The temporal integration and resolution of velocity signals

00424989 91 33.00 + 0.00 Copyright\Q 1991 PergamonReu pk

Vi.wm Res. Vol. 31. No. 5. pp. 907-914. 1991 F’rinwd m Great Bntain. All ri&hu rc.scmcd

THE TEMPORAL

INTEGRATION AND RESOLUTION VELOCITY SIGNALS

OF

ROBERTJ. SNOWDEN* and OLIVERJ. BRADDICK Kenneth Craik Laboratory. Department of Experimental Psychology, University of Cambridge. Cambridge CB2 3EG. U.K. (Recciced 9 Februury 1990) Abstract-The temporal properties of human visual motion detection were explored. Experiment I measured thresholds for speed discrimination as a function of stimulus duration. Thresholds fell asymptotically lo a Weber fraction around 0.06 over a period of approx. IOOmsec, with faster speeds asymptoting a( slighrly shorter stimulus durations. A second experiment required subjects lo discriminate a pattern that was modulated between two speeds from one which remained at a constant speed. The minimum depth of the modulation required lo make this judgement was found lo be equivalent to a Weber fraction of 0.3 at low modulation rates. around five times greater than when the velocities were presented in isolation (cxpl I). At some higher modulation rate performance dramatically declined. The modulation rate at which this occurred decreased with stimulus speed, and increased with stimulus size. The results of cxpt I seemconsistent with the known properties of primary motion sensors, while the results of the latter expcrimcnts may arise from a later stage integrating the output of these primary motion sensors. Motion pcrccplion

Velocity discrimination

Temporal integration

INTRODUCl’ION Current

thcorics

of visual motion

processing generally suppose that perceived velocity dcpends on some form of spatial integration of local signals. which serves both to resolve intrinsic ambiguities (Hildreth, 1984; Movshon, Adelson, Gizzi & Newsome, 1985; Yuille & Grzywacz, 1988) and to ease signal/noise problems (Change & Julesz. 1983; Van Doorn & Koenderink, 1983; Williams & Sekuler, 1984). Such integration is helpful because the velocity field is mostly locally uniform or smoothly varying in space. Variations of velocity with time are also quite constrained in natural images, suggesting that we may expect to find also some integration of velocity signals over time. Recent evidence for temporal integration in the detection of motion comes from experiments with random-dot kinematograms. The combination of information from several successive displacements in a kinematogram, compared to a single displacement, could enhance the upper limit for directional discrimination and improve signal/noise performance at a range of displace-

*Present address. to which correspondence should be sent: School of Psychology, University of Wales, Cardifi’ CFI 3YG, U.K. 907

Random dot patterns

ments (Nakayama & Silverman, 1984; Snowden & Braddick 1989a. b). The experiments reported here were intended to study more quantitatively the extent of temporal integration in visual motion processing. Temporal integration in domains such as luminance has classically been investigated by two approaches. First, the threshold for detecting a stimulus varies as a function of duration (Bloch’s law) up to some time at which an asymptotic performance is attained; this limiting duration indicates the extent of any significant temporal integration. Secondly, the stimulus can be modulated repetitively in time, and the threshold modulation depth measured as a function of frequency (e.g. De Lange, 1954). As a variant, the frequency can be varied at constant modulation depth to find a critical flicker frequency above which the modulation is not detectable. The fall-off of performance at high temporal frequencies is taken to reflect temporal integration, which smooths out the effects of high-frequency modulation and so makes the stimulus appear uniform in time. Thus the two approaches test the ability of the systems for temporal integration and temporal resolution respectively. In a simple system, these two types of performance will reflect, in inverse ways, the same underlying temporal properties;

ROBERTJ. SNOWDEN

908

if the system shows linear summation they may be expressed in terms of the system’s impulse response function. A form of motion modulation was used in the experiments of Nakayama and Tyler (198 I), in which velocity in a dot pattern varied sinusoidally in both space and time. They found that the threshold amplitude for detecting the motion fell off at temporal frequencies above 2 Hz. However, the use of an oscillating motion whose amplitude provides the “modulation depth” means that speed cannot be varied independently. We wished to examine the temporal properties of the system at different speeds. We therefore used a display in which the motion does not reverse direction, but its speed is repetitively modulated. The measure of performance is then the threshold modulation for detecting the speed variation. For comparison with these temporal resolution data, we tested temporal integration in an analogous task of speed discrimination; that is, we examined how the threshold for distinguishing the speed of motion in two distinct intervals varied with the duration of the intervals. ME-II IODS

