12 12
Group Group
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8 8 8
8
a
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=
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g 8 8 LV ("/s)
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g 4 8 4
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ae ee tt or OS 0
<
2
3 4 4
“7
3
3
® 1s 8
0 200 400 600 800 0 200 400 600 800
Segment Duration (msec) Segment Duration (msec)

Figure 6
Group mean oculomotor responses to multisegment motion sequences characterized by a
temporally global velocity (GV) and a temporally local velocity (LV). Pursuit velocity (upper
panels) and cumulative saccadic amplitude (lower panels) are shown. as a function of segment
duration for each LV, for a GV of 0 deg/sec (left panels) and a GV of 4 deg/sec (right panels).
Each data point represents the average of the response measures for 4 successive 500-msec
periods, beginning 1.5 sec after onset of a motion sequence, for each of 3 trials for 3 observers.
The pursuit-velocity for a given 500-msec period was itself the average of up to 300 measures.

14


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31



The experimenter aligned the eye-position monitor between the second and third blocks
and then stayed in the subject booth until the end of the session. Each third-block trial was
preceded by the computer-controlled calibration sequence. If the calibration criteria were not
met, the calibration sequence was repeated. At the discretion of the experimenter, the position
sensors were realigned following several calibration failures. A small flashlight was used when
such an adjustment was required. Intertrial variation in the observer’s level of dark adaptation
was introduced by these adjustments as well as by the long durations (60-90 min) of a typical
experimental session.

After an acceptable calibration, a fixation cross was presented for 2 sec in the center of
the display. At the end of the following frame, a small rectangle presented at the bottom of the
display (and masked from view) caused the ADC to begin sampling. The motion sequence
began on the next frame. Eye position was sampled for 5 sec (3000 samples), regardless of the
length of the motion sequence.

Head position was stabilized by a chin rest throughout the session. In addition, a dental
biteboard and a forehead-restraining strap were used during the third block of trials. The
observation booth was dark except for light emitted by a small shrouded lamp on the floor and
stray light from the CRT and the eye-position monitor.

The observers viewed the stimuli binocularly. They were instructed to track the target
throughout the trial and then, at the end of the trial, to push one of three buttons to classify their
percept. (The perceptual data will be reported in a separate paper.) These instructions made it
explicit that the perceived form and motion of the target could vary from trial to trial. No
feedback was provided.

Data Reduction and Analysis

To ensure that the data were free of artifacts and blinks, a computer-generated display of each
eye-position record was examined visually before it was processed. For each acceptable record, a 10-
msec velocity estimate V was computed for each eye position sample, s, 3 <s <2,998, according to the
formula V,=(P, +3 -P; . 3) (6/sampling rate), where P is eye position. Saccades were detected by an
algorithm employing both a velocity criterion and a duration criterion. The accuracy of the algorithm
was checked by visual inspection of each eye-position record.

The time and amplitude of each saccade were stored for subsequent analyses. Velocity estimates
identified as part of a saccade were removed from the original set of 2,994. All remaining values were
considered to be measures of smooth pursuit.

Our goal was to characterize the oculomotor response after the visual system had fully processed
the composite waveform and before the onset of any anticipatory end-of-trial effects. Ideally, in
selecting the interval over which measures would be averaged, we would hold constant the main factors
likely to affect system response: the time from trial onset, the duration of the interval, and the number of
local segments preceding and included within the interval. Although the variation in segment duration


12 12
TB TMB LV (*/s)
~ GV=0%s 12
3 8 8
g
a 8
S
3B 4 4
2
8
s 0 0 0..
3 4
S
2 4 4
a 8
8 8
0 200 400 600 800 0 200 400 600 800
12 3 12
z Gv=0%s
2 8 LV (*is) 8
Hy 8
z
3 4 4 4
2
EO fmm cee ee eeeeeeseseeeeeneees 0
<
g
B44 4
°°
3
a
8 8
0 200 400 600 800 0) 200 400 600 800
Segment Duration (msec) Segment Duration (msec)

Figure 9
Mean oculomotor responses of observer TB to multisegment motion, sequences characterized by
a temporally global velocity (GV) and a temporally local velocity (LV). Pursuit velocity (upper
panels) and cumulative saccadic amplitude (lower panels) are shown as a function of segment
duration for each LV, for a GV of 0 deg/sec (left panels) and a GV of 4 deg/sec (right panels).
Each data point represents the average of the response measures for 4 successive 500-msec
periods, beginning 1.5 sec after onset of a motion sequence, for each of 3 trials. The pursuit
velocity for a given 500-msec period was itself the average of up to 300 measures.

18


Figure

12
13
14
15
16

17

List of Figures (concluded)

Spectrum of Motion Sequence with a Global Velocity of 4 deg/sec, a Local
Velocity of -4 deg/sec, and a Segment Duration Of 67 Mse€C.......v.esressesssesenessenes
Spectra of Motion Sequences with a Global Velocity of 4 deg/sec, a Segment
Duration of 67 msec, and Local Velocities of -8 deg/sec and 0 deg/Sec.........00++
Spectra of Motion Sequences with a Global Velocity of 4 deg/sec, a Segment
Duration of 67 msec, and Local Velocities of 8 deg/sec and 12 deg/sec..
Spectra of Motion Sequences with a Global Velocity of 4 deg/sec, a Local
Velocity of -4 deg/sec, and Segment Durations of 200 msec and 400 msec......
Spectra of Motion Sequences with a Global Velocity of 0 deg/sec, a Local
Velocity of -8 deg/sec, and Segment Durations of 67 msec and 200 msec.......
Spectra of Retinal Images Formed During Tracking in Accord with the
Global Velocity of Motion Sequences..........cssccsscsssseessenesssesseneenee sessesenessnecensesseeesees

25

26

27

28


consistently predominant, across LVs, only for the lowest spatial frequency sampled (i.e., 0.23
cycles/deg). The maximum spatial frequency at which the temporal-frequency spectrum was in
accord with the GV increased as the sawtooth speed decreased.

Human observers can track drifting gratings with fundamental spatial frequencies well in
excess of 0.23 cycles/deg. The data presented here do not indicate that sawtooth speed affected
the duration at which the LV began to have an effect on pursuit velocity. Perhaps the pursuit
system weights the velocity information provided by a given spatiotemporal-frequency
component according to how well it matches the velocity specified by the lowest spatial
frequencies: In the spectra of the multisegment motion sequences, the higher sawtooth speeds
were characterized by fewer very low spatial frequencies but a greater number of higher spatial
frequencies with a drift velocity equal to the GV (see Figs. 13 and 14).-In any case, these
multisegment motion sequences had very complex spectra, and the response of the pursuit
system (up to a segment duration of about 167 msec) was very consistent. If the motion sensors
for the pursuit system begin with a spatiotemporal filtering process, the velocity signal must be
heavily dependent upon the velocities of very low spatial frequency components.

