Journal of Experimental Psychology:
Human Perception and Performance
1997, Vol. 23, No. 6, 1764-1782
Copyright 1997 by the American Psychological Association, Inc.
0096-1523/97/$3.00
Perception and Control of Altitude: Splay and Depression Angles
Rik Warren
John M. Flach
Wright State University
Armstrong Laboratory, Wright-Patterson Air Force Base
Sheila A. Garness, Leigh Kelly, and Terry Stanard
Wright State University
In 3 experiments altitude control was examined as a function of texture type and forward
speed. Four texture types were used: grid (rectangular grid with neutral colored cells); dot
(small triangles distributed randomly on the ground surface); splay (rows of colored texture
parallel to the direction of motion); and depression (rows of colored texture extending
perpendicular to the direction of motion). The first 2 experiments required participants to track
a constant altitude. Experiment 3 required participants to descend as low as possible without
crashing. Results showed an interaction between texture type and forward speed. At low
speeds, there was little difference between performance with the depression and splay textures.
However, performance with the depression texture deteriorated with increasing forward
speeds. Performance with the splay texture was independent of forward speed.
Gibson, Olum, and Rosenblatt (1955) presented one of the
first mathematical descriptions of the optical flow field that
results from locomotion through a textured environment (in
particular, landing an aircraft). From their analysis Gibson et
al. concluded that "the motion perspective of a surface like
the earth, or a floor or wall, carries information about the
direction of one's locomotion (the angle of approach to the
surface) as well as a great deal of information about the
surface itself" (p. 381). Gibson et al. identified two distinct
characteristics of flow in the visual field—pattern and
amount. The radial pattern of flow was identified as a
primary source of information for the direction of motion
relative to a surface. The gradients of "amount" of flow
were identified as a cue for the perception of distance to the
surface. The analysis of the gradients of amount of flow led
John M. Flach, Sheila A. Garness, Leigh Kelly, and Terry
Stanard, Department of Psychology, Wright State University; Rik
Warren, Armstrong Laboratory, Wright-Patterson Air Force Base,
Dayton, Ohio.
This research was conducted at the Armstrong Laboratory,
Wright-Patterson Air Force Base. Support for this research was
provided by the Air Force Office of Scientific Research, Air Force
Systems Command, under Grants F49620-92-J-0511 and F4962093-J-0560.
Experiment 1 was completed in partial fulfillment of the
requirements for a master's degree at Wright State University for
Leigh Kelly. Experiment 2 was completed in partial fulfillment of
the requirements for a master's degree at Wright State University
for Sheila A. Garness. Jeffrey Light contributed to the design and
data collection for Experiment 3 as part of his senior honors project
in psychology.
Walt Johnson gave us important feedback based on an earlier
version of this article; the final product is greatly improved as a
result.
Correspondence concerning this article should be addressed to
John M. Flach, Department of Psychology, 309 Oelman Hall,
Wright State University, Dayton, Ohio 45435. Electronic mail may
be sent via Internet [email protected].
to the following claims about the information available to
the observer (O):
O's linear velocity (ground speed) is represented in the optical
flow-pattern. Subjective velocity is proportional to the overall
velocity of the whole pattern, or to the velocity of any part of
it, or to its maximal velocity. The perpendicular distance from
O to the surface (altitude) is also represented in the optical
flow pattern, and so is distance to the surface on the line of
locomotion in the case of a landing glide. Both are inversely
proportional to its velocity. Ground-speed and altitude are not,
however, independently determined by the optical information. A more rapid flow-pattern may indicate either an increase
in speed or a decrease in altitude. Length of time before
touching down, however, seems to be given by the optical
information in a univocal manner (Gibson et al., 1955, p. 382).
Twenty years passed before Gibson et al.'s (1955) hypothesis—that geometrical properties of the flow field are the
basis for control of locomotion—was tested empirically. R.
Warren's (1976) evaluation of observers' ability to identify
the direction of motion was one of the early empirical
studies to test Gibson et al.'s hypothesis. Since that time a
number of empirical investigations have attempted to link
human performance to various geometrical properties of
flow fields (e.g., Cutting, 1986; Cutting, Springer, Braren, &
Johnson, 1992; Larish & Flach, 1990; Owen & Warren,
1987; Owen, Warren, Jensen, Mangold, & Hettinger, 1981;
Royden, Banks, & Crowell, 1992; W. H. Warren & Hannon,
1988, 1990; W. H. Warren, Mestre, Blackwell, & Morris,
1991; W. H. Warren, Morris, & Kalish, 1988).
The experiments presented here continue this program of
searching for empirical links between geometric properties
of flow fields and the control of locomotion. In particular, we
focus on two geometrical properties of flow fields—splay
angle and depression angle—and the role that these properties might play in the regulation of altitude. In the following
sections, we first define splay angle and depression angle.
Then we review the previous empirical work. Finally, we
report a series of empirical studies designed to test a
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ALTITUDE CONTROL
1765
hypothesis suggested by Flach, Hagen, and Larish (1992) to
account for apparently disparate findings in the literature.
Geometric Analysis
The first step in an analysis of the geometric properties of
a flow field is to identify the surface texture elements that
"carry" the flow. For example, Gibson et al.'s (1955)
analysis assumed points as the texture elements. Demon's
(1980) research on judgment of driving speed (edge rate) is
an example in which the significant texture elements were
edges. In the present analysis, the texture elements are
edges. "Of course, there is a mapping from points to edges
and from edges to points. In fact, it may well be that the
distinction between points and edges has far greater implications for the geometrical analysis than for perception.
However, some aspects of flow are more easily visualized
and modeled as properties of points, whereas others are
more easily visualized as properties of edges. Splay and
depression angles are most easily visualized as properties of
edges. Splay angle is a property of edges parallel to the
direction of motion. Depression angle is a property of edges
perpendicular to the direction of motion.
Splay Angle
Optical splay angle was identified as a source of information for altitude by R. Warren (1982). R. Warren cited Biggs
(1966), who noted that when an observer maintains a
constant distance from an edge on the ground plane (e.g., the
curb of the road), despite shifting optical positions of the
individual points composing the edge, the optical position of
the edge is invariant. For an edge parallel to the direction of
motion, the invariant optical position can be defined in terms
of the angle at the vanishing point formed by the edge and a
reference line perpendicular to the horizon along the ground
trace of forward motion, as shown in Figure 1. This angle is
defined by the equation
= tan"
where S is the splay angle, Yg is the lateral displacement of
the line from the perpendicular, and z is the altitude
(eyeheight) of the observer. The equation describes the
projection of the ground texture onto the frontal plane for an
observer moving parallel to the ground. For rectilinear
motion over a flat ground plane, splay angle is constant
when altitude is constant.
The rate of change in splay angle with respect to change in
observer position is specified by the following equation
(dotted variables are used to specify temporal derivatives):
cos 5 sin 5 + |— cos2 5.
z
The first term, —(z/z) cos S sin S, indexes change in splay
angle as a function of changes in altitude (z). The negative
Figure 1. Texture lines extending to the horizon parallel to the
forward direction of motion provide information for altitude in the
form of splay angle. Splay angle is the angle between the texture
line and the motion path at the convergence point on the horizon.