SIitnuli

Random-dot patterns were produced by software run on a PDP 1l/IO minicomputer. The dots were plotted on a HP 1319 CRT display (P31 phosphor) controlled by a Sigma QVEC display processor. All element positions on the x-axis were plotted relative to the same starting point using an increment procedure, the increment value being chosen randomly from point to point. The increment function automatically “wraps” around form one side of the display to the other, hence all x-coordinates were constrained to fall within the display window. The y-coordinate for each element was chosen randomly. 400 dots (dia. 0.5 mm) were displayed in an area which would normally be 19.5 cm square. However, for some experiments this was shrunk to a 5 cm square by means of a potentiometer applied to the x-axis and by redefining the possible coordinates for the y-axis. When viewed from 3 m this subtended a 3.7 (or 0.95) deg arc square. To produce kinematograms the x-coordinate of all dots was increased by simply repositioning the starting point. Thus all displacements were horizontal. The shifted pattern was then displayed. This process could be repeated for as many exposures as were required.

and OLIVER J. BRADDICK

The effect was of uniform displacement within a window. However. it became clear that this procedure had problems in that “alpha-stripes” (Koenderink & van Doom, 1980) became visible at some velocities. In order to eliminate these stripes, points which were to be wrapped around were given a new y-coordinate. This appeared to eliminate alpha-stripes. The screen was refreshed at a rate of 100 Hz-i.e. the pattern was displaced every 10 msec. Some of the major effects described in this paper were also repeated for a refresh rate of 200 Hz. No differences were found so detailed results at the higher frame rate are not reported. Procedure

Experiment 1 measured Weber fractions for velocity discrimination using random dot patterns. A two-alternative forced-choice (2-AFC) procedure was employed. Patterns were presented in two equal intervals (ranging from 30 to 200 msec). separated by 500 msec. In one interval the pattern moved at a standard velocity, and in the other at a “test” velocity (the test velocity was always greater than the standard). The test could be either in the first or second interval and the subject pressed one of two buttons to indicate in which interval hc perceived the pattern to be moving fastest. No feedback was provided. Stimuli levels were governed by APE (adaptive probability estimation; Watt & Andrews, 1981) an adaptive version of the Method of Constant Stimuli. 120 trials were performed for each datum point (the first 20 being discarded) to determine the 8 I % correct level (see Watt & Andrews, 1981). During expt 2, two procedures were used to obtain thresholds. The results for field size of 0.95 deg arc used a two-alternative forcedchoice procedure. Two 1000 msec intervals occurred separated by 500 msec. In one interval the pattern oscillated (in squarewave form) between two velocities Vi and V2, and in the other moved steadily at V3 (where V3 = [VI + V2]/2). Direction of movement (left or right) was not only randomized from trial to trial but also within trials so as to avoid both adaptation effects (e.g. Thompson, I98 I) and any anticipatory eye movements. A small fixation point was displayed at the centre of the patterns commencing 500 msec prior to the first interval and was extinguished 500 msec after the end of the second interval. Subjects were given instructions to maintain strict fixation. Such strict fixation was vital as any tracking eye movements easily