As segment duration increased, the spectrum of a multisegment motion sequence was
decreasingly in accord with the GV and increasingly in accord with the LV (see Fig. 15). This
spectral difference could, of itself, account for the gradual shift from a pursuit velocity in accord
with the GV to a pursuit velocity in accord with the LV. However, without limiting the temporal
window over which velocity computations occur, the shift toward a spectrum dominated by the
LV is quite specific to our stimuli. It would not characterize composite waveforms formed by
adding a constant velocity ramp and a high frequency waveform with equal motion in both
directions--such as a sinusoid or a triangle. Nonetheless, Martins et al. (1985), who presented
sinusoidal target motion, found a similar shift from global (i.e., 0 deg/sec) to local tracking as the
period of the sinusoid increased. The size and shape of the temporal window for velocity
computations is likely to be an important component of any adequate model of the motion sensor
for the pursuit system.

Finally, there is the question of the stimulus for the maintenance of pursuit. During any
period of constant-velocity smooth pursuit, the spatiotemporal frequency spectrum of the retinal
image would be sheared with respect to the spectrum of the motion sequence: The temporal
frequency of every spatiotemporal frequency component would be increased by the product of its
spatial frequency and the velocity of the eye. If pursuit velocity were exactly matched to the GV
of a motion sequence, the GV of the retinal image would equal 0 deg/sec and the LV of the
retinal image would equal the STV. For example, during perfect tracking of the GV of a motion
sequence with a GV of 4 deg/sec, an LV of -4 deg/sec, and a segment duration of 67 msec (Fig.
12), the spectrum of the resulting space-time retinal image would equal that of a motion sequence
with GV Of 0 deg/sec, an LV of -8 deg/sec, and a segment duration of 67 msec (left panel, Fig.
16).

29



for LV =-4, 0, 8, and 12 deg/sec for GV4. (The LV of -8 deg/sec was excluded from the GV4 analysis
to limit the STVs to + 4 and + 8 deg/sec for both GVs.) The results support the previous description: The
LV x duration interaction was significant (F >, = 4.65, p < .001) in the GV4 analysis, whereas neither
the duration nor the LV x duration interaction approached significance (F,g = 2.12, p> .10 and Fg =
0.82, respectively) in the GVO analysis. This was true in spite of the fact that the observer x LV x
duration interaction, which served as the error term for the LV x duration effect, was itself significant in
the former but not in the latter analysis (Fz, 199 = 3.92, p< .0001 and F.¢) = 0.53, respectively).

Figures 7 - 9 illustrate the observer x LV x duration interactions for both GVs and response
measures. (Recall that for GV4 this three-way interaction was statistically significant for both measures,
whereas for GVO, only the observer x LV and observer x duration interactions were significant.) As
inspection of these figures indicates, the basic pattern of results held over observers. For each, mean
pursuit velocity was in accord with the GV for the shortest segment durations and shifted progressively
toward the LV as segment duration increased. The shifts in cumulative saccadic amplitude paralleled
those in pursuit velocity. The differences among observers were quantitative rather than qualitative.

Specifically, as shown in Figure 7, DS’s response curves were very similar to the mean response
curves for the 3 observers (Fig. 6). KAK’s responses (Fig. 8) were relatively unaffected by the sawtooth
waveform. For GVO, her means for both measures were approximately 0 deg/sec until the segment
duration was 400 or 500 msec (for LV = -8 and -4 deg/sec, respectively), whereas the means for the other
two observers deviated from 0 deg/sec for segment durations greater than 200 ms. Moreover, KAK’s
mean pursuit speeds and saccadic amplitudes for the longest durations were less than those of the other
two observers. For GV4, the segment durations at which she first showed effects of the sawtooth were
shorter for the negative STVs (resulting in a decrease in pursuit velocity) than for positive STVs, and she
showed little effect of speed in either direction. Finally, TB’s oculomotor system seemed to “prefer”
high speeds (Fig. 9). For the relatively long segment durations, his mean pursuit speeds and saccadic
amplitudes were higher than those of the other two observers, and for GV4, the shift from GV tracking to
composite-waveform tracking occurred at shorter segment durations for the positive sawtooths than for
the negative sawtooths.

A somewhat different view of the accuracy of pursuit during a local motion segment is provided
by Figure 10, where pursuit gain relative to the local velocity of the target (i.e., gain = pursuit velocity/
LV) is plotted as function of segment duration for the six conditions with a nonzero LV. Note that for
observer DS (upper panels) and observer TB (lower panels), about the same level of gain was obtained
for all six conditions. For observer KAK, gain for the longest segment duration varied substantially with
the motion sequence velocities. In general, for this measure of gain, when the STV and the GV were in
opposite directions, tracking accuracy never exceeded and was usually less than that when the
component velocities were in the same direction.

We also assessed gain with respect to the sawtooth velocity (i.e., gain = [mean pursuit velocity -

GVJ/ STV). With that measure, gains for the longest segment durations tended to be highest for LV = 0
and lowest for the two positive sawtooths (i.e., for LV = 8 and 12 deg/sec).

15


motion sequence is the product of the transform of a single local-motion sequence and the
transform of the sampling function.

Figures 11 and 12 illustrate this derivation of the spatiotemporal-frequency spectrum of a
representative, multisegment motion sequence. In these and subsequent illustrations of
amplitude spectra, the horizontal dimension represents horizontal spatial frequencies u from -30
cycles/deg to 30 cycles/deg, and the vertical dimension represents temporal frequencies w from -
30 Hz to 30 Hz. (Note that this orientation differs from that in Figs. 2 - 5). The brightness of a
given point indicates its magnitude. Each pair of points symmetrically displaced from the origin
represents a sinusoidal component with a drift velocity of -w/u.

To create these spectra, the lowpass spatial filtering of the CRT’s electron spot was
approximated in the space-time representation of a motion sequence: A low level of luminance (a
digital value of 50) was assigned to one point on the left and to one point on the right of each
target position (which had a digital value of 255). Consequently, in the motion-sequence spectra
(but not in the sampling-function spectrum), magnitude is a decreasing function of spatial
frequency, as it was in the space-time display images. Because a CRT does little temporal
filtering, the bands of energy in the spectra should be understood to extend in the temporal
frequency dimension well beyond the + 30 Hz range that is depicted.

The spatiotemporal-frequency spectrum of a single 67-msec motion sequence with a
velocity of -4 deg/sec is illustrated in the left panel of Figure 11. Several characteristics of the
spectrum should be noted. First, the band of energy through the origin is in accord with the local
velocity (i.e., its slope is 4), although there is considerable spread in both the spatial- and
temporal-frequency dimensions and thus in the velocities of the individual components. (Spread
in the w dimension is inversely proportional to the duration of the local motion sequence; spread
in the u dimension is inversely proportional to the spatial extent of the sequence, which is
roughly equal to the product of the segment duration and the LV). The side bands represent
aliased frequencies. With a temporal sampling rate of 60 Hz, aliasing will occur for any
component with w > 30 Hz. Note that the velocities of the aliased components differ
substantially from the LV: All are drifting at the wrong speed; many are drifting in the opposite
direction.

The right panel of Figure 11 illustrates the spectrum of a sampling function in which
successive impulses are separated in time by 67 msec (the segment duration) and in space by
0.267 deg (i.e., duration - GV ). The lines in this spectrum have a slope of -GV. ‘They are
separated in w by the temporal sampling rate (i.e., 1/0.067 sec = 15 Hz) and in u by the spatial
sampling rate (i.e., 1/0.267 deg = 3.75 cycles/deg). Note that only the spatiotemporal frequency
components that lie on the line through the origin are consistent with the GV of the motion
sequence.

