. At 90 msec (6 frames), the distribution of perceived type II pattern directions shifted to a more vertical direction (not shown). At 150 msec (10 frames), the perceived direction of type II patterns was closer to the IOC predicted resultant direction, but continued to show a small bias towards the components‘ direction (Ferrera & Wilson, 1990). It was interesting that the perceived directions of type I patterns were always consistent with the IOC rule ( - 60 . 0 . i- 60”) at (b) 28
)
CY: 22.3”
Type II
20
20 c
$ 3 P I;
B
s
T! t.L IO
IO
I
+40*
-40.
i
: .:.
-90’
-40.
0'
'40'
'.+gOD
20 G s s e IL IO
-90.
+40'
-400 Direction match
+90' Direction
match
FIGURE 5. Raw data obtained from direction matching experiment. Perceived directions are plotted on the x-axes. The frequency which subject chose the pointer direction are plotted on the y-axes using bins IO” wide. Top panels in (a) and (b) indicate results obtained in one experiment with presentation duration set at 60 msec. Bottom panels in (a) and (b) indicate results obtained in another experiment with presentation duration set at 15Omsec. Double headed arrows indicate IOC predicted resultant directions. Type I motion (conditions 1, 3, 5 from Fig. 3) data indicated by solid columns were duration independent and were veridical at 60 msec. Type II motion (conditions 2 and 4 from Fig. 3) data indicated by gray and light gray columns were duration dependent. Different column widths in (b) were used to show the overlapping nature of perceived directions.
MOVING TWO-DIMENSIONAL
the shortest presentation duration even though the pattern speed was calculated to be the same as that of the type II patterns [case l(c)]. To show the duration dependence of perceived direction of type II patterns and the duration independent nature of type I pattern perception more succinctly, the data are presented in another format in the following figures. The perceived directions of the five patterns are plotted on the y-axis and the duration of presentation is plotted on the x-axis in Fig. 6. Symbols for type II data points have been shifted laterally by 2 msec to avoid overlap. It can be seen that perceived type I motion is constant with respect to time but perceived type II motion is not. At 60 msec, the perceived type II pattern directions for both subjects deviated from the IOC prediction by about 55” which happened to be the vector
. rl
sum direction (55.5”) of type II patterns with component direction difference of 22.3” (case 1). Speed variations
The perceived direction change was next investigated with different pattern speeds. Perceived directions are plotted on the y-axis and presentation duration is plotted on the x-axis in Fig. 7 as in the previous figure. Data obtained with different speeds have been plotted on each graph to facilitate the comparison of perceived direction as a function of pattern speed. Type I pattern direction matching data are not shown because they are veridical and duration independent for all subjects. For subject CY:22.3’
Type II;
90 60 -
KXCond.1 Condition1 Condition2 Condition3 Condition4 Condnion 5 IOCCond.5
..1-.....
V -r+ e V SW___
141
PA’ITERNS
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140
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(msec)
FIGURE 6. Perceived direction as a function of presentation duration. Perceived directions for the five conditions are plotted on the y-axis, duration is plotted on the x-axis. Dashed dotted line indicates predicted IOC direction for type I motion in condition 1 and dashed line indicates predicted IOC direction for type I motion in condition 5. Solid circles, solid squares and solid triangles indicate the perceived directions of type I motion in conditions 1, 3 and 5 respectively. Open circles and open triangles connected by heavy black lines indicate the perceived directions of type II motion in conditions 2 and 4 respectively. Error bars indicate standard deviations. For both subjects, type I motion was veridical at the shortest presentation durations. Type II pattern motion required a distinct time lag before approximating IOC pedicted resultant direction. At 60 msec, both subjects perceived type II patterns to move in its vector sum direction (55.5’).
2.5%~
-60
(mnd.2)
2.S0/sec (wnd.4) -90 40
60
60
100 Duration
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140
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(msec)
FIGURE 7. The effect of speed on perceived direction of type II patterns. There is a 1Zfold difference in speed for CY, 3-fold difference for JCH, and a 4-fold difference for JH. Perceived directions are plotted on the y-axis, presentation duration is plotted on the x-axis. Solid lines connecting dark symbols indicate patterns drifted at the faster speed. Dotted line connecting open symbols indicate patterns drifted at a slower speed. Dashed lines connecting square symbols indicate patterns drifted at the slowest speed. Top left graph show that speed variation has little effect on perceived motion for CY. For subjects JCH and HJ, the faster 22.3 and 47.4” type II patterns converged quicker. Therefore increasing speed tend to increase rate of convergence.