As an observer moves from high altitudes (ZO to lower altitudes
(ZJ, the splay angle increases as the texture lines fan out (pivot at
the convergence point) toward the horizon. Yg = lateral distance
from the observer to the edge.
sign indicates that as altitude decreases, splay angle increases, and vice versa. The term -(z/z) specifies fractional
change in altitude, or change in altitude scaled in eyeheights.
This term indicates that the relation between change in
altitude and change in splay angle depends on the initial
altitude. At high altitudes (large z), any given change in
altitude would result in a smaller change in splay angle than
when initial altitude was lower. As noted by R. Warren
(1988), " '[S]ensitivity' of the display [optical splay rate]
varies inversely with altitude, the lower the altitude, the
more change in visual effect for equivalent altitude change
commands. At very low altitudes this optical activity is
dramatic and even 'optically violent' " (p. A121). The
-(z/z) term is independent of optical position of an edge. It
scales the rate of change for every edge in the field of view.
For this reason, it has been termed "global perspectival
splay rate" (Wolpert, 1987). The sine and cosine terms index
the dependence of splay rate on the optical position of each
edge. Figure 2 shows the change of splay angle for a 5-ft
(1.5-m) decrease in altitude from an initial observation
height of 25 ft (7.6 m) as a function of the initial splay angle.
For edges with 0° splay angle (perpendicular to the horizon
at the expansion point) and ±90° splay angle (the horizon),
the rate of change will be zero. From these minima, the
absolute change in splay angle for a given fractional change
in altitude will increase to a maximum at a splay angle of
±45°,
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FLACH, WARREN, GARNESS, KELLY, AND STANARD
-90\
-75
-0.1 -L
Angular Position In Field of View
Figure 2. The change of splay or depression angle for a 5-ft (1.5-m) decrease in altitude from an
initial altitude of 25 ft (7.6 m) as a function of the initial angular position is illustrated as a sine
function with peaks at ±45° (dotted line). The change of splay and depression angle as a function of a
5-ft fore-aft or lateral displacement is illustrated as a cos2 function with peak at 0° (solid line). The
full range of initial splay angles is typically visible in the frontal visual field of view. However, all
initial depression angles are not visible. For the field of view simulated in our experiments, initial
depression angles below 51.87° were outside of the field of view.
The second term in the equation for change in splay angle,
(Yg/z) cos2 5, indexes change in lateral distance (Yg) from the
observer to the edge such as might result from a lateral
movement of the observer. For straight-ahead forward
motion there is no change in lateral distance, and this term
has no impact on the optical splay angle. For this reason, this
term has not typically been included in analyses of splay
angle. However, lateral displacements have sometimes been
included in the events that have been simulated to study
altitude control. Thus, it is important to understand the
effects from this term. The first half of the term (Yg/z)
specifies lateral displacement rate scaled in eyeheights.
Changes in lateral distance result in proportional changes in
splay angle. The second half of the term (cos2 S) indicates
how change in splay angle varies as a function of the optical
position of a particular line element. Figure 2 illustrates the
change in splay angle as a function of initial position for a
lateral change of -5 ft (-1.5 m) at an altitude of 25 ft (7.6
m). As can be seen in Figure 2, change in splay angle
decreases from a maximum for the texture line directly
below the observer (5 = 0°) to a minimum at the horizon
(5 = ±90°). It is important to note that whereas changes in
altitude have symmetrical effects on edges spaced equal
distances to each side of the observer, lateral motions cause a
reduction in splay angle for edges in the direction of the
lateral motion (negative splay angles become less negative
for movement in a negative [left] direction) and an increase
in splay angle for edges in the opposite direction from the
lateral motion (positive splay angles become more positive).
Thus, changes in altitude result in changes in splay angle
that are symmetric around the motion path, whereas changes
in lateral position have asymmetric effects.
Depression Angle
Optical depression angle provides yet another potential
source of information for changing altitude. Optical depression angle (8) has been defined as the angular position below
the horizon of an edge perpendicular to the direction of
motion (Flach et al., 1992). However, to make the angles
comparable to those used for splay angle, we use the
convention of measuring optical depression angle from the
point directly below the observer, as illustrated in Figure 3.
The benefit of this convention is that splay and depression
angles are both referenced to the observer, whereas with the
older convention, splay angle was indexed to the observer
and depression angle was indexed to the horizon. This angle
can be expressed as a function of altitude (z) and the
principal distance on the ground from the observer to the
texture element (xg):
8 = tan"
For rectilinear motion over a flat ground plane, the rate of
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ALTITUDE CONTROL
Optical
Horizon
Optical Horizon
Figure 3. Texture lines perpendicular to the forward path of travel
provide information for change in altitude in terms of depression
angle. As the observer moves from a high altitude (Z\) to a lower
altitude (ZJ the depression angle becomes larger and the texture
lines move up in the field of view toward the horizon. Z = altitude,
d = depression angle, Xg = distance on the ground from the
observer to the texture element.
change of the optical depression angle will be
cos 8 sin 8 +
cos2 8.
The first term, —(Hz) cos 8 sin 8, shows the contribution of
changes in the observer's altitude on the optical depression
angle. The relation between depression angle and altitude is
qualitatively identical to the relation between splay angle
and altitude. As with splay angle, the rate of change in
depression angle scales with fractional changes in altitude.
Also, as with splay angle, the rate of change of depression
angle will depend on the initial optical position of a texture
element. Rate of change of depression angle will be zero at
depression angles of 0° (directly below the observer) and
90° (the frontal horizon) and will be maximum at a
depression angle of 45°. This function is identical to the
function for splay angle shown in Figure 2. However, where
splay angles over the range from -90° to +90° are all
visible in the frontal field of view, for depression angle, only
the range from 0° to +90° is visible in the frontal field of
view (from 0 to -90° is behind the observer). In many
practical situations an even smaller range of depression
angles will be available owing to limits in the frontal field of
view (e.g., occlusion that is due to the bottom edge of a
display or window). The solid segment in Figure 2 shows the
range of depression angles visible for the viewing conditions
used in our studies.
The second term in the equation for rate of change of
depression angle, (xjz) cos2 8, indexes changes in depres-
sion angle as a result of forward motion of the observer. In
the first part of this term, xg is proportional to the speed of the
observer. The term (Xg/z) is speed scaled in eyeheights. This
term has been identified as global optical flow rate (R.
Warren, 1982). Thus, the rate at which depression angle
changes is affected by both altitude and speed. The remaining part of this term (cos2 8) accounts for changes in
depression angle that are due to the initial optical position of
a texture element. Rate of change of depression angle due to
forward motion will be minimum at the horizon (90°) and
will increase to a maximum (i.e., exactly xjz) at a point
directly below the observer (0°). This can be seen in Figure
2, where the effects for a 5-ft (1.5-m) backward motion are
shown for an altitude of 25 ft (7.6 m). Thus, the lower the
texture element is in the forward field of view, the greater
will be the rate of change in depression angle for a given
speed of observer movement. Remember, however, that
much of the forward field is occluded so that only a subset of
the curve (indicated by the solid line) will normally be
visible.