Temporal

integration

revealed which pattern was changing in velocity. Subjects were told to press one of two buttons to indicate in which interval they thought the velocity modulation had occurred. No feedback was provided. To obtain thresholds the difference between the velocities VI and V2 was changed according to a staircase procedure. Three consecutive correct judgements decreased the value of V2 by 5% or by the smallest step possible (i.e. I pixel [3.33 set arc] per IO msec if this was greater than 5%). and a single incorrect response increased V2 in a similar way. Such a procedure tracks the 79% correct level (Cornsweet. 1971). Three or more correct responses followed by an incorrect response was termed a reversal. Each staircase (corresponding to a single rate of oscillation) commenced with VI = V2 and continued for eight such reversals. The first two were ignored and all trials after this were recorded and their mean and standard deviation calculated. If V2 became lower than VI the staircase was terminated. This method had several disadvantages. First, increases in V2 necessarily lead to increases in the mean velocity. When results are reported for a velocity of X deg/scc this will actually refer to VI. and not V3. Though this complicates the quantitative interpretation of high Weber fractions. we believe the overall trend in the data still remains valid. Our second method, described below, dots not have this disadvantage and where thresholds were calculated for both methods for the same nominal velocity they were found to correspond well. Secondly, the task was extremely laborious and time consuming. In one sesssion lasting up to I hr thresholds could only be gathered for four rates of oscillation at a single velocity. Thirdly, as each interval was only I set this corresponded to a different number of cycles at each temporal frequency. As this is a somewhat novel stimulus, the confounding effects of such variables are not known. Finally subjects could not help occasionally making eye movements, which made the task quite trivial. As this was a 2-AFC procedure the subjects could not “ignore” this information and so some results could be contaminated by the effects of such eye movements. Our second method (used primarily for the larger field size) was to present a single pattern whose velocity was modulated between two values which were in the ratio [v2 - Vl]/Vl = 0.6. Subjects were then asked to adjust the temporal frequency of the oscillation until the “‘jitter” of the changing velocities could not be

of velocity

909

seen. A single value of mean velocity was tested in each experimental block and four such settings were made at each temporal frquency. with the order of presentation randomized. All patterns started at a “low” temporal frequency (randomized to some value between 1 and 3 Hz). The main advantages of this method are that they bypassed the problems outlined above i.e. (I) the mean velocity was always constant, (2) many more thresholds could be gathered in a given time, (3) as the viewing time was unlimited the number of modulation cycles is no longer a problem, (4) subjects could ignore any conscious eye movement and adjust threshold until they were happy that this was the threshold in the absence of any eye movement. To aid fixation a fixation point was continuously present. The main drawback was the subjective nature of the threshold. However, as both methods yielded similar thresholds we are happy that the results are robust. Subjects were seated without any restraints in a dimly lit room so that the edge of the display and surrounding laboratory equipment were visible. All viewing was binocular. Subjects

Both subjects reported here had normal or corrected to normal vision. They were highly experienced observers with many hours experience in motion related psychophysical tasks. R.C. was naive to the exact aims of the experiment. Other casual observers have been shown the main effects and all agreed on pattern of results. RESULTS

E.rperimenr

I

The aim of this experiment was to verify that the results of McKee and Welch (1985) were also applicable to the simuli employed in this study. McKee and Welch measured Weber fractions for velocity discrimination as a function of the duration of the movement of single lines. The present study uses complex random dot patterns which have two major advantages. (I) Changes in duration in McKee and Welch’s study were accompanied by changes in path length, and therefore changes in the relative amount of peripheral and fovea1 stimulation. Whilst changes in path length have been shown to have little effect (McKee, 1981) it has been shown that velocity discrimination performance is poorer in the peripheral retina, at

ROBERT J. SNOWDEN and OLMR J. BRADDICK

910

least for slow movements (Orban, van Calenberg, De Bruyn & Maes, 1985; McKee & Nakayama, 1984). The random dot patterns used here are confined to the same region of the field no matter what their duration. (2) Single line stimuli may activate both the long- and short-range motion systems (Braddick, 1980). By employing random dot patterns we hope to isolate only the short-range process. Since these experiments were performed a similar and more complete set of experiments have been published by De Bruyn and Orban (1988). We therefore present only the briefest report of our findings. Our results are in complete accord with those of De Bruyn and Orban’s study and interested readers are referred to their study for a more complete picture of these results. The results of greatest importance are outlined in Fig. 1. Weber fractions (VI - VZ]/Vl) of discrimination fall as a function of the duration of the stimulus. Asymptotic performance is around 0.06 (i.e. a velocity of I7 deg/sec may be discriminated from I8 deg/sec), and this was true for most velocities tested (though very slow velocities showed a small decrease). Weber fractions of velocity discrimination as a function of velocity have been previously reported (Orban, De Wolf & Maes, 1984) and generally show a U-shaped function. with fractions as low as 0.05 for intermediate velocities. A second point is that Weber fractions fall more quickly with duration (and asymptote sooner) at faster velocities, though this effect is not very marked. This was also found by De Bruyn and Orban (1988) and