Figure 12 illustrates the spectrum of a multisegment motion sequence with a GV of 4

deg/sec, an LV of -4 deg/sec, and a segment duration of 67 msec. It represents the product of the
spectra shown in Figure 11. In this spectrum, the components that fall on the line through the

21



12 12

KAK KAK
GV=0%s GV=441s
= LV (/s)
A 8 8 12
2 8
= 4 4
2
8 4 0 ;
s *
2
@ -4 4
=
a
8 8 _
0 200 400 600 800 10) 200 400 600 800
12 12
- KAK KAK
3 GV=0%s . GV=418
2 8 8
r=)
3 LV (/s)
@ 4 4
3 Lv (is)
=z 0 0
<
2
34 4
9
3
a
-8 8
(0) 200 400 600 800 0 200 400 600 800
Segment Duration (msec) Segment Duration (msec)

Figure 8
Mean oculomotor responses of observer KAK to multisegment motion sequences characterized
by a temporally global velocity (GV) and a temporally local velocity (LV). Pursuit velocity
(upper panels) and cumulative saccadic amplitude (lower panels) are shown as a function of
segment duration for each LV, for a GV of 0 deg/sec (left panels) and a GV of 4 deg/sec (right
panels). Each data point represents the average of the response measures for 4 successive 500-
msec periods, beginning 1.5 sec after onset of a motion sequence, for each of 3 trials. The
pursuit-velocity for a given 500-msec period was itself the average of up to 300 measures.

17


Tracking of the GV was, of course, never perfect (see Fig. 3). To assess the effects of
these imperfections, the space-time “retinal image” for a trial was calculated by subtracting each
target position from the average of the ten samples of eye position for each frame of the motion
sequence. For these calculations, the first target presentation was assumed to occur half a frame
after the first eye-position sample.

Figure 17 illustrates the retinal-image spectra for trials in which the pursuit velocity was
well matched to the GV. The left panel depicts the spectrum for a trial in which the GV was 0
deg/sec, the LV was -8 deg/sec, and the duration was 67 msec. The right panel depicts the
spectrum for a trial in which the GV was 4 deg/sec, the LV was -4 deg/sec, and the duration was
67 msec. Note that these spectra are nearly identical: In each, high amplitudes are found for a
narrow band of spatial frequencies (centered at 0 cycles/deg) with a temporal frequency near 0
Hz as well as for narrow bands of spatial frequencies near + 15 Hz. The former are consistent
with a velocity of about 0 deg/sec, the latter with a velocity of -8 deg/sec. The temporal
frequencies for the higher spatial frequencies (see the left panel of Fig. 16) are spread over the
temporal frequency space. Although pursuit in accord with the GV did not reduce retinal image
motion to zero, it did stabilize the position of low spatial frequencies in the retinal image. It may
be that pursuit is maintained not by the absence of retinal image motion but by the presence of
appreciable spectral energy for components with a drift velocity of approximately zero.

30


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12


In the experiment reported here, we recorded eye movements for observers attempting to
track a target moving in accord with a variety of composite waveforms, each of which
represented the sum of a constant velocity ramp and a sawtooth. These motion sequences were
all characterized by speeds known to elicit good pursuit (Leigh & Zee, 1991). To assess whether
the addition of a nonzero constant-velocity ramp has any appreciable effect on the response of
the oculomotor system to a sawtooth waveform, we presented a ramp with a velocity of 0 deg/sec
as well as one with a velocity of 4 deg/sec. We varied the period, direction, and speed of
sawtooth motion. By so doing, we varied both the interval between samples of the constant
velocity ramp and the velocity of the target during those intervals.

METHOD
Observers

Three Armstrong Laboratory employees (2 males, 1 female) served as observers. Two of
the three (TB and DS) were emmetropic; the third (KAK) was myopic and wore corrective
contact lenses. TB and KAK were in their twenties; DS was 41 years old.

Several months earlier, TB and KAK had served as observers in experimental sessions in
which eye movements were measured for a subset of the stimuli used in the present experiment
as well as for a number of related motion sequences. Observer DS had not previously
participated in eye-recording sessions.

Apparatus

A Silicon Graphics IRIS 4D/80GT workstation was programmed to generate the stimuli
and to control the timing and sequencing of the experimental sessions. By the use of double-
buffering, the displayable graphics memory was modified only during the intervals between
vertical scans; by appropriate setting of priorities, the UNIX operating system was prevented
from interrupting a motion sequence. Tests were conducted to ensure that the IRIS consistently
maintained the specified 60-Hz update rate.

The horizontal position of the left eye was measured by means of a custom-designed eye-
position monitor that used an infrared reflectance technique to sense the iris-sclera borders. The
analog signal was subjected to a first-order lowpass filter with a 100-Hz break frequency before
being sampled by a 12-bit, Data Translation analog-to-digital converter (ADC). The ADC was
mounted in an Everex 386/25 PC, which was connected to the IRIS by a serial line. For the
calibration procedure, a signal from the experimenter caused the Everex to initiate sampling by
setting the ADC’s internal trigger. For the motion sequences, a pulse originating from a
phototransistor mounted on the face of the CRT set the ADC’s external trigger. In both cases,
the eye-position signal was sampled at 600 Hz.

The stimuli were displayed on a high-resolution (1280 horizontal x 1024 vertical), 60 Hz,

noninterlaced, RGB Hitachi Monitor. The width of the display raster was 34 cm. From the
viewing distance of 90 cm, the interval between pixel centers subtended a visual angle of 1 arc

4


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27



origin with a slope of -4 deg/sec define the set of sinusoidal components with a drift velocity of 4
deg/sec (ie., in accord with the GV). Note that the GV is predominant for only a narrow band of
spatial frequencies. Spatiotemporal frequencies in accord with the LV are present only where the
lines in the spectrum of the sampling function “sliced” through the nonaliased energy in the
spectrum of the single local-motion sequence. The remaining high-amplitude spatiotemporal-
frequency components are consistent with neither velocity.

The component (Fig. 11) and composite (Fig. 12) spectra differ systematically for
different values of GV, LV, and segment duration. The LV determines the slope, the number of
bands of energy, and for a given segment duration, the spread along the spatial frequency
dimension of the spectrum of a single segment. The effects of these differences on the spectra of
the multisegment motion sequences are illustrated in Figures 13 and 14, which depict the spectra
for sequences with a GV of 4 deg/sec and a segment duration of 67 msec, for LVs of -8, 0, 8,
and 12 deg/sec. Note that the length of the central lobe of the constant velocity (GV) line is
inversely proportional to the sawtooth speed.

Increasing the duration of a local-velocity segment decreases the spread of its spectrum.
It also increases the spatiotemporal interval between impulses in the sampling function and thus
decreases the spacing between replicas in its spectrum. As a result, in the spectrum of the
multisegment motion sequence, the number of spectral components consistent with the GV
decreases, and the number consistent with the LV increases. This effect is illustrated in Figure
15, which depicts the spectra for sequences with a GV of 4 deg/sec, an LV of -4 deg/sec, and
segment durations of 200 msec (left panel) and 400 msec (right panel) .