Both splay angle and depression angle are components of
an expansion of texture that is associated with approach to a
surface. Lee (1976,1980) showed that this expansion pattern
may provide important information for control of locomotion in terms of tau, or time to contact. Lee's analysis reflects
Gibson et al.'s (1955) observation that although altitude and
speed are not specified unambiguously, time before touching
down is given in a "univocal manner." It is important to note
that although speed and altitude are ambiguous for the flow
of dots (global optical flow) and for the flow of horizontal
edges (change in depression angle), change in splay angle
specifies change in altitude independent of forward speed.
This point is critical to our hypothesis for predicting an
interaction between texture (depression angle, which is
perpendicular to the line of motion, versus splay angle,
which is parallel to the line of motion) and forward speed for
the perception and control of altitude.
Human Performance
Wolpert, Owen, and Warren (1983) compared observers'
ability to detect loss in altitude in a simulation of flight with
constant forward speed using three types of texture, as
shown in Figure 4: splay (parallel, vertical, or meridian)
texture, depression (perpendicular, horizontal, or lateral)
texture, and grid (square or checkerboard) texture. They
chose splay texture to isolate the information available from
optical splay, and they chose depression texture to isolate the
information available from global optical density. The
results indicated that observers were best able to detect loss
in altitude with splay texture. Performance was nominally
worse with grid texture and was significantly worse with
depression texture. A number of similar studies were summarized by Wolpert (1987; Wolpert & Owen, 1985). Wolpert
(1987) noted that in these studies, "loss of altitude scaled in
eyeheights proved to be the functional variable, performance
improving over increasing levels of that variable. In contrast, ground-unit-scaled loss in altitude showed a minimal
effect over the different levels" (p. 24). Because the rate of
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FLACH, WARREN, GARNESS, KELLY, AND STANARD
GRID
SPLAY
DEPRESSION
Figure 4. Three types of texture that have been used to isolate components of the expansion pattern
associated with change in altitude. Grid texture simulates a checkerboard ground surface. It includes
both splay and depression angles. Splay texture simulates vertical strips of texture parallel to the
forward direction of motion. It isolates splay angle as a source of information for altitude. Depression
texture simulates horizontal strips of texture perpendicular to the forward motion path. It isolates
depression angle as a source of information for altitude.
change of optical splay is directly related to change of
altitude scaled in eyeheights (—[zlz]) whereas optical density is related to change in altitude scaled in ground units,
splay was nominated as the effective source of information
for judging change in altitude. At that time, no analysis of
depression angle had been made. This conclusion must be
reconsidered in light of the analysis of change in depression
angle, which shows that change of visual angle in the
depression texture also scales with fractional change in
altitude.
Johnson, Tsang, Bennett, and Phatak (1989) employed a
strategy similar to that used by Wolpert et al. (1983) to
isolate the optical information available for control of
altitude. They used three texture types: splay texture only,
which isolates optical splay; depression texture (with a
single meridian-line roadway to indicate flight path), which
was intended to isolate optical depression angle; and grid
texture, which contains both optical splay and optical
depression information. Unlike Wolpert et al., who measured performance in a passive psychophysical judgment
task, Johnson et al. used an active control task. Johnson et al.
introduced disturbances in both the vertical and lateral axes.
Participants were to minimize the effects of the vertical
disturbance using a single-axis velocity control. Participants' control actions had no effect on the lateral disturbance. The lateral (side-to-side) disturbance was introduced
to prevent participants from using local information such as
the position of a meridian texture line on the bottom of the
display (e.g., distance from the corner of a rectangular
display) to control altitude. In apparent contradiction to the
results of Wolpert et al., Johnson et al. found superior
performance (lower tracking error) with the depression and
grid textures. Higher tracking error was found for the splay
texture.
A second study by Johnson and his colleagues (Johnson,
Bennett, O'Donnell, & Phatak, 1988) examined active
control of altitude in a hover task. In this task, Johnson et al.
included disturbances on three axes: altitude (z), lateral (Yg;
visible only in splay texture), and fore-aft (xg; visible only in
depression texture). Performance was examined for numerous texture types, four of which were of particular interest
for the present discussion: splay, depression, grid, and dot.
The results showed equivalent performance (both in terms of
tracking error and correlated control power) for depression,
grid, and dot textures. Performance with the splay texture
showed greater tracking error and lower correlated control
power. Again, this result is in apparent contradiction to the
findings of Wolpert et al. (1983).
Two differences between Johnson et al.'s (1988, 1989)
studies and the earlier work of Wolpert et al. (1983) were the
inclusion of disturbances on axes other than the altitude axis
and the use of an active control task. Wolpert (1988) used an
active altitude regulation task with disturbances in altitude
and roll (participants controlled only altitude). Note that a
roll disturbance affects the optical activity of both parallel
and perpendicular textures, but not the angular relations of
splay and depression angles. Wolpert (1988) found that
"altitude was better maintained over parallel [splay] texture
than over square [grid] or perpendicular [depression] texture" (p. 17). Wolpert found that whether the roll disturbance
was included had no effect on performance.
Flach et al. (1992) also measured performance in an active
control task with disturbances similar to those used by
Johnson et al. (1988), except that whereas Johnson et al.
used a hover task, Flach et al. used a task with forward
velocity so that the fore-aft disturbance, implemented as a
variable headwind, affected forward velocity, not position.
Flach et al.'s results were consistent with Wolpert's (1988).
Performance was best with splay and grid textures—both of
which contain splay information. Performance was poor in
the depression texture conditions, contrary to Johnson et
al.'s results.
Wolpert (1988) also included optical flow rate as a
variable in his study. He found a performance decrement for
increasing levels of global optical flow rate. This is consistent with the results of previous research by Wolpert and
Owen (1985). They used global optical flow rates corresponding to walking speed (1 eyeheight/s) and very low flight
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ALTITUDE CONTROL
(0.25 and 0.5 eyeheights/s) and found that detection of
descent over square texture deteriorated with increasing
global optical flow rates. This is interesting in light of the
optical analysis presented earlier. Optical splay angle is
independent of global optical flow rate. However, optical
depression angle is dependent on global optical flow rate.
Global optical flow rate (Xg/z) changes as a function of
altitude (z). However, changes in global optical flow are not
specific to altitude. Global optical flow is directly proportional to forward velocity (xg) and inversely proportional to
altitude. This ambiguity had been previously noted in the
optical analysis of Gibson et al. (1955).
It is interesting to note that the global optical flow rates
examined by Wolpert (1988) and Flach et al. (1992) were all
greater than 0.25 eyeheights/s. However, the optical flow
rates examined by Johnson et al. (1988,1989) ranged from 0
for the hover task to 0.25 eyeheights/s. Thus, in the Johnson
et al. studies the optical flow rates were lower than in
previous studies. Also, in each of the studies discussed
above, the texture that isolated the most effective optical
information (whether splay or depression angle) always
yielded performance that was superior to (though not
typically significantly superior to) the texture that combined
the two sources of information (grid or dot texture). Wolpert
et al. (1983) and Wolpert (1988) found that performance was
better with splay texture than with grid texture. Johnson et
al. (1988, 1989) found that performance was better with
depression texture than with grid or dot textures. Also, R.
Warren (1988) found that altitude control with splay-only
texture was superior to that with splay-plus-superimposeddot texture. Why does the combination of multiple sources
of information result in performance degradation?