0.5‘ 0.5

0,

Fig. I. The Wckr fraction of discrimination ([VZ - V I]/Vt) is plotted as a function of the duration of the stimulus. Data at three ditfercnt velocities are presented. The field size was 3.6deg and the subject is R.S. Note that all velocities asymptote with Weber fractions of around 0.06. but that this asymptote is reached in a shorter time for faster velocities.

0.04 0

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4

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10

Ttmponl 4qwncy

. 12

. 14

. 16

. 18

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of adultion (Xtt

Fig. 2. Wcbcr fractions of discrimination are plotted as a function of the rate of oscillation between the two velocities. Data arc prcscntcd for six velocities (see inset for symbols and velocities). The field size was 0.95 deg and the subject is R.S. The function at each velocity has an asymptotic ngion (typically Weber fraction = 0.3) for a range of temporal frequencies. At some higher temporal frquency performance deteriorates. Note that the temporal frequency at which this deterioration occurs is lower for faster velocities.

by McKee and Welch (1985) and thus seems a small but robust effect. Experiment 2

The second experiment sought to examine how two velocities closely spaced in time interact with one another. Figure 2 shows the Weber fractions (Iv2 - Vl]/Vl) for velocity discrimination as a function of the temporal frequency of oscillation of the pattern. At all velocities the results are qualitatively similar, thresholds for low rates of oscillation are around 0.25-0.40 (2540% difference in velocities). At some higher temporal frequency, however, thresholds rise quite sharply. Measurements at even higher temporal frequencies (not displayed) often gave the sensation of two patterns moving through one another. Such phenomena have been reported previously when two different patterns are presented in alternation and are moving at quite different velocities (Van Doorn & Koenderink, 1982), but not when a single pattern is alternated between two velocities. The major two points to note for this plot (and from Fig. 3 which plots results for the same experiment but for a different observer R.C.) are that even at very low rates of oscillation Weber fractions are still high compared to when the patterns move in temporal isolation (around 0.06). Secondly that the temporal frequency at which performance breaks down changes systematically with velocity. This break-down point was set, arbitrarily, to a Weber fraction of 0.6 and the temporal frequency at which each curve passes this point is plotted in Fig. 4.

911

Temporal integration of velocity

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Fig. 3. As Fig. 2. only for a different subject R.C. The standard deviation on each point is also presented. This was omitted in Fig. 2 to avoid cluttering. though similar standard deviations were also present in that data.

Thresholds were also gathered for another field size (3.6deg3. The results are plotted in Fig. 5. As with the smaller field size, there is a systematic decline in the temporal frequency at which the pattern appears to have a uniform velocity, as mean velocity is increased. It is also clear that this decline occurs far more slowly at this larger field size. If a simple regression line is plotted through the data points of Figs 4 and 5 we get the equations: TF,,, = l5.3-2.64v

. . . . . . . . . . for Fig. 4;

TF,,, = 13.8 - 0.77 V . . . . . . . . . . for Fig. 5. Hence these lines cut the abscissa (i.e. TF,,, = 0) at 5.8 and 18.0deg/sec respectively.

DlSCU!SSION

Both experiments show that performance in velocity discrimination can be improved, up to a point, by an increase in the time for which the velocity is maintained. The interpretation of these findings is complicated by the fact that

Fig. 4. The temporal frequencies at which the functions of Figs 2 and 3 rose sharply (this was arbitrarily set to when the function passed the Wcber fraction =0.6 point) arc plotted as a function of the velocity in the pattern. This point shows a monotonic decrease with increasing velocity.