For a GV of 0 deg/sec, the impulses in the sampling function were separated only in time.
Therefore, the lines in the spectrum of the sampling function are horizontal and occur at w = 0
Hz and multiples of the temporal sampling rate. Figure 16 illustrates the spectra of multisegment
motion sequences with a GV of 0 deg/sec, an LV of -8 deg/sec, and durations of 67 msec (left
panel) and 200 msec (right panel). Note that, in both spectra, there are numerous spatial
frequencies with a temporal frequency of zero (i.., in accord with the GV) and that the other
velocities more-or-less cancel each other out. A comparison of the right panel of Figure 16 and
the left panel of Figure 15 suggests why the LV affected pursuit velocity at shorter segment
durations for a GV of 4 deg/sec than for a GV of 0 deg/sec. Although both spectra represent a
segment duration of 200 msec, the number of spectral components in accord with the LV is
greater for GV4 than for GVO.

As was shown in Figures 12-14, GV motion was predominant for only a narrow band of
spatial frequencies when the segment duration was 67 msec. This band decreased as segment
duration increased. To assess the bandwidth for the longest segment duration at which there was
no effect of the LV, we plotted the temporal frequency spectra of spatial frequencies up to 5
cycles/deg for each of the GV4 motion sequences with a segment duration of 133 msec. We
used 256 x 256 point FFTs (with motion sequences of appropriately limited durations) and
spatial- and temporal-sampling rates of 60 cycles/deg and 60 Hz, respectively. These spectra,
which provided a spatial-frequency resolution of 0.23 cycles/deg, indicated that GV motion was

24


SMOOTH EYE MOVEMENT RESPONSE TO COMPLEX MOTION SEQUENCES

INTRODUCTION

Eye movements are typically categorized in terms of their speed, the type of stimulus, and
the “goal” of the eye-movement system. Smooth pursuit eye movements are relatively slow and
occur when an observer attempts to track a small target moving in the visual field. It is generally
accepted that the purpose of smooth pursuit is to keep the image of the target near or on the fovea
and to reduce the speed at which the target’s image moves across the retina. Thus, accurate
tracking of a target facilitates perception of its spatial form, both by positioning the target’s
image on the area of the retina with the highest visual acuity and by reducing the speed of that
image.

The spatial resolution of a flight simulator’s visual system is usually much less than that
of the fovea. Therefore, the details (high spatial frequencies) of a target are not represented in
the display image, and accurate tracking of a target may not enhance target perception. To
reduce this problem, a few simulation systems track head and eye movements and use that
information to position a high resolution area of interest (AOI) within the display image.
Optimal positioning of the AOI requires an algorithm that can accurately predict future direction
of gaze. Clearly, a better understanding of the pursuit system would improve such prediction. It
might also support the development of “intelligent” image generation systems which could, for
example, selectively vary spatial or temporal resolution in order to elicit tracking of a given
target or to optimize the representations of targets that are likely to be tracked.

In prior studies of smooth pursuit, the target has typically moved along a simple,
predictable trajectory. With target position plotted as a function of time, common waveforms
include a ramp (constant-velocity motion); a step-ramp (abrupt change in position followed by
constant-velocity motion); a sawtooth (periodic abrupt change in position followed by constant-
velocity motion); a triangle (constant-velocity motion in one direction followed by constant-
velocity motion in the opposite direction); and a sinusoid (sinusoidally varying velocity, with the
speed decreasing to zero before a change in direction). Smooth pursuit has also been tested with
pseudorandom trajectories representing a sum of sinusoids or bandlimited white noise. Pursuit
performance is usually measured in terms of gain (eye velocity/stimulus velocity or, for
sinusoidal motion, eye amplitude/target amplitude). Gain has been shown to be affected by
several parameters of target motion, such as velocity (Collewijn & Tamminga, 1984) and
acceleration (Lisberger, Evinger, Johanson & Fuchs, 1981), as well as by nonvisual factors such
as expectations (Kowler, 1989).

The smooth-pursuit system is often viewed as a control system featuring a negative and a
positive feedback loop (Hallet, 1986; Leigh & Zee, 1991; Lisberger, Morris, & Tychsen, 1987;
Robinson, Gordon, & Gordon, 1986; Young, 1971). Figure 1 depicts a typical, if simplified,
model of this type. In this model, the stimulus for smooth pursuit is taken to be velocity (as
opposed to acceleration or position), nonvisual influences and system limitations are disregarded,
and the head is assumed to be stabilized. A retinal velocity error is obtained by subtracting the



PREFACE -

This research was conducted at the Armstrong Laboratory, Aircrew Training Research
Division (AL/HRA), by University of Dayton Research Institute (UDRI) under Contract No.
F33615-90-C-0005, Work Unit 1123-B2-06, Flying Training Research Support, and continued by
Hughes Training, Inc., Training Division (HTI), under Contract No. F41624-95-C-5011. Ms.
Patricia A. Spears and Mr. Dan Mudd were the Contract Monitors. Drs. Elizabeth L. Martin and
Byron Pierce were the technical monitors.

Timothy Askins’ contribution was conducted under UDRI contract. He is currently
employed elsewhere.

We thank Ledr David Shinn (USN), Kathy Keslin (UDRI), and Todd Baruch (AL/HRA)
for the many hours they patiently and conscientiously served as observers. We also thank Ms.
Debra Bolin (UDRI/HTI) and Ms. Margie McConnon (UDRI/HTI) for preparing several of the

figures.



The LV x duration interactions are show in Figure 6, where group mean pursuit velocity (upper
panels) and cumulative saccadic amplitude (lower panels) are plotted as a function of segment duration
for each of the seven conditions (GVO, left panels; GV4, right panels). The general pattern of results is
clear: For the shortest segment durations, mean pursuit velocity was in good agreement with the GV and
cumulative saccadic amplitude was approximately 0 deg/sec. As segment duration increased, mean
pursuit velocity shifted from the GV toward the LV, and mean cumulative saccadic amplitude shifted
from zero toward the cumulative amplitude of the sawtooth step (in deg/sec).!

When the GV was 0 deg/sec, the mean pursuit velocities (Fig. 6, upper left panel) for both
LV =~ and LV=-8 were approximately 0 deg/sec (-0.11 to 0.06 deg/sec) for segment durations < 200
msec. Mean pursuit velocities were slightly below zero (-0.58 and -0.86 deg/sec for LV = -4 and -8
deg/sec, respectively) for a segment duration of 250 msec and continued to decline out to a segment
duration of 700 msec. Pursuit speed for LV =-8 deg/sec was roughly twice that for LV = ~4 deg/sec for
segment durations = 300 msec.

The pattern of results for the measure of cumulative saccadic amplitude (Fig. 6, lower left panel)
is highly similar to the pattern for pursuit velocity. For segment durations < 200 msec, mean amplitudes
were approximately 0 deg/sec. The LV = -4 and LV =-8 means were both above zero for a segment
duration of 250 msec, and they became increasingly positive, with a ratio of about 2:1, as the segment
duration increased to 700 msec.

When the GV was 4 deg/sec (Fig. 6, right panels), the mean pursuit velocities for segment
durations < 133 msec were well matched to the GV for all 5 LVs. The average pursuit velocities for the
two positive and three negative sawtooths differed by 0.87 deg/sec for a segment duration of 167 msec.
This difference increased to 1.98 deg/sec for a segment duration of 200 msec. As segment duration
increased from 200 to 700 msec, the means shifted progressively toward the LVs of the motion

sequences.