Perhaps the optical activity resulting from forward motion
(global optical flow rate) makes it more difficult for the
observer to pick up the optical activity that specifies changes
in altitude. In splay-only textures, global optical flow rate is
invisible, so there should be no interference. If the rate of
forward motion is slow or altitude is high, then the
contribution of global optical flow will be small, so interference will be small. But if global optical flow rate is high and
can be seen in the display (i.e., perpendicular texture
elements or dots are present in the display), then the "noise"
created by this optical activity may make it difficult for the
observer to distinguish changes in altitude from changes of
fore-aft position.
Table 1 shows optical activity as a function of texture and
motion. In the experiments reviewed, altitude motion is the
"signal" to which observers should be responding. Optical
activity from fore-aft or lateral motions is "noise." By
"noise" we do not mean random or unstructured activity. We
mean simply that it is not correlated with the control
dimension. Thus, it is at least uninformative, and perhaps it
is even misinformative (noise) to the extent that it makes it
more difficult to pick up the dimensions of flow that are
informative (i.e., correlated with the control dimension). The
hypothesis posed by Flach et al. (1992) suggests that
differential signal-to-noise ratios across the experiments
caused the variations in performance observed. We tested
this hypothesis in the following experiments.
Table 1
Source of Optical Activity
Noise
Signal
Texture
Grid
Altitude
- cos 5 sin S
,z
Fore-aft
— cos2 8
Lateral
—
cos2S
— - cos 8 sin 8
Dot
/z\
- - cos S sin 5
xg\
— cos2 8
- - cos 8 sin 8
Depression
Splay
z\
- cos 8 sin 8
z/
z\
- cos S sin 5
- cos2 8
Z;
z/
Z
cos2 5
Experiment 1
We designed this experiment to evaluate possible interactions between the type of texture available to an observer
and the observer's forward speed. Four types of textures
were used. This included the three textures shown in Figure
4 plus a texture composed of randomly distributed dots. We
chose a range of forward speeds to span those speeds used in
previous studies (0, 0.25, 1, and 4 eyeheights/s). The
hypothesis was that depression texture would result in
performance mat was better or equivalent to that for other
textures for the 0 eyeheights/s speed but that for all other
forward speeds, splay texture would lead to superior performance. Dot and grid textures were predicted to result in
intermediate levels of performance at all levels of forward
speed. In other words, performance with depression texture
should get worse with increasing forward speed. Performance with splay texture should be independent of forward
speed.
Method
Participants. There were 12 participants, with 6 in each group.
Participants were all right-handed men with normal or corrected-tonormal vision. They were recruited from a contractor participant
pool at the Armstrong Laboratory at Wright-Patterson Air Force
Base and were paid at the rate of $5 per hour. Six were nonpilots
and 6 were licensed civilian fixed-wing pilots with ratings ranging
from private pilot through flight instructor. None were airline
transport pilots. One also held a helicopter license. Four held
instrument ratings. Flight experience ranged from approximately
150hrtoover500hr.
Apparatus. A 33-MHz 386 computer with an XTAR Falcon
4000 Graphics board set was used to generate the real-time
graphics displays. These 1,024 X 768 pixel displays were projected
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FLACH, WARREN, GARNESS, KELLY, AND STANARD
onto a 7.6 X 5.7 ft (2.3 X 1.7 m) front projection screen using a
high-resolution Electrohome ECP3000/4000 projection system.
Each participant was seated approximately 5.8 ft (1.8 m) from the
projection screen. Thus, the display subtended 66.47° of visual
angle in the horizontal direction and 51.87° in the vertical direction.
Participants wore occluding goggles that permitted a monocular
circular field of view of approximately 40°. When the participant
was looking at the aim point, the edges of the screen were outside
this field of view. Participants' heads were not fixed, so it was
possible for them to scan the display and to look at edges—
however, they were instructed to look straight ahead.
Scene. The software for the real-time interactive graphics used
in the experiment was developed by Engineering Solutions, Inc.
(Columbus, OH). The ground was simulated as an island 125,000 ft
(38,100 m) long and 800 ft (244 m) wide. For the splay texture
condition the island was textured by 20 columns (40 ft [12.2 m]
across). For the depression texture condition the island was
textured by 500 rows (250 ft [76.2 m] deep). For the grid texture
condition the island was textured with ground-colored (various
shades of green) rectangular patches. These patches measured 40 ft
(12.2 m) across and 250 ft (76.2 m) in depth. For the dot texture
condition the island was textured by small triangles. The number of
triangles was equal to the number of intersections in the grid
display. The triangles were randomly displaced from the grid
intersection positions by up to half the distance between intersections. The result was a randomly appearing texture pattern. The
triangle texture elements changed size appropriately to the perspective.
Task. A Gravis two-dimensional spring-loaded joystick was
used for control input. Rate of change of altitude was proportional
to joystick displacement in the fore-aft direction (velocity control
dynamics). Thus, altitude was manipulated directly; there were no
intervening changes in pitch. Therefore, the simulated vehicle
behaved more like a flying elevator than like a fixed-wing aircraft.
The objective was to maintain a constant altitude in the presence
of wind disturbances. Wind disturbances were applied to three
axes: up-down, or altitude; headwind-tailwind, or fore-aft; and
right-left, or lateral. Three different wind disturbances each were
composed of a sum of five sine waves of different frequencies—
two low-frequency sine waves with amplitudes of 10.74 ft (3.27 m)
and three higher frequency sine waves with amplitudes of 4.80 ft
(1.46 m). The root-mean-square (RMS) for the disturbance was
7.75 ft (2.36 m), which is comparable to a 90th-percentile wind (a
strong wind gust). The frequencies for the three disturbances (high,
medium, or low) were chosen so that there was an interleaving
between frequencies. The interleaving allows the use of frequency
as a signature for tracing the disturbances through the control loop.
Correlations between power in the disturbances and power in the
human's control actions can be used to infer which disturbances are
driving the control actions.
Procedure. Each participant was tested over 2 days. Participants received two blocks of trials per day. Each block contained 16
trials. The 16 trials within a block resulted from the crossing of four
textures with four speeds. A different random order of conditions
was used for each of the four blocks. Each trial was 130 s and
consisted of a 10-s preview interval in which the participant viewed
the scenes without control or any wind disturbance (to establish a
visual altitude reference), followed by a 10-s ramp-in of the
disturbance, at which point the participant was given control,
followed by a 100-s data-collection interval and a final 10-s
ramp-out of the wind disturbance. An auditory tone signaled the
end of the preview period. Participants were instructed to view the
scene during the 10-s preview period in order to establish the target
altitude (25 ft [7.6 m]). Once the tone sounded, they were to
maintain a constant altitude (i.e., null out the effects of the wind
disturbance on the vertical axis). Although disturbances were
presented on three axes (up-down, side-to-side, and fore-aft), the
participants could control only altitude (up-down).
Design. A 4 X 4 X 4 X 2 mixed design was used, with texture
(grid, dot, horizontal, and vertical), initial global optical flow rate
(0, 0.25, 1, and 4 eyeheights/s), and repetition (1-4) manipulated
within subjects. Experience was a between-subjects factor (half the
participants were pilots, and half had no flight experience). The
dependent variables included root-mean-square height error (RMSE)
and correlated control power (CPP) between the control inputs and
the disturbances on each axis.