142
CHRISTOPHER
YO
CY, a 12-fold difference in type II pattern speed did not produce any conspicuous difference in the duration needed to achieve IOC resultant direction even though the mean bias at 60 msec of the 1.33 deg/sec pattern was significantly larger (P < 0.0005) than that of the 16 deg/sec patterns. For subject JCH, a 3-fold difference in speed produced about 2-fold difference in the total duration needed to perceive a direction close to the IOC prediction, i.e. the duration in the slower case [l(e)] was 300 msec and in the faster case [ 1(c)] was about 150 msec. Comparing the 47.4” type II patterns traveling at 2.5 deg/sec [case 2(a)] to those traveling at 10 deg/sec [case 2(b)], HJ showed a 2-fold difference in the time delay, i.e. the perceived biases in the slower case [2(a)] at 90 and 150 msec corresponded to the perceived biases in the faster case [2(b)] at 45 and 75 msec respectively. For subject CY, the magnitude of the direction biases in case 2(a) failed to differ significantly from those in case 2(b) at the 0.1 level (data not shown) at 90 and 150 msec (by ANOVA). These results show that the duration required for perceived direction to converge toward IOC prediction is not consistently affected by speed and therefore not related to distance traveled when presentation duration exceeds 60 msec. At short presentation durations (660 msec), all type II patterns have a large bias. To show that with presentation durations exceeding 60msec, perceived direction bias for type II pattern is not due to the limited distance traveled, the pattern was presented at different durations while keeping the distances traveled by the components constant. If direction bias was due to distance, then it would appear to move in the same direction for any presentation duration. In Fig. 8, we show that perceived directions of the 5 conditions (refer to Fig. 3) for two subjects with type II patterns which had a component angular difference of 22.3 and 51.6” [case l(d), 3(a) and (b)]. The component spatial frequencies under cases l(d), 3(a) and (b) were 4.5, 1.Oand 3.0 c/deg respectively (Table 1). Most importantly, notice the perceived directions of the type II patterns indicated by open symbols that are connected by heavy black lines. The presentations at longer durations utilized the same phase shifts in creating the motion perception at 90 msec [case l(d)] and 60 msec [cases 3(a) and (b)], but each frame has been presented multiple times (double, triple and quadruple times). These results show that the critical variable in altering perceived direction is duration rather than distance traveled. With long enough presentation duration, even though the speed is slower, the perceived direction of type II patterns will approximate IOC rule predictions. Taken together, all the above results indicate that the perceived direction bias for type II patterns is not due to distance traveled. It depends on presentation duration and therefore is consistent with the notion that additional slower neural processes are required for accurate type II motion processing. On the other hand, type I motion processing is almost instantaneous as its perceived direction is accurate with short presentation durations (d 90 msec).
and HUGH
R. WILSON
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FIGURE 8. Perceived directions at different durations with constant distance traveled. Symbol designations are the same as those in Fig. 6. CY was tested with patterns in cases l(d) (22.3”, 4.5 c/deg) and 3(b) (51.6”, 3 c/deg), HJ was tested with patterns in case 3(a) (51.6-. 1 c/deg). With multiple presentations of the same four (60 msec) or six (90 msec) initial phase shifts, perceived directions for type II patterns changed by more than 30” to approximate IOC predicted direction for both subjects. If perceived direction change was due to distance traveled, it would not have occurred. Therefore, perceived direction change for type II patterns is due to duration and not due to distance traveled.
Spatial frequency
variations
Spatial frequency was tripled by increasing the monitor viewing distance 3-fold. By this maneuver, the window size was reduced by 3 times but a constant number of nodes and antinodes for the two-dimensional patterns was displayed. The effect on perceived direction was performed on four subjects. In some cases, the effect of spatial frequency differences was examined with temIDora1 freauencv I , being constant while in others. the
MOVING TWO-DIMENSIONAL
pattern resultant speed was held constant. A 3-fold differences in spatial frequency (1 vs 3 c/deg 51.6” patterns; 1.5 vs 4.5 c/deg 22.3” patterns) did not produce any conspicuous difference in the overall time course for type II patterns to approach IOC predicted direction. Mean direction biases between patterns having a 3-fold difference in spatial frequency measured at different time intervals did not show significant differences by the post hoc Tukey HSD test at the 0.05 level (Wirier, 1971). For all subjects under all spatial frequency conditions, type I pattern direction perception was accurate and duration independent. Further details are available elsewhere (Yo, 1990). Contrast
143
PATTERNS 60
CY: 22.3”; case Ic
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YJZ
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; case Ic
variations
If one temporally modulates the type II pattern contrast using a Gaussian envelope, the perceptual direction change near the beginning and end of the presentation is apparent. When the contrast gradually increased at the beginning of the presentation, the perceived direction changed from the component vector sum direction to the predicted IOC resultant direction. When the contrast decreased after the peak of the Gaussian, the perceived direction deflected back to the component vector sum direction. To quantify this observation, we measured the perceived direction of two-dimensional patterns as a function of contrast. As contrast variations of 5-100% had no effect on type I pattern direction perception, their perceived directions will not be shown in the following figure. Figure 9 contains semilog plots of direction bias vs duration at different contrasts for three subjects. Type II pattern bias represented averaged magnitudes obtained under conditions 2 and 4 (refer to Fig. 3). All subjects under all conditions showed a marked lengthening of the time course with decreasing contrast; and at 5-10% contrast, a substantial bias was observed even after 1 set of presentation. The direction matches at 5 and 100% contrasts for subject YJZ were only performed once. Experienced subject CY noticed that 47.4” [case 2(b)] type II patterns cohered at 50 and 100% contrast, but were incoherent when contrast was reduced to 5%. For experienced subject HRW, the average bias for 51.6” [case 3(a)] type II patterns with 1 set of presentations at 5% contrast was 15”; and he noticed the patterns being incoherent during some of the trials. Judging from HJ’s large perceived directional bias (about 36”) after 1 set of presentation in case 3(a) at 5 and 10% contrast, the type II motions could have been incoherent, as his direction match was close to the direction of the faster component (33.6” from the vertical). Thus, it is apparent that the neural units processing type II motion have higher thresholds than those mediating type I motion.