00s

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Fig. 5. Temporal frequency thresholds for detecting the temporal variation in velocity between a pattern oscillating between two velocities (V and 1.6V) are plotted as a function of velocity. The field size used was 3.6deg. Once again temporal frequency thresholds fall as the velocity of the pattern increases. Note there is a systematic difference between R.S. and R.C. This is probably due to the subjective nature of the threshold measure, when a two-alternative forced-choice procedure was used (as in Fig. 4) this difference disappeared.

motion processing is intrinsically temporal; any practical system for measuring velocity cannot act instantaneously but requires a finite time to gather information about spatial changes. Thus an improvement in performance with time could have two possible bases: (i) the primary process of acquiring velocity information operates better if a longer time is allowed; (ii) the results of this primary process, operating continuously, can be integrated over time to improve performance. On the first proposal, the limiting duration would be expected to be reduce with increasing velocity, since a given spatial change takes a shorter time at higher velocities. On the second alternative, there is not strong a priori reason to predict that integration time should increase or decrease with velocity. In the first experiment we found that the limiting duration, for which the Weber fraction reaches its asymptotic value, was reached more rapidly for faster motions. This pattern of results agrees with studies of velocity discrimination by McKee and Welch (1985) and De Bruyn and Orban (1988). Shorter times at higher velocities would be expected if the discrimination was based on path length during the interval, rather than on a true velocity judgement. However, this suggestion is implausible for random-dot displays and is not quantitatively consistent with our data; the limiting duration for the different velocities does not yield a constant path length (or a constant differential in path length), and this is even more apparent over the wider range of velocities covered in De Bruyn and Orban’s data.

9iz

Ro&nr

J. SNOWDEN and OUVER J. BRADDKK

We have suggested elsewhere (Snowden & Braddick, 1989a) that the limiting time for “recruitment” reported by McKee and Welch can be understood in terms of the temporal parameters of the primary (“short-range”) process of motion detection. The 80-100 msec limit they found is similar to the 90-120 msec limiting duration in the data of Fig. 1. These times are close to the maximum deiay between frames that yields motion perception in a random-dot kinematogram (Morgan & Ward, 1980; Baker & Braddick, 1985), a limit which can be interpreted in terms of the maximum temporal “span” of the motion detectors involved. Van Doom and Koende~nk (1983) propose that any one velocity may be signaIled by detectors with a range of temporal and spatial “spans”, a notion with physiological support (Baker, 1988). As the duration of a motion stimulus is increased, detectors with longer temporal spans can contribute up to the maximum of this range, leading to an improvement of performance we have termed “hetero recruitment” (Snowden & Braddick. 1989a). The decrease in “integration time” with increasing velocity would be expbztcd if the dettxtors for faster velocities have a lower range of temporal spans. Van Doorn and Koendcrink (1982) provide psychophysical evidence that detectors tuned to higher velocities have shorter temporal spans, and this is also consistent with studies of the det~tabiIity of moving gratings (Kelly, 1979; Burr & Ross, 1982) if some plausible simple assumptions are made. Newsome, Mikami and Wurtz (1986) find a corresponding variation in the maximum temporal interval for directional selectivity in cells tuned to different velocities in macaque cortical areas VI and MT. Cells in cat striate cortex show a similar variation in the temporal integration properties with respect to velocity (Baker, 1988). It should be noted, however, that none of these data imply variations in temporal properties to be the predominant source of differences in velocity tuning. We suggest then, that the way performance improves with duration in our first experiment can be understood in terms of the temporal parameters of the short-range process, with the limiting duration being reached at the maximum time-span of detectors tuned to the particular velocity. This implies that the results do not necessarily reflect any integrative process which combines over time the information from motion detectors. In our work on the improvement of directional ~rforman~e with multiple