Results
RMSE was used as a measure of the participants' ability
to maintain a constant altitude. A square-root transform was
performed on the RMSE data because the variance tended to
scale with the mean. That is, participants in the depression
texture condition had a higher mean and had greater
variance. The transformed data were evaluated with a 4 X
4 X 4 X 2 mixed-design analysis of variance (ANOVA).
The predicted interaction between texture type and flow
rate was found to be significant, F(9, 90) = 2.09, p = .039,
T|2 = 1.32. As shown in Figure 5, the RMSE for the splay,
grid, and dot textures was relatively constant across levels of
flow rate. However, the RMSE for the depression texture
increased with increasing flow rates. This pattern is consistent with our hypothesis. No other interactions were significant.
Significant main effects were found for texture type, flow
rate, and repetitions. For texture type, RMSE increased from
21.34 ft (6.50 m) for splay texture to 78.85 ft (24.03 m) for
depression texture, F(3, 30) = 27.86, p < .001, t\2 = 21.32.
Grid and dot textures were intermediate, with RMSEs of
26.83 ft (8.18 m) and 43.03 ft (13.12 m), respectively. For
flow rate, RMSE increased with increasing flow rate (35.52
[10.83 m], 37.33 [11.38 m], 39.19 [11.95 m], and 48.02 ft
[14.64 m] for the 0, 0.25, 1, and 4 eyeheights/s flow rates,
respectively), F(3, 30) = 6.08, p = .002, rf = 1.09.
Repetitions showed a reduction in RMSE with practice from
49.70 ft (15.15 m) on the first block to 32.38 ft (9.87 m) for
the fourth block, F(3, 30) = 2.96, p = .039, t\2 = 1.84. The
main effect of experience was not significant, F(l, 10) =
4.48, p = .06, T|2 = 5.61. However, pilots did perform
nominally better with all texture types (RMSE = 29.92 ft
[9.12 m]) than did nonpilots (RMSE = 51.12 ft [15.58 m]).
The second dependent measure, CCP, evaluated the
correlation between power in a participant's control input
and power in the disturbance as a function of frequency. If
the correlation is high, then the control activity is specific to
the disturbance. Figure 6 shows power as a function of
frequency for both control and the three disturbances for a
sample participant. Note that the peaks in the control power
spectrum correspond to the peaks in the spectrum for the
altitude disturbance. This indicates that this participant's
1771
ALTITUDE CONTROL
120 T
100-
depression
&
iu
60- •
dot
40' •
20' •
splay
0
1
2
Global Optical Flow Rate (eyeheight/s)
3
4
Figure 5. Significant interaction between texture type and forward flow rate (in eyeheight/s) for
root mean square (RMS) altitude error (in feet; 1 ft = 0.3048 m) found in Experiment 1. Error for
depression texture increases with increasing flow rate. Error for splay texture is independent of flow
rate.
30-
i
25-
j.
20- ,
;•
>!
Disturbances
f
Ij
Fore-aft
1
• '.
I
'
1
10-
!if
!i
5 •
1
' JU, i
0.5
!
Lateral
Altitude
U Ji ft H AA-- S ,HA
1.5
2.5
,
3.5
30
25
20
Control Inputs (stick)
10- •
0.5
1.5
4-
•H
2
2.5
3.5
Frequency (radians/s)
Figure 6. Spectral analysis of three disturbance inputs (altitude, fore-aft, and lateral) and
participant's control output. Relative power is shown as a function of frequency. Note correspondence between peaks in control spectrum and peaks in the altitude disturbance.
1772
FLACH, WARREN, GARNESS, KELLY, AND STANAR0
control responses were specific to the gust-induced changes
in altitude.
Because of software error, CCP data for the grid and dot
textures were not collected at all flow rates. A 4 X 3 X 2 X
4 X 2 mixed-design ANOVA was performed on the CCP
data for the other two textures. Flow rate (0, 0.25, 1, or 4
eyeheights/s), disturbance (altitude, fore-aft, or lateral),
texture (splay or depression), and repetition (1-4) were
manipulated within subjects. Experience (pilots vs. nonpilots) was the between-subjects variable.
Figure 7 shows the significant three-way interaction
between texture, flow rate, and disturbance for CCP, F(6,
60) = 3.93, p = .002, T|2 = .46. Note that the correlation
between control and the disturbances on the lateral and
fore-aft axes is very low for all textures and flow rates. The
correlations between control and the disturbances on the
altitude axis are much higher. The highest correlations were
with splay texture, and these correlations are uniformly high
across flow rates. For depression texture, the correlation is
highest at a flow rate of 0 eyeheights/s and decreases with
increasing flow rates. The two-way interactions between
texture and disturbance, F(2, 20) = 43.61, p < .001, t\2 =
9.18, and between flow rate and disturbance, F(6, 60) =
7.70, p < .001, T|2 = 1.01, were also significant. There were
also significant main effects for texture, F(l, 10) = 2.62,
p < .001, T|2 = 2.84; flow, F(3, 30) = 8.50, p < .001, if =
.47; and disturbance, F(2, 20) = 310.98, p < .001, rf =
74.96. These effects can be seen in Figure 7. Correlations
were higher for splay texture. Correlations were higher at the
lower flow rates. Finally, correlations were highest for the
altitude disturbance.
Discussion
The interactions between flow rate and texture obtained
for the dependent variables of RMSE and CCP (see Figures
5 and 7) are consistent with the signal-to-noise ratio
hypothesis. Performance with splay texture was independent
of flow rate. Performance with depression angle was best for
the flow rate of 0 eyeheights/s and deteriorated (higher
RMSE and lower correlations) with increasing levels of flow
rate. Although the interaction is consistent with the hypothesis, there was no crossover at 0 eyeheights/s. Thus, Johnson
et al.'s (1988, 1989) results remain an anomaly. In Experiment 1, even for a global optical flow rate of zero,
performance with splay texture was superior. Johnson et al.
(1988, 1989) found superior performance with depression
texture.
One explanation for the anomalous results of Johnson et
al. (1988, 1989) might be their use of local information
within the flow field to control altitude. A local strategy
might be to maintain an invariant relationship between a
specific texture element and a landmark in the field of view
(e.g., the edge of the display or, in operational environments,
the edge of the windscreen or a smudge or local discontinuity on the windscreen). Thus, the pilot might try to keep the
lowest perpendicular texture element in the field of view a
fixed distance above the bottom edge of the screen. It should
be impossible for an observer using such a strategy to
distinguish a change in altitude from any other motion that
affects the relative optical position of the edge. Consistent
with this observation, Johnson et al. (1988) found high
levels of cross talk in their participants' altitude control
0.8
splay
0.7- •
0.6- •
0.5- •
\
0.4"
a 0.3- •
1
depression
Altitude
Fore-aft
8 0.2Lateral
0.1 - •
0 ••
-0.1
1
2
Global Optical Flow Rate (eyeheights/s)
Figure 7. Significant three-way interaction between texture, flow rate, and disturbance direction
obtained in Experiment 1. The correlation between power in the participant's control and power for
each disturbance direction (altitude, fore-aft, and lateral) is shown as a function of texture (splay or
depression) and flow rate (0,0.25,1, or 4 eyeheights/s).