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(msec)
FIGURE 9. Contrast dependence of type II motion perception in the fovea. Direction bias on the y-axis represents the average magnitude of bias found in conditions 2 and 4. The vector sum directions of case l(c) and 3(a) type II motions are 55.5 and 37.7” from the vertical respectively whereas the directions of the faster component are 48.2 and 33.6” from the vertical. Data points for JH when tested with 5 and 10% contrast case 3(a) patterns were close to the direction of the faster component indicating that the type II pattern might have been incoherent at these contrasts.
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Contrast
Peripheral
2-D Motion
Perception
Scaling
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FIGURE 10. Contrast dependence of type II motion perception in the periphery. Direction bias on the y-axis represents the average magnitude of bias obtained in conditions 2 and 4. Triangular and circular symbols indicate measurements made on subjects PJ and CY respectively. Solid and open symbols indicate measurements made in the lower oblique and upper visual sectors respectively.
144
CHRISTOPHER Combined
across
subjects
YO and HUGH R. WILSON
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FIGURE 11. Average peripheral direction error for type I and II patterns. Top panel compares average magnitude of perceived direction error for type I and II patterns with component vector angular diierence of 22.3”. Lower panel compares average magnitude of perceived direction error for type I and II patterns with component vector angular difference of 51.6”. L-dn refers to downward moving patterns presented in the lower visual field. L-up refers to upward moving patterns in the lower visual field. LO refers to foveofugally moving patterns in the lower oblique quadrant. LO-dn refers to vertically downward moving patterns presented in the LO quadrant. Temp, UO and U refer to the temporal visual field, the upper oblique sector and the upper visual field respectively. Perceived direction error ascertained with type II patterns showed a directional anisotropy in both L and LO visual fields in that perceived direction error was lower in the foveofugal directions. Also shown are the predicted errors if type II direction was judged according to the vector sum addition rule and according to the faster moving component vector indicated by the dashed and dashed-dotted lines respectively.
visual fields. It was not performed in the temporal visual field along the horizontal meridian due to the interference of the blind spot. Data for four subjects did not show significant difference (P > 0.15) in visual acuity ascertained in the four peripheral locations. Grating acuity averaged 7 times lower than fovea1 acuity. Peripheral direction matching experiments were performed at a distance 6 times closer than those in cases l(d) and 3(b). As we were concerned about maintaining a large enough display size and yet not placing the monitor too close to the subject’s eye, a scaling of 6 times the fovea1 distance provided a satisfactory compromise.
L-dn
L-up
LO
LO-dn
Temp
UO
U
FIGURE 12. Combined standard deviation of peripheral direction match across subjects. x-axis notation is explained in the legend of the previous figure. In both cases, type I pattern direction standard deviation was greatest in the LO and UO visual field loci. Standard deviation of perceived directions for type II patterns were greater than type I patterns in all the visual field locations.
Contrast
variations
Fovea1 data indicated that type II motion perception was contrast dependent. Pilot experiments in the periphery were performed in the upper and lower oblique visual field loci at three different contrasts with patterns drifting away from the fovea. Direction bias (y-axis) is defined as the difference (in deg) between the pattern direction calculated by the IOC rule and the subject’s orientation match using a rotating pointer displayed on the computer monitor after 1 see of pattern presentation (see Methods). Results from two subjects tested with 51.6” type II patterns are shown in Fig. IO. Direction bias was larger in the upper visual sector compared to the lower oblique visual sector at all three contrasts. The bias was smaller for higher contrast but tended to level off beyond 20% contrast. In subsequent direction matching experiments performed in the other visual field locations, a 20% pattern contrast was therefore used. Peripheral
type I motion perception
The top panels in Figs 11 and 12 compare type I and II motion data collected using patterns with 22.3”
MOVING TWO-DIMENSIONAL TABLE 2. Student’s t-test for data measured with 22.3” type II patterns Error LO < L-dn
CY
HJ
IW
PJ
JC
RB
yes
yes
no
no
no
no
yes
yes
yes
no
P < 0.05P < 0.01 L-dn < U
yes
yes
P < 0.01 P