displacements of an random-dot kinematogram, we found evidence for such an integrative process (which we termed “homo recruitment*‘) over the range of velocities used here (Snowden & Braddick, 1990). However, if such a process is acting in the present experiment, it does not appear to be determining any variation in performance in the range of durations tested beyond 100 msec. The second experiment gives a quite different pattern of results (Figs 4 and 5). The critical temporal frequency declines steadily with velocity, implying that higher velocities lead to longer duration of processing. This would be difficult to explain if the processing duration simply reflected the time-spans of motion detectors; it suggests a further process of temporal integration which is longer lasting for high velocities. Comparison of Figs 4 and 5 shows a marked effect of field size on the range of velocities over which this relation, between velocity and temporal integration, can be demonstrated. The intercepts of the regression lines on the abscissa represent a velocity whose modulation cannot be detected even at the lowest frequencies. This velocity increases by a factor of about three when the field dimensions are increased by a similar factor (3.8: 1). An approximately proportional relationship has previously been found between field size and upper velocity limits (Van de Grind, Van Doorn & Koenderink, 1983) or upper displacement limits (Baker & Braddick, 1982). Thus, it is possible to regard the progressive decline with velocity in performance for high modulation frequencies as an approach to the upper velocity limit for any particular field size (though the upper velocity limit produced by the present method is around half that produced by Van de Grind et al., 1983 see their Fig. 4). On this view, increasing velocity progressively degrades the precision of motion info~ation, in a way similar to the introduction of noise. This degraded precision combines with the reduction in the effective modulation due to temporal intergration, to make the resulting decline of performance apparent at lower modulation frequencies for higher velocities, until a velocity is reached at which useful discrimination performance is no longer possible whatever the contribution of temporal integration. Spatial integration may well interact with the effects of velocity in an analogous way. Performance in random-dot kinematograms can be

Temporal

integration

tested by the ability to discriminate a shape segmented from its surround by differential coherent motion. In some displays, this shape discrimination collapses at displacements (or velocities) for which direction discrimination is still good (Chang & Julesz, 1983; Sato, 1989). This can be described as a progressive loss of spatial resolution with velocity, although it would be of interest to confirm this with more formal quantitative testing of resolution. We have suggested that the temporal integration determining performance in the second experiment may be of the “home” type. i.e. a combination of information from elementary motion detectors with similar properties, and we have proposed elsewhere (Snowden & Braddick, 1989b; Snowden, 1989) that the mechanisms of this combination is mutual facilitation of the detectors in a co-operative network. A characteristic of this interaction is an asymmetry in time (it can be initiated rapidly. but at stimulus offset shows a hysteresis effect and dissipates slowly; Snowdcn, 1989). It would be of interest to test whether any asymmetries can be dcmonstrated in the discrimination of temporally adjacent velocities. A striking feature of our results is the differencc bctwccn the optimal discrimination pcrformance achicvcd in the two experimental proccdurcs. When subjects had to discriminate two temporally separated velocities, Weber fractions were around 6%. This is of the same order as the performance found by McKee (1981) and Dc Bruyn and Orban (1988). However, when the velocity alternated between two values without an intervening interval, the asymptotic performance for low modulation rates was about 30%. This agrees with other reports of the discrimination of velocities closely spaced in time (Hick, 1950; Notterman & Page, 1957; McKee, 1981; McKee & Nakayama, 1988), but is in contrast to the general finding that most sensory discriminations are improved if they involve the detection of a transient between temporally or spatially adjacent stimuli, rather than the comparison of separated presentations (Laming, 1986). It suggests that temporal diffcrential mechanisms do not play an important role in the discrimination. i.e. we are not well adapted to the detection of acceleration (Gottsdanker, 1956). It should be noted that, in our experiment, the modulation of velocity was abrupt, not gradual. Thus at 2 Hz the subject had the opportunity to integrate information from a constant velocity

of velocity

913

for 250msec, longer than the duration for asymptotic performance in the first experiment, and yet discrimination is worse by a factor of about five. This comparison suggests the possibility that integration of velocity information may be a controllable process. In the first experiment, the period over which the velocity information has to be gathered is demarcated by temporal events (the onset and offset of the display) which do not themselves depend on motion processing. In the second case, the integration occurs in a continuous stream of velocity signals, with no temporal markers available (at least at threshold) to define the intervals to be compared. The difference between the ways in which information collection over time can be controlled in the two cases may help to explain effects of velocity on temporal measures of performance. The idea that the extent of integration may be flexible, to optimize performance in different configurations, may be applicable to integration of motion information over space as well i1S over time. Such controllable flexibility could help to resolve the tension between the requirement for spatial integration (to resolve ambiguities by achieving a smooth velocity field) and local diffcrcntial operations rcquircd to locate motion boundaries and provide information required to compute a three-dimensional structure from motion (Hutchinson. Koch, Luo & Mead, 1988). Acknowlrdgcmmrs-I

thank

Robert Clcary

for acting as a

subject. This work was supported by a S.E.R.C. to

R.