1773
ALTITUDE CONTROL
responses such that there was a relatively large amount of
control power correlated with the fore-aft disturbance. On
the other hand, we in Experiment 1 and Flach et al. (1992)
took care to minimize local strategies by using circular
frames so that no local cues were available in terms of
corners or edges. Also, in Experiment 1 the edge of the field
of view was created by goggles worn by the participants so
that the frame was not fixed but moved with the head. In
these studies there was little cross talk. That is, control
power was not correlated with the nonaltitude disturbances.
In summary, it seems that splay plays an important role in
the perception and control of altitude. However, other
sources of information are available and can be used. These
sources include other global variables such as optical density
and depression angle as well as local variables such as the
relative position of particular discontinuities within the field
of view. W. W. Johnson (personal communication, June
1989) has told us that helicopter pilots are sometimes trained
to maintain altitude in hover by picking out an object in their
forward field of view and keeping that object at a fixed
position on their windscreen. Note that this strategy will
work only in a hover (when one is moving across the
surface, everything flows) and that depending on where the
object is in the field of view this will result in some cross talk
as a result of fore-aft motions. Johnson and Phatak (1989)
modeled this local control strategy and found close agreement between the model and human performance in their
altitude control studies.
Experiment 2
We manipulated two dimensions of the display in Experiment 2 to test the possibility that local sources of information were the source of differences between the results of
Experiment 1 and the results of Johnson et al. (1988, 1989).
First, we manipulated viewing condition in Experiment 2a.
Half of the participants viewed the display through the
circular occluding goggles, and the other half viewed the
rectangular screen directly.
Second, we controlled the angular rate of change of
texture motion in the field of view. The angular rate of
change depends on both the motion of the observer and the
angular position of the texture element in the field of view, as
shown in Figure 2. Much of the depression texture is
occluded by the bottom edge of the screen. However, the full
range of splay texture is always in the field of view. The
positioning of texture elements in Experiment 1 resulted in
greater angular change for the splay texture. In Experiment
2, we positioned the texture elements so that the angular
rates of texture flow corresponding to a change in altitude
were geometrically equivalent for each texture type. Thus, in
Experiment 2b, we could examine the texture by flow rate
interaction with this additional control for local rates of
change.
As in Experiment 1, we included four texture types (splay,
depression, block, and dot) in Experiment 2. In Experiment
2a we examined performance in a hover condition only (i.e.,
global optical flow rate equal to 0 eyeheights/s). In Experiment 2b we compared performance at two levels of global
optical flow rate (0 and 3 eyeheights/s). The hypothesis for
Experiment 2a was that there would be an interaction
between viewing condition and texture. Performance would
be superior for depression texture in the unrestricted viewing
condition (without goggles) but would be superior for splay
texture in the restricted viewing condition (with goggles).
This prediction was based on the assumption that participants would use local cues in the unrestricted viewing
condition, as suggested by Johnson and Phatak (1989). The
hypothesis for Experiment 2b was that an interaction would
be found between texture and global optical flow rate—with
depression angle resulting in better control for hover (0
global optical flow rate) than for when a forward motion
component is present and with splay resulting in performance that is independent of forward motion.
Experiment 2a
Method
Participants. Twenty right-handed men with normal or corrected-to-normal vision served as participants. They were recruited
from the Logicon participant pool at Wright-Patterson Air Force
Base. They had no prior flight experience and were paid at the rate
of $5 per hour. Because of computer and procedural errors, data for
3 participants (1 from the goggles group and 2 from the no-goggles
group) were not included in the analyses.
Apparatus. The apparatus was identical to that used in Experiment 1 with the exception that half of the participants viewed the
66.47° (horizontal) by 51.87° (vertical) projection screen directly
with binocular vision. The other half wore occluding goggles that
allowed a monocular, circular, 40° field of view.
Scene. The ground was simulated as an island 10,000 ft (3,048
m) long and 1,000 ft (305 m) wide. For the grid texture condition
the island was textured with ground-colored (various shades of
green) rectangular patches. These patches measured 100 ft (30 m)
across and 100 ft in depth. For the splay texture condition the island
was textured by 5 columns (200 ft [61 m] across). For the
depression texture condition the island was textured by 500 rows
(200 ft deep). For the dot texture condition the island was textured
by small triangles. The triangles were distributed on the ground
according to the same procedure described for Experiment 1.
Task. The task was identical to that used for Experiment 1. The
participant's task was to maintain a constant altitude (25 ft [7.6 m])
using the information available in the visual display. Although the
flight path was perturbed on three axes (vertical, lateral, and
fore-aft), participants' control actions affected only the vertical
axis. The control dynamics on the vertical axis were first-order.
Thus, the rate of change in altitude was proportional to displacement of the stick. At the beginning of each trial there was a 10-s
preview period with no disturbances and no control possible. This
was followed by a 10-s ramp-in period in which control was
possible and in which the disturbances were gradually introduced.
This was followed by a 100-s tracking period in which performance
was measured.
Procedure. Each individual participated in 36 trials per day for
a period of 3 days. The 36 trials reflect a complete crossing of the
four textures, the three magnitudes of lateral disturbance, and the
three magnitudes of fore-aft disturbance. A trial lasted for 120 s.
Design. This experiment used a 2 X 4 X 3 X 3 mixed design.
Viewing condition (with or without occluding goggles) was
manipulated between subjects. Texture (splay, depression, grid, and
dot) was manipulated within subjects. Also, the magnitude of
1774
FLACH, WARREN, GARNESS, KELLY, AND STANARD
disturbances to the fore-aft and lateral axes of the vehicle were
independently manipulated within subjects. The magnitudes of
these disturbances were 0.1, 1, or 10 times the power of the
disturbance to altitude (RMSs of 2.45, 7.75, and 24.5 ft, respectively [0.75, 2.36, and 7.47 m]). Dependent measures included
RMSE and the correlation between control and disturbances in the
frequency domain (CCP).
Depression and grid textures showed relatively large correlations (.12 and .09) with the fore-aft disturbance. Splay
texture showed a small correlation (.06) with the lateral
disturbance. Dot texture showed the largest correlation with
the altitude disturbance (.853), which had correlations of
.837, .836, and .834 with the splay, grid, and depression
textures, respectively.
Results
The RMSE data from the third block of trials were
analyzed with a 2 x 4 X 3 X 3 mixed-design ANOVA. This
analysis showed a significant main effect for texture, F(3,
42) = 9.81, p = .017, T]2 = 3.49. Performance was best with
depression texture (9.76 ft [2.97 m]); block and dot texture
were intermediate (11.89 ft [3.62 m] and 11.49 ft [3.50 m]);
and splay texture showed the greatest error (12.39 ft [3.78
m]). There were no other significant main effects or interactions. The hypothesized interaction between viewing condition (goggles or no goggles) and texture was not significant,
F(3,42) = 0.69, p = .563, rf = .63.
The CCPs measured in the third block were analyzed with
a 2 x 4 x 3 X 3 X 3 mixed-design ANOVA. The factors
were the same as those for the RMSE analysis but with the
addition of a fifth within-subjects factor that specified the
direction of the disturbance (altitude, fore-aft, or lateral).