The mean cumulative saccadic amplitudes for the motion sequences with a GV of 4 deg/sec
ig. 6, lower right panel) roughly mirrored the mean smooth pursuit velocities, except that they diverged
from a baseline amplitude of 0 deg/sec rather than a baseline velocity of 4 deg/sec. In particular, this
measure first showed an effect of the sawtooth waveform for a segment duration of 167 msec, after
which the magnitude of the effect increased with duration.

To test the statistical significance of the difference between GVO and GV4 in the segment
durations for which effects of the sawtooth were first apparent, ANOVAs were conducted on the mean
pursuit velocities for the 5 lowest segment durations (67 - 200 msec) for each of the LVs for GVO and

" If the motion had been continuous, each sawtooth step would have equaled minus the product of the
STV and the segment duration. Multiplying this value by f,, the sawtooth frequency in cycles/sec, would
give the cumulative amplitude of the sawtooth step, in deg/sec. It would be equal to minus the STV,
regardless of the duration of a sawtooth-defined segment. For our sampled-motion sequences, however, the last
position within a segment was not displayed, and the last displayed position in segment n was separated from the
first position in segment n + 1 by Af. The size of a sawtooth step was therefore reduced by At (STV + GV)- thatis,
by Af- LV. Asa result, the cumulative amplitude of the sawtooth step, in degrees per second, equaled - (STV - fy-
At- LV).

13


Hempstead (1966) examined form and motion perception during-attempts to track a target
following a staircase trajectory: Successive horizontal displacements of the target were in accord
with a velocity of zero for k - 1 and a velocity of kv for 1 out of every k presentations (for k= 2
and 4). He reported that if the observer fixated a stationary spot on the screen, the perceived
motion was not continuous. In contrast, during tracking instructions, a multiline target appeared
to move continuously across the display. Hempstead proposed that tracking was in accord with
velocity v (see also Lindholm 1992a,b).

A staircase is a composite waveform representing the sum of a constant velocity ramp
and a sawtooth. In Hempstead’s study, the velocity v corresponded to the velocity specified by
the ramp. Although Hempstead did not record eye movements, we have confirmed that some
staircase trajectories elicit pursuit eye movements in accord with the ramp velocity (Lindholm,
1991). This suggests that the pursuit system extracts a constant velocity signal when the
intervals between samples of constant velocity motion are filled with multiple presentations of
the target at the last sampled location. In addition, it means that a constant pursuit velocity is
maintained in spite of the fact that retinal image motion persists. The question, then, is twofold:
For staircase motion, why is the velocity signal seemingly in accord with the ramp rather than the
composite waveform, and why is the pursuit velocity maintained even though retinal image
motion is not reduced to zero?

A similar failure to follow high frequency waveforms was reported by Martins, Kowler,
and Palmer (1985). They found poor pursuit of targets undergoing small-amplitude (< 30 arc
min) sinusoidal motion when the frequency of the sinusoid was 1 Hz or greater, despite relatively
low velocities and accelerations. When the frequency of the sinusoid was 4 Hz, they report that
smooth pursuit occurred only during the “initial seconds” of a trial, after which the eye position
records were comparable to those observed when the target was stationary. Martins et al. argue
that the failure to track high frequency oscillations is not the result of motor limitations but “is
likely to arise from slow processing of information about changes in the direction of retinal
motion or from the inability to change expectations quickly about the direction of future motion”
(Martins et al., 1985, p. 241).

The results of Martins et al. can be viewed as merely a failure of the pursuit system to
respond to high frequency sinusoidal motion. However, if the sinusoidal trajectories are taken as
the sum of a sinusoid and a zero-velocity “ramp,” then their results suggest that the pursuit
system responded in accord with the velocity specified by the ramp when the frequency of the
sinusoid was high.

Regardless of the interpretation of the Martins et al. study, clearly some target trajectories
that can be decomposed into a constant velocity ramp and a high frequency waveform elicit
smooth pursuit in accord with the ramp. If the discrepancy between eye motion and target
motion does not result from motor limitations, then it presumably arises from the velocity signal
extracted by the motion sensors. Composite waveforms of this type therefore offer a useful tool
for examining the spatiotemporal properties of these sensors.



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Segment Duration (msec)

Segment Duration (msec)

Figure 10

Mean gain, relative to the temporally local velocity (LV), for multisegment motion sequences with
temporally global velocities (GV) of 0 deg/sec (left panels) and 4 deg/sec (right panels). Gain is plotted
as a function of segment duration for each LV + 0. Each data point represents the average gain for 4
successive 500-msec periods, beginning 1.5 sec after onset of a motion sequence, for each of 3 trials.
The pursuit velocity for a given 500-msec period was itself the average of up to 300 measures.

19


4

<DOAPDOWUFPr AZOWDAVHEZWyY

AL/HR-TR-1996-0040

SMOOTH EYE MOVEMENT RESPONSE TO COMPLEX
MOTION SEQUENCES

Julie Mapes Lindholm
Paul A. Wetzel
Timothy M. Askins

Hughes Training, Inc., Training Operations
6001 S. Power Road, Bidg. 561
Mesa, AZ 85206-0904

DTIC QUaLIrY InspEorED ‘

HUMAN RESOURCES DIRECTORATE
AIRCREW TRAINING RESEARCH DIVISION
6001 S. Power Road, Bldg. 558
Mesa, AZ 85206-0904

September 1996

Final Technical Report for Period June 1991 - June 1995

Approved for public release; distribution is unlimited.

AIR FORCE MATERIEL COMMAND
BROOKS AIR FORCE BASE, TEXAS

19961223 054



Component Waveforms Composite Waveforms

Ramp Sawtooth Continuous Sampled

+
Space
tl
Space
y
Space

Space

Time

+
Space
"
Space
4
Space

Space

Time Time

Figure 2
Examples of motion sequences created by summing a ramp and a sawtooth waveform. In the
upper panels, the motion represented by the (ramp of the) sawtooth is in the same direction as
that represented by the ramp; in the lower panels, the ramp and sawtooth motions are in opposite
directions.

local velocity (LV) of a segment, defined by the ramp of the composite. The LV equaled the
sum of the GV and the STV.

Sampled versions of 7 composite waveforms were presented, 2 with'a GV of 0 deg/sec
(GV0) and 5 with a GV of 4 deg/sec (GV4). The velocities characterizing these 7 conditions are
summarized in Table 1. (Positive values indicate left-to-right motion.) Twelve local-motion
segment durations were presented for each GV x LV condition: 67, 100, 133, 167, 200, 250, 300,
350, 400, 500, 600, and 700 msec (4, 6, 8, 10, 12, 15, 18, 21, 24, 30, 36, and 42 presentations of
the target, with successive presentations separated by 16.7 msec).

For GVO, the location of the first target presentation for each local-motion segment was
offset from the display center by one-half the segment path. Thus, regardless of the duration of a
segment or the velocity of the target during that segment, the trajectory was always centered
horizontally on the display. The trial duration for GVO was set at 5.0 sec.


min. The front of the monitor was enclosed in a black, three-sided, cardboard box with a 37 cm
x 18 cm opening. The box served to mask both the monitor frame and the phototransistor (used
to trigger the ADC), which was attached to the lower left-hand corner of the display area.