Snowdcn

and

an M.

R. C.

project

studentship grant

to 0.

Braddick.

REFERENCES Baker, C. L. Jr (1988). of directionally

Spatial and temporal

sclcctive velocity prcfrrcncc

neurons. Journul of Neurophysiology. Baker. C. L. Jr % Braddick.

determinants in cat striate

59. 1557-1514.

0. J. (1982). The basis of area

and dot number effects in random dot motion perception. Vision Reseurch, 22, 85 I-856. Baker, C. L. Jr & Braddick. ties of

the

Perception.

short

range

14. I8

I - 192.

Braddick, 0. J. (1980). apparent Socirry.

motion.

0. J. (1985). Temporal

proper-

process

motion.

Low-level and high-level processes in

Philosophical

velocities.

Julcsz,

anisotropy

in random

23. 639-646.

Contrast

sensitivity at high

Vision Research, 22, 479484.

J. J. &

directional nation

Transuctions of the Royal

London E, 290, 137-151.

Burr. D. C. & Ross. J. (1982). Chang.

in apparent

B. (1983).

Displacement

limits.

and direction versus form discrimi-

dot cinematograms.

Vision Research.

91-J

ROBERT J. SUDDEN

Comsweet.

T. N. (1971).

physics. American

The staircase method in psycho-

JOLUMI of Psychology.

De Bruyn. B. 8 Orban. direction

a.nd OLIVER J. BRADOICK

G. A. (1988).

discrimination

75, 485-491.

Human

velocity and

measured with random

dot pat-

terns. Vision Research, 28, 1323-1335. De Lange.

H. (1954).

frquency eye.

Relationship

of

the Optical

characteristics

Society

of

of the

America,

44,

380-389. R. M. (1956). The ability of human operators

to detect Bulletin.

acceleration

of target

motion.

Psychological

53, 477-487.

velocity of a seen object. Quarterly tal Psychology. Hildreth.

37. 63-I

E. (1984).

Cambridge.

networks. D.

H.

Koenderink.

Motion

threshold

and

and

C. (1988).

binary

resistive

vision-II.

Stabilized

1349. A. J. (1980).

and spatial periodicity

(1986).

Dual percept

in stroboscopically

Juurnul 01 the

Optical

Suciery of

S. P. (19X1).

McKee.

London:

Academic

A local mechanism

for dilTerential

Vision Reseurch. 21, 491-500.

S. P. & Nakayama.

motion in the peripheral

K. (1984).

The detection

of

visual held. Vi.don Rrsearch. 24.

along

the trajectory.

K. (1988).

Orban,

motion.

for the velocity

H.

(1986). Psycho-

Journal

of

of a seen object.

De Wolf.

J. &

Maes,

H. (1984).

Factor

velocity coding in the human visual system.

G. A.. Van Calenberg, Velocity

F.. De Bruyn, B. & Maes. H.

discrimination

in central and peripheral A,

2. 1836-1847. patterns. Snowden.

Reversed apparent motion with random dot

Vision Research, 29. 1749-1758. R. J. (1989). Motions in orthogonal suppressive. Journal

America Snowden,

directions are

of the Optical

Society

of

A. 6. 1096-1101. R. J. & Braddick. 0. J. (1989a).

motion

signals

over

time.

The combination

Vision

Research,

29,

1621-1630. Snowdcn.

R. J. & Braddick.

displacement Snowdcn.

limits

motion.

Extension

of

sequences of

0. J. (1990). apparent

DiITerences in the

motion at small and

Visiun Research, 30. I21 I-1222.