The effect that bears most directly on the hypothesis was a
significant interaction between disturbance and texture, F(6,
90) = 20.11, p < .001, rf- = 0.82, which is shown in Figure
8. Note the evidence for cross talk in which disturbances in
the fore-aft axis resulted in control adjustments with the grid
and depression textures and disturbances in the lateral axis
resulted in control adjustments with the splay texture.
Experiment 2b
A third group of participants were tested with a forward
global optical flow rate of 3 eyeheights/s. This group wore
goggles. In Experiment 2a we showed that the presence or
absence of goggles had no effect and did not interact with
any of the other factors. We prefer to have participants use
goggles because they reduce cues that the screen is flat and
thus enhance the illusion of motion in depth that we are
attempting to simulate. We compared the performance of
this group with the performance of the goggles group from
Experiment 2a in order to test whether geometrically
equating the absolute change in visual angle that is associated with the splay and depression textures would affect the
pattern of interaction between texture and flow rate.
Method
Participants. Nine additional right-handed men were tested in
the high forward flow condition. These participants were also
recruited from the same pool and paid at the same rate as the
participants in Experiment 2a.
Procedure. The scenes, task, and procedures were identical to
those of Experiment 2a except that instead of the zero forward flow
Bfore-aft D lateral §3altitude
Dot
Depression
Splay
Texture Type
Figure 8. Significant interaction between texture (grid, dot, depression, or splay) and disturbance
direction (fore-aft, lateral, or altitude) for correlated control power found in Experiment 2a.
1775
ALTITUDE CONTROL
rate that was simulated in Experiment 2a, a flow rate of 3
eyeheights/s was simulated for this group.
Design. This experiment used a 2 X 4 x 3 X 3 mixed design.
Global optical flow rate (0 or 3 eyeheights/s) was manipulated
between subjects. Texture (splay, depression, grid, and dot) was
manipulated within subjects. Also, the magnitude of disturbances
to the fore-aft and lateral axes of the vehicle were independently
manipulated within subjects. The magnitudes of these disturbances
were 0.1, 1, or 10 times the power of the disturbance to altitude.
Dependent measures included RMSE and the correlation between
control and disturbances in the frequency domain (CCP).
Results
A 2 X 4 X 3 X 3 mixed ANOVA was used to analyze the
RMSE dependent measure. This analysis showed a significant interaction between texture and flow rate, F(3, 48) =
13.88, p < .001, T|2 = 7.00, as shown in Figure 9. For the
zero flow rate condition, RMSE is lower with depression
texture, but for the higher flow rate (3 eyeheights/s), RMSE
is lower with splay texture. This crossover interaction is
exactly what would be predicted by the signal-to-noise
hypothesis. Error with splay texture was independent of flow
rate. Error increased for the three other textures (grid, dot,
and depression), all of which contain increased optical
activity associated with the forward flow. The increase was
most notable for the depression texture, which contains no
splay information for altitude change. There was also a main
effect for texture, F(3, 48) = 9.68, p < .001, rf = 4.88.
Overall, RMSE was lower for splay texture (13.4 ft [4.1 m])
than for depression texture (23.96 ft [7.30 m]). There was
also a main effect for flow rate, F(l, 16) = 48.26, p < .001,
T|2 = 14.32. Error was lower for the lower flow rate (11.27
vs. 26.42 ft [3.44 m vs. 8.05 m]).
The CCP data were analyzed with a 2 X 4 X 3 X 3 X 3
mixed-design ANOVA. The factors were the same as those
40
for the analysis of RMSE but with the addition of a fifth
factor—the disturbance direction (fore-aft, lateral, and altitude). Figure 10 shows the significant three-way interaction
between texture type, flow rate, and disturbance direction,
F(6, 96) = 20.411, p < .001, r? = 0.68. Most notable in
Figure 10 is the pattern of CCP for the altitude disturbance.
CCP is uniformly high across textures for the flow rate of 0
eyeheights/s, but there is a clear reduction in power correlated with the altitude disturbance for the depression texture
at the flow rate of 3 eyeheights/s. Also, there are small peaks
associated with the fore-aft disturbance for the depression
and grid textures and for the lateral disturbance with the
splay texture at the low (zero) flow rate; this cross talk is
washed out in the higher flow condition. These patterns
again are consistent with the signal-to-noise hypothesis.
Discussion
The null result associated with viewing condition in
Experiment 2a suggested that the differences in local cues
that are associated with the corners of the screen were not a
factor. The results of both Experiments 2a and 2b support the
hypothesis that the value of particular textures as information for the control of altitude depends on the presence of
global optical flow. The support can clearly be seen in the
crossover interaction for RMSE (see Figure 9). In the hover
condition (0 eyeheights/s, no global optical flow), the
depression texture resulted in lower RMSE. These results
are consistent with the results of Johnson et al. (1988,1989)
for altitude control at low flow rates. However, for high
global optical flow rates, the splay texture resulted in better
performance, which is consistent with the results of previous
studies (Flach et al., 1992; R. Warren, 1988; Wolpert, 1988;
Wolpert & Owen, 1985; Wolpert et al., 1983) that tested
altitude control with high global optical flow rates.
BO eyeheight/s D3 eyeheights/s
35
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o
£ 25
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1 20 +
< 15-CO
DC
10
5 ••
Grid
Depression
Dot
Splay
Texture Type
Figure 9. Significant interaction between texture (grid, dot, depression, or splay) and forward flow
rate (0 or 3 eyeheights/s) for root mean square (RMS) altitude error (in feet; 1 ft = 0.3048 m) found
in Experiment 2b.
1776
FLACH, WARREN, GARNESS, KELLY, AND STANARD
Correlated
Control Power
3
0
3
Lateral
Altitude
Global Optical
Flow Rate
Fore-aft
Texture Type
Figure 10. Significant three-way interaction between texture type (grid, dot, depression, or splay),
flow rate (0 or 3 eyeheights/s), and disturbance direction (altitude, fore-aft, or lateral) for correlated
control power found in Experiment 2b.
An important difference between Experiment 2 and
Experiment 1 was that in Experiment 2, differences in the
rate of angular change in the optic flow field that were due to
the position of the texture elements in the field of view were
equated for the depression and splay textures. The distances
for the nearest splay-texture elements were equated to the
distance for the nearest visible depression-texture element.
This allowed a cleaner comparison of splay angle and
depression angle, unconfounded by differences in the magnitude of the angular changes associated with the different
textures.
The results of Experiment 2 are consistent with the
hypothesis suggested by Flach et al. (1992) that the ability to
pick up information about altitude from optic flow depends
on the amount of optical flow activity specific to altitude
(signal) relative to the flow activity arising from other
factors (e.g., motion in the fore-aft and lateral axes—noise).
The optical flow that results from forward motion (global
optical flow rate) is visible in the depression, dot, and block
textures. This "noise" makes it more difficult to differentiate
the optical activity specific to changes in altitude. With splay
texture, there is no change in the flow as a result of forward
motion. Therefore, performance with splay texture is independent of global optical flow rate. The cross talk evident in
Figures 8 and 10 is consistent with this hypothesis. Increased
CCP with the fore-aft disturbance (noise) is seen with
depression texture. Increased CCP with the lateral disturbance (noise) is seen with splay texture. The Flach et al.
hypothesis provides an explanation for these data and
accounts for results from previous studies that had appeared
to be inconsistent.