The observer sat in a small booth that consisted of a metal frame covered with a heavy
black cloth. The eye position monitor and a head and chin rest were mounted on a sturdy table.
A three-button computer mouse and a computer joy stick were provided for observer and
experimenter input, respectively.

Calibration of Eye-Position Monitor

The infrared emitter and detectors of the eye-position monitor were manually aligned at
the beginning of each eye-recording session. Then, during an initial rough calibration, the
observer was instructed to shift his or her gaze between three 21 x 21 pixel fixation crosses
which were positioned in the center and on the far left and right edges of the display. Gain and
balance controls were adjusted to ensure that these excursions produced a signal of
approximately +8 volts. :

The experimenter initiated a computer-controlled calibration sequence prior to each trial.
A 21 x21 pixel fixation cross served as the target for this procedure. Following an initial
presentation in the center of the display, the target was displaced to the right in four steps of 157
pixels (approximately 2.6 deg). It then returned to the center and was successively displaced to
the left. The target was presented at each location for 1.5 sec. Eye position was continuously
sampled throughout the 15-sec sequence.

The eye position data for the first center presentation were discarded. For each of the
remaining nine positions, calibration statistics were based on the initial 125 msec (75 samples) of
the last 500 msec of the 1500-msec presentation. A calibration was accepted only if it met two
criteria: (a) the standard deviation of the 75 samples for each target position was less than 0.6%
of the difference between the means for the farthest left and farthest right positions; and (b) the
squared correlation between the nine eye-position means and the target-position values was
greater than 0.998. The first criterion ensured that fixation was steady during the 125-msec
period; the second criterion ensured that there was a linear relationship between measured eye
position and target position. If these criteria were met, the slope and intercept values derived
from a least squares linear regression were used to calibrate the eye-position data for the
following trial.

Motion Sequences

The target was a short, “white,” vertical line (1 x 11 pixels) centered vertically on a dark
display. Its horizontal position varied over time in accord with a composite waveform formed by
adding a constant velocity ramp and a sawtooth (Fig. 2). Each multisegment motion sequence
was thus characterized by three velocities: the temporally global velocity (GV), defined by the
ramp; the sawtooth velocity (STV), defined by the ramp of the sawtooth; and the temporally



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eye velocity from the target velocity. The retinal velocity error is added to a copy of the pursuit
command (efference copy), providing a reconstruction of the original target-velocity signal. This
signal drives the pursuit system. Thus, if the eyes are stationary, the retinal velocity error will
stimulate the pursuit system. If a moving target is being tracked accurately, the retinal error
signal will be reduced to zero and the efference copy will cause pursuit to continue. It follows
then that if the target is not moving, but nonetheless remains stationary (if intermittent) on the
retina while the eyes are engaged in smooth pursuit, the system will respond by maintaining that
pursuit. This is the situation for “sigma motion” and related phenomena (Heywood, 1973;
Stoper, 1973; Lamontagne, Desjardins & Pivik, 1993).

efference copy
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Figure 1

Typical Model of the Smooth Pursuit Eye Movement System

The term retinal velocity error is sometimes defined as the difference between eye and
target velocity. The term is also used to refer to the velocity signal extracted from the
spatiotemporal pattern of light on the retina by direction-selective cortical cells. The two are not
necessarily equivalent. Moreover, the velocity signals for the pursuit system may be the same as
those for the perceptual system, but they cannot be assumed to be so. In the following
discussion, we will use the term retinal image motion to refer to variation over time in the retinal
locus of the target’s image and the term velocity signal to refer to the output of the relevant
motion sensors. Our primary interest is in the features of the time-varying retinal image that
account for the effective velocity signal.

Smooth pursuit eye movements are routinely elicited by temporally sampled motion
rather than by continuous motion. Moreover, for a target following a triangular trajectory,
Morgan and Turnbull (1978) found smooth tracking for sampling intervals that were too long
(150 msec) to support perceived continuity. Thus, it appears that the neural mechanisms that
provide input to the smooth pursuit system can extract a constant velocity signal from relatively
infrequent samples of constant velocity motion. Once the velocity of smooth pursuit is well
matched to the velocity represented by such a motion sequence, the retinal locus of the target’s
image will be approximately constant and, according to the model depicted in Figure 1, efference
copy will cause that pursuit velocity to be maintained.

2


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Figure 7
Mean oculomotor responses of observer DS to multisegment motion, sequences characterized by
a temporally global velocity (GV) and a temporally local velocity (LV). Pursuit velocity (upper
panels) and cumulative saccadic amplitude (lower panels) are shown as a function of segment
duration for each LV, for a GV of 0 deg/sec (left panels) and a GV of 4 deg/sec (right panels).
Each data point represents the average of the response measures for 4 successive 500-msec
periods, beginning 1.5 sec after onset of a motion sequence, for each of 3 trials. The pursuit-
velocity for a given 500-msec period was itself the average of up to 300 measures.

16


Lisberger, S. G., Mortis, E. J., & Tychsen, L. (1987). Visual motion processing and sensory-
motor integration for smooth pursuit eye movements. Annual Review of Neuroscience,

10, 97-129.

Martins, A. J., Kowler, E., & Palmer, C. (1985). Smooth pursuit of small-amplitude sinusoidal
motion. Journal of the Optical Society of America, A2, 234-242.

Morgan, M. J., & Turnbull, D. F. (1978). Smooth pursuit tracking and the perception of motion
in the absence of real movement. Vision Research, 18, 1053-1059.

Robinson, D. A., Gordon, J. L., & Gordon, S. E. (1986). A model of the smooth pursuit eye
movement system. Biological Cybernetics, 55, 43-57.

Stoper, A. (1973). Apparent motion of stimuli presented stroboscopically during pursuit eye
movements. Perception and Psychophysics, 13, 301-311.

van Santen, J. P. H., & Sperling, G. (1984). A temporal covariance model of motion perception.
Journal of the Optical Society of America, A1, 451-473.

Watson, A. B., & Ahumada, A. J., Jr. (1985). A model of human visual-motion sensing. Journal
of the Optical Society of America, A2, 1600-1606.

Young, L. R., (1971). Pursuit eye tracking movements. In P. Bach-y-Rita, C. C. Collins, & J. E.
Hyde (Eds.), Control of eye movements, pp. 429-443. Amsterdam: Elsevier.

34


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CONTENTS -

Observers..
Apparatus.
Calibration of Eye-Position Monitor.

Procedure..
Data Reduction and Analysis..

List of Figures

Typical Model of the Smooth Pursuit Eye Movement System.
Examples of Motion Sequences.
Eye Movement Records for Motion Sequences with a Segment

Duration of 167 msec... ase weasecseconsenscoes
Eye Movement Records for Motion “Sequences: with 2 a 2 Segment

Duration of 300 msec.
Eye Movement Records for Motion Sequences with a Segment ~
Duration of 700 msec... eoseseeecsosceseccesenses
Group Mean Oculomotor Responses...

Mean Oculomotor Responses of Observer 'D
Mean Oculomotor Responses of Observer KAK..
Mean Oculomotor Responses of Observer TB.
Mean Gain for Multisegment Motion Sequences.
Spatiotemporal-Frequency Spectra..