P. G. (1981).

subsequently

J. (l989b).

Vision Research. 29, 1777-1789.

large displacements. or adaptation

0.

in multiple-exposure

R. J. & Braddick.

Velocity

to moving

after-ctTects: The effects

stimuli

on the perception

seen moving stimuli.

of velocity.

A. 2, 243-25 I .

dynamic

Journul

R. (1980).

visual

of rhe Oprical

Virion

for motion

Rrsearch,

20,

J. A., Ad&on.

W. T. (1985).

E. H.. Giui,

M. S. & Newsome,

The analysis of moving visual patterns. R. & Gross, C. (Eds.).

In

Srudr wek

on: Parrrrn recognition mechanisms (Vol. 54, pp. I I7- I5 I ). Pontiliciar spatial

Academiae

Scientiarum

K. & Silverman, characteristics

motion

in

of the upper

random

dots.

Temporal

displacement

Visiun

Rrsearch.

and limit 24,

293-299. Nakayama,

K.

&

Tyler,

C.

W.

(1981).

Psychophysical

of coherent

random-dot

Van Doorn.

Viriun

Research,

of 21,

patterns.

A. J. & Koenderink. movcmcnt Journal

A. J. & Kocndrrink.

the

Opricul

of moving

spatial

Bruin Research, 45. 179-188.

A. J. & Kocnderink.

integration

of

J. J. (1982). The temporal

of the visual detectability

Van Doorn.

J. J.

in peripherally

7-J. I674 - 1683.

white noise. Experimmral

J. J. (1983).

in the detectability

Spatiotem-

of motion.

Vision

Reseurch. 23. 47-56. Watt.

R. J. & Andrews,

probit

estimation

Psychologicul Williams,

Scripta Varia.

G. H. (1984).

W. A., Van Doorn.

Detection

Sucivry of Americu.

poral

Chagas. C.. Gattass,

Nakayama.

(1983).

prop&es

Conditions

noise.

in

431-435. Movshon.

Van dc Grind, viewed

the discrimination

in

and

Sequcntinl rccruitmcnt

Sbciery oJ’ America

M. J. & Ward,

Ophrhalmolugy

29. 266.

S. P. & Welch, L. (1985).

Morgan,

Velocity integration

lnvestigariae

Visuul Science (SuppI.).

for

R.

337-34s. S. P. & Nakayama.

flow

A..

Thompson.

2s 32.

McKee.

of apparent

processing of short-range

velocity detection.

Wurtz.

55. 1340-135 I.

threshold

G.

apparent

Sensory unalysis.

Press. McKee,

&

126. 652.

influencing

of

70. 456-458.

D.

Orban,

A.

J. M. & Page. D. E. (1957). Weber’s law and the

difference

mutually

surface. Journal of the Opricul

69. I340-

moving noise patterns. America.

Mead.

21, X-61.

J. J. & Van Doom

of movement

of visual motion.

J. &

using analog

Suciety of America.

McKee,

Nottetman.

Sato. T. (1989).

Luo.

Computer,

(1979).

spatiotemporal

Mikami,

Neurophysiology,

(1985).

Press.

C.,

motion IEEE

T..

selectivity in macaque visual cortex-III.

visual field. Journal of the Optical Society of America

The meusuremenl

J.. Koch,

Computing

Journal o/Experimen-

IS.

Mass.: MIT

Hutchinson.

Laming,

W.

Motion

Vision Research, 24, 33-39.

Hick, W. E. (1950). The threshold for sudden changes in the

Kelly,

Newsome,

Science,

Gottsdanker.

sensitivity by removal of familiar

physics and physiology

between critical Bicker

and a set of low I’rquency

Journal

isolation of movement

position cues. Vision Research, 21. 427-433.

motion

D.

Yuille,

Revirw.

W.

percepts

Research.

of

D. P. (1981).

An adaptive

functions.

Currenr

I. 20s -2 IS.

& Sekuler. from

A.P.E.:

psychometric R. (1984).

stochastic

Coherent

global

local motions.

Vision

21, 55-62.

A. L. & Grzywacz.

N. M. (1988).

theory

for

the perception

Nature.

Londun, 333. 71-74.

of coherent

A computational visual

motion.