Experiment 3
The altitude tracking task used in Experiments 1 and 2
allowed the use of frequency analyses to trace the impact of
the altitude, fore-aft, and lateral disturbances on the participants' control actions. This was an important test of the
signal-to-noise hypothesis. In Experiment 3 we used an
alternative task. In this experiment, trials were initiated at a
high altitude and participants were asked to bring the plane
as close as possible to the ground and to maintain level flight
at the lowest possible altitude without crashing into the
ground. Dependent variables included the rate of descent,
the altitude at which asymptote was achieved, and the
variability about the asymptote. We used this alternative task
to test the generality of the inferences we made using the
altitude tracking task.
The hypothesis was that the rate of descent and the
asymptote would differ as a function of the quality of
information available to the participant. If altitude is well
specified, then high rates of approach and low asymptotes
are expected. If altitude is not well specified, then a more
conservative performance profile is expected in which the
participant compensates for the lack of information by
maintaining a buffer between the plane and the ground. We
predicted an interaction between forward speed and texture.
At low forward speeds we expected depression texture to
provide the best information for altitude control. At higher
speeds, we predicted splay texture would provide the best
information for altitude control.
Method
Participants. Eighteen right-handed men were recruited from
the Logicon participant pool at Wright-Patterson Air Force Base.
Participants had no previous experience with the task. They
participated in three experimental sessions (approximately 1 hr per
session) over 3 days. They were paid $5 per hour for their
participation. Also, a $10 bonus was paid to the participant in each
of the three velocity conditions who had the fewest crashes during
the third block of trials.
ALTITUDE CONTROL
Apparatus. The apparatus was identical to that used in Experiments 1 and 2. Participants wore the occluding goggles and thus
had a monocular view of approximately 40°.
Scene. The software for the real-time interactive graphics used
in the experiment was the same program used in Experiments 1 and
2. The ground was simulated as an island 100,000 ft (30,480 m)
deep and 1,000 ft (305 m) wide. For the grid texture condition the
island was textured with ground-colored (various shades of green)
rectangular patches. These patches measured 125 ft (38 m) across
and 125 ft in depth. For the splay texture condition the island was
textured by 8 columns (125 ft across). For the depression texture
condition the island was textured by 800 rows (125 ft deep). For the
dot texture condition the island was textured by small triangles (5 ft
[1.5 m] per side), as described for previous experiments.
Task. A Gravis two-dimensional spring-loaded joystick was
used for control input. Rate of change of altitude was proportional
to joystick displacement in the fore-aft direction (velocity control
dynamics).
A trial began at an altitude of 400 ft (122 m). The participants
were instructed to descend as close as possible to the ground
without passing through it (i.e., crashing). Once they were as close
to the ground as possible, they were to maintain level flight while
keeping as close to the ground as possible without crashing. Wind
gust disturbances were applied to the altitude, fore-aft, and lateral
axes.
Procedure. There were three groups of 6 participants. Each
group received a single level of forward speed (0, 35, or 70 ft/s [0,
10.7, or 21.3 m/s]). Participants took part in three blocks of trials
over 3 days. A block consisted of 24 trials—six replications of each
of the four texture types. A different random order of trials was used
1777
in each block. A trial lasted 103 s. The trial began with a 3-s
preview period with no control and no wind disturbances. This was
followed by a 5-s period in which the wind disturbances were
gradually ramped in. There were then 90 s for data collection. The
trial ended with a final 5-s period in which the wind disturbances
were gradually ramped out.
Design. This experiment used a 3 X 3 X 4 mixed factorial
design. Three levels of speed were manipulated as a betweensubjects variable (0, 35, or 70 ft/s [0, 10.7, or 21.3 m/s]). Blocks
and texture type were manipulated as within-subjects variables.
Performance was measured over three blocks of 24 trials each.
Four different textures similar to those used in the other experiments were used (grid, dot, depression, and splay). Dependent
measures include the rate of approach, asymptote level, and
variability about the final asymptote. The rate of approach and
asymptote level were derived from fits of the time histories to an
exponential model of approach. This fit is illustrated in Figure 11,
which shows actual time history data for a participant and the
model fit to the data. The equation for the model was as follows:
altitude = (400 - a) Xe-r<'-*> + a
where a is the asymptote, r is the rate of approach, t is time, and k
reflects delays in initiating the descent response. Values for these
parameters were derived on the basis of a nonlinear least squares fit
to participants' time histories for each trial from the final experimental session (Day 3). For the trial shown in Figure 11, a = 16.61, r =
.2238, and k = 8.114. This model provided very good fits for most
of the time histories.
250 n
200
• raw dat •
•model •
- residual
150
g
jj 100-
SO' •
IJ\
38.'
'./jfO
* V50
V
60
70
./"SO
90
-so-1Time (s)
Figure 11. A sample of a typical time history (altitude in feet [ 1 ft = 0.3048 m] as a function of time
in seconds; dotted line) and the exponential model (altitude = [400 — a] X e -»<'~*> + a; solid line)
for approach to the surface obtained for Experiment 3. Values for the model parameters were as
follows: a = 16.61, r = .2238, k = 8.114.
100
1778
FLACH, WARREN, GARNESS, KELLY, AND STANARD
Results
Data for 1 participant from the hover (global optical flow
rate = 0) group were not included in the final analysis. The
performance of this participant clearly deviated from the
group means. This participant alone accounted for 54% of
the variance on the dependent variable of rate of approach
and 64% of the variance on asymptote level.
The mean value for the asymptote for the exponential
approach to the surface was 25.37 ft (7.73 m; SD = 11.76).
This is very close to the target altitude of 25 ft (7.6 m) used
in Experiments 1 and 2. The asymptote data for the last
session were analyzed with a 3 X 4 mixed-design ANOVA.
Velocity (0, 35, or 70 ft/s [0, 10.7, or 21.3 m/s]) was a
between-subjects variable. Texture type (grid, dot, depression, or splay) was a within-subjects variable. Figure 12
shows the interaction between texture type and flow rate.
This interaction was significant, F(6,382) = 3.93, p < .001,
T|2 = 3.14. No other effects were significant for this measure.
The mean value for the rate of exponential approach to the
surface was 0.2348 (SD = 0.0412). At this rate of approach,
participants would be within 3.5 ft (1 m) of an asymptotic
level of approximately 25 ft (7.6 m) from the initial altitude
of 400 ft (122 m) in approximately 20 s. The rate data for the
last session were analyzed with a 3 X 4 mixed-design
ANOVA identical to that used for the asymptote data. Again,
the predicted interaction was significant, F(6, 382) = 2.37,
p = .029, T|2 = 3.00, as shown in Figure 13. No other effects
were significant for this measure.
Discussion
The interaction pattern for the asymptote (see Figure 12)
did not completely conform to our expectations. For the dot
and depression textures, the asymptotes were closer to the
ground at low speeds than at higher speeds. This is
consistent with expectations; because both textures contain
depression information, there should be increased "noise"
with respect to the altitude control task at the higher speeds.
Thus, participants were expected to maintain a greater safety
cushion to compensate for the lower signal resolution. This
was also expected for the grid texture, but the trend was in
the opposite direction. Also, no effect of increasing