Page

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12
14
16
17
18
19
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precluded this level of control, inspection of the eye records indicated that the oculomotor response for
individual trials was typically well established after 1.0 to 1.5 sec. Moreover, the variability of smooth
pursuit velocity within a segment appeared comparable to that between segments, and saccades were not
tightly linked to segment onset. It thus seemed unlikely that systematic distortions would be introduced
by summarizing the data over intervals that in some cases contained many segments and in other cases
contained less than one segment.

In order to compute the desired summary response measures, we initially divided each 5-sec eye
position record into bins of 500 msec and calculated the average smooth-pursuit velocity and the
cumulative saccadic amplitude for each bin. The latter measure was obtained by summing the signed
amplitudes of the saccades that began within the bin.

‘The data for the first three bins were discarded so that, in all cases, at least two full cycles of the
composite waveform would have been presented prior to the assessment interval. Because some of the
motion sequences had a duration of only 3.5 sec, the data for the last three bins were discarded.
Preliminary analyses of variance (ANOVAs) of the mean velocities and cumulative saccadic amplitudes
for Bins 4 to 7 indicated that the main effect of Bin and interactions involving Bin contributed relatively
little variance to the data. Therefore, the velocity and saccadic measures were each averaged over the
four bins for further analysis.

Univariate analyses of variance (ANOVA) were performed on the mean pursuit velocity and the
cumulative saccadic amplitude measures for each GV. The three trials per observer per LV x duration
combination were treated as replications. Thus, each of the four ANOVAs included four factors:
observer, LV, segment duration, and replication. Both observer and replication were treated as random
variables. Error terms were not pooled.

RESULTS

Representative records of eye and target position are presented in Figures 3-5. As Figure 3
illustrates, for segment durations less than about 167 msec, smooth pursuit velocity was in accord with
the GV, and saccades were infrequent and of small amplitude. For segment durations of “intermediate”
length, mean pursuit velocity shifted towards the LV, and saccades were more frequent and of higher
amplitude (see Fig. 4). For the longest segment durations, mean pursuit velocity approached the LV, and
saccades were of high amplitude (see Fig. 5). Note (in Figs. 4 and 5) that saccades were not consistently
linked to the end of a sawtooth period and that, concomitantly, the periods of saccade-free smooth
pursuit varied in duration. Saccades were, however, usually in the direction of the sawtooth step.

The results of the ANOVAs indicated that LV, segment duration, observer, and the interactions
of these factors had significant effects on mean pursuit velocity and mean cumulative saccadic
amplitude. With the exception of the main effects of LV for GVO (F}2= 9.41, p> .05 and F, = 7.65,
p>.10, for the pursuit and saccade measures, respectively), the main effects (observer, LV, duration) and
first-order interactions (LV x duration; observer x LV; and observer x duration) were all significant
(p<.0001 in most cases) in each of the four analyses. In addition, the observer x LV x duration
interactions were both significant for GV4.


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‘Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering
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1204, Afington, VA’ 4302, and to the ' = buen, to Washington Head quater edacton Bcjex 07080166) Washington De 256, .
1. AGENCY USE ONLY (Leave blank) | 2. REPORT DATE 3, REPORT TYPE AND DATES COVERED
September 1996 Final - June 1991 to June 1995
4, TITLE AND SUBTITLE 5, FUNDING NUMBERS
. C-F41624-95-C-5011
Smooth Eye Movement Response to Complex Motion Sequences PE - 62205F
PR- 1123
Fulks Mipes 2 inahoim TA-B2
Paul A. Wetzel WU - 06
Timothy M. Askins
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
REPORT NUMBER
Hughes Training, Inc.
Training Operations
6001 South Power Road, Bldg. 561
Mesa, AZ 85206-0904 - AL/HR-TR-1996-0040
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING
‘AGENCY REPORT NUMBER
Armstrong Laboratory
Human Resources Directorate
Aircrew Training Research Division
6001 South Power Road, Bldg. 558

Mesa, AZ 85206-0904

41, SUPPLEMENTARY NOTES
Armstrong Laboratory Technical Monitor: Dr. Elizabeth L. Martin (602) 988-6561

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release;distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

To examine the spatiotemporal properties of the motion sensors for the smooth pursuit system, we presented horizontal
motion sequences in which successive target displacements were in accord with a composited waveform representing the sum
of a constant velocity ramp and a sawtooth. The sequences differed in global velocity (GV = ramp velocity = 0 or 4 deg/sec),
local velocity (LV = ramp velocity + sawtooth velocity = -8 or -4 deg/sec, for GV = 0, and -8, -4, 0, 8, 12 deg/sec, for GV =
4), and local-segment duration (12 values between 67 and 700 msec). When the duration of a local-velocity segment was
relatively short (< 133 msec, for GV = 4 deg/sec; < 200 msec, For GV = 0 deg/sec), meah pursuit velocity matched the GV.
As the segment duration increased, mean pursuit velocity shifted gradually toward the LV. Changes in cumulative saccadic
amplitude mirrored the changes in smooth pursuit velocity. The spatiotemporal-frequency spectra of the motion sequences
suggested that the pursuit system responded in accord with the drift velocities of very low spatial frequencies. The spectra of
the space-time retinal images suggested that pursuit was maintained not by the absence of retinal image motion but by the
presence of appreciable spectral energy for components with a drift velocity of approximately zero.

14, SUBJECT TERMS . : oa . 45. NUMBER OF PAGES
Efference copy; Eye movements; Fourier transform; Motion sensors; Retinal images, Retinal
roy error; Saccadic eye movements; Smooth pursuit eye movements; Spatiotemporal 16. PRICE CODE
17. SECURITY CLASSIFICATION | 16. SECURITY CLASSIFICATION | 19. SECURITY CLASSIFICATION | 20. LIMITATION OF
OF REPORT OF THIS PAGE OF ABSTRACT ABSTRACT
Unclassified Unclassified Unclassified UL
NSN 7540-01-280-5500 Standard Form 208 (Rev 2-00) Presonbed by ANSI Std 2-s0-16

298-102 COMPUTER GENERATED



REFERENCES -

Adelson, E. H., & Bergen, J. R. (1985). Spatiotemporal energy models for the perception of
motion. Journal of the Optical Society of America, A2, 284-299.

Collewijn, H., & Tamminga, E. P. (1984). Human smooth pursuit and saccadic eye movements
during voluntary pursuit of different target motions on different backgrounds. Journal of
Physiology, 351, 217-250.

Hallet, P. E. (1986). Eye movements. In K. R. Boff, L. Kauffman, & J. P. Thomas (Eds.),
Handbook of perception and human performance, Vol. 1, Chapter 10. New York: Wiley.

Hempstead, C. F. (1966). Motion perception using oscilloscope display. IEEE Spectrum,
128-135. -

Heywood, S. (1973). Pursuing stationary dots: Smooth eye movements and apparent movement.
Perception, 2, 181-195.

Kowler, E. (1989). Cognitive expectations, not habits, control anticipatory smooth oculomotor
pursuit. Vision Research, 29, 1049-1057.

Lamontagne, C., Desjardins, F. J., & Pivik, R. T. (1993). Smooth pursuit along a solid line: A
new variation on the theme of efference-copy-bound eye tracking. Perception, 22, 477-
482.

Leigh, R. J., & Zee, D. S. (1991). The neurology of eye movements (2nd edition). Philadelphia: F.
A. Davis Co.

Lindholm, J. M. (1991). Perceptual consequences of the filtering characteristics of the pursuit
system. Bulletin of the Psychonomic Society ,29 , 477.

Lindholm, J. M. (1992a). Perceptual effects of spatiotemporal sampling. In M. A. Karim (ed.)
Electro-Optical Displays (pp. 787-807). New York: Marcel Dekker.”

Lindholm, J. M. (1992b). Temporal and Spatial Factors Affecting the Perception of Computer-
Generated Imagery. AL-TR-1991-0140. Williams AFB, AZ: Operations Training
Division, Air Force Human Resources Laboratory.

Lisberger, S. G., Evinger, C., Johanson, G. W., & Fuchs, A. F. (1981). Relationship between eye

acceleration and retinal image velocity during foveal smooth pursuit in man and monkey.
Journal of Neurophysiology, 46, 229-249.

33



DISCUSSION -

The purpose of this experiment was to examine the spatiotemporal properties of the
motion sensors for the smooth pursuit eye movement system. In an earlier study, Morgan &
Turnbull (1978) demonstrated that the pursuit system could extract the constant velocity signal
from motion sequences in which successive presentations of the target were separated in space
by 27 arc min and in time by up to 150 msec. We found that, for similar spatial and temporal
intervals, the pursuit system could extract the temporally global velocity from motion sequences
in which the target was presented repetitively between successive samples of that velocity. (For
a motion sequence with a GV of 4 deg/sec and a segment duration of 133 msec, corresponding
points in successive segments were separated by 32 arc min.) The pursuit system could do this
not only when the target was stationary between successive samples of the GV (i.e., when the
spatiotemporal trajectory was a staircase), but also when the target was successively displaced, in
accord with a constant temporally local velocity, during the GV-sampling interval. In the latter
case, neither the direction nor the speed of motion between samples of the GV (ie., during a
local-velocity segment) had a consistent effect on pursuit velocity for motion sequences with a
local-segment duration < 133 msec. Thus, for such motion sequences, pursuit in accord with the
GV was maintained despite the failure of smooth eye movements to reduce the retinal image
motion to zero.

When the pursuit system responded in accord with the GV of a motion sequence, it
necessarily failed to follow the temporally local motion. In good agreement with the research of
Martins et al (1985), who found that the pursuit system showed little if any response to low-
amplitude sinusoidal motion with frequencies of 4 to 5 Hz, we found no effect of local velocity
for GVO sequences with segment durations of up to 200 msec. Although this segment duration
was longer than that (133 msec) supporting highly accurate GV tracking for the GV4 sequences,
the similarity of the results for the two GVs suggests that the pursuit system was actively
matching the GV of 0 deg/sec rather than merely failing to follow the LV.

It has been proposed that the analysis of motion in the retinal image begins with a
spatiotemporal filtering process (Adelson & Bergen, 1985; van Santen & Sperling, 1984; Watson
& Ahumada, 1985). If this view is correct, then an analysis of the spatiotemporal frequency
spectra of our motion sequences may provide some insight into the basis of the velocity signal
for the initiation of smooth pursuit as well as the characteristics of the retinal image necessary to
maintain pursuit at a given velocity.

In Figure 2, the multisegment motion sequences were shown to represent sampled
versions of composite waveforms constructed by summing two component waveforms: a
constant velocity ramp and a sawtooth. Such sequences can also be constructed by convolving
the space-time representation of a single local-motion sequence with a sampling function in
which successive impulses are separated in time by the duration of the sequence and in space by
the product of that duration and the GV (e., with a sampled version of the ramp). Because
convolution in the space-time domain is equivalent to multiplication in the spatiotemporal-
frequency domain, the Fourier transform of the space-time representation of a multisegment

20


NOTICES

When Government drawings, specifications, or other data are
used for any purpose other than in connection with a definitely
Government-related procurement, the United States Government
incurs no responsibility or any obligation whatsoever. The fact that the
Government may have formulated or in any way supplied the said
drawings, specifications, or other data, is not to be regarded by
implication, or otherwise in any manner construed, as licensing the
holder, or any other person or corporation; or as conveying any rights
or permission to manufacture, use, or sell any patented invention that
may in any way be related thereto. .

The Office of Public Affairs has reviewed this report, and it is
releasable to the National Technical Information Service, where it will
be available to the general public, including foreign nationals.

This report has been reviewed and is approved for publication.

Si Wizalaty L. Mask
BYRON J. PIERCE ELIZABETH L. MARTIN
Project Scientist Technical Director

Lyn “ARROLL, Colonel, USAF

Chief, Aircrew Training Research Division

Please notify AL/HRPP, 7909 Lindbergh Drive, Brooks AFB, TX 78235-5352, if your
address changes, or if you no longer want to receive our technical reports. You may
write or call the STINFO Office at DSN 240-3853 or commercial (210) 536-3853.



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Temporal Frequency (Hz)

Spatial Frequency (c/d)

Figure 12
Spectrum of motion sequence with a global velocity of 4 deg/sec, a local velocity of -4 deg/sec,
and a segment duration of 67 msec (4 target presentations). This spectrum represents the product
of the spectra in Figure 11. The horizontal dimension represents horizontal spatial frequencies
from -30 cycles/deg to 30 cycles/deg, and the vertical dimension represents temporal frequencies
from -30 Hz to 30 Hz. The brightness of a point indicates its magnitude.

23


Table 1. Motion Sequence Velocities ~—

Global Sawtooth Local
(deg/sec) (deg/sec) (deg/sec)
0 -8 -8
0 4 4
4 -12 8
4 -8 4
4 4 0
4 4 8
4 8 12

For GV4, left and right margins (offsets from the edge of the display raster) of 5 pixels
were established to ensure that the full path of the target was visible through the opening of the
box that masked the CRT frame. If the LV was positive or zero, the initial target position was on
the left edge of the resulting display area. If the LV was negative, the initial target position was
offset to the right so that the last position of the first segment fell on the left edge. Trial duration
for a given trajectory was determined by the number of complete local motion segments that
could be written across the 21.2-deg display. Before beginning each segment, the computer
software calculated whether the initial target position (for the negative sawtooths) or the final
target position (for the positive sawtooths) of the segment would extend beyond the maximum
display position. If it would, the trial was terminated before initiating that segment. For GV4,
then, the total trial duration varied from 3.5 to 5.3 sec. The shortest trial durations occurred for
the motion sequences with high local speeds and long local segments.

Procedure

Each observer participated in a minimum of 21 experimental sessions, 3 for each of the 7
conditions. A different pseudo-random order of the 7 conditions was generated for each
observer, with the restriction that each of the 7 conditions be presented once within each third of
the experiment. Due to observer fatigue or repeated failure to meet calibration requirements, a
few sessions were terminated before a full set of data had been gathered. The data for other trials
were discarded due to eye blinks. Motion sequences for which data were missing or discarded
were presented during the next scheduled session or in one or more extra, partial sessions at the
end of the experiment.

A complete experimental session consisted of 3 blocks of 12 trials. The trials differed in
segment duration. The order of presentation of the 12 durations was randomized independently
for each block within a session. The first 2 blocks of trials served to familiarize the observer
with the type of motion sequence. Eye position was recorded during the third block.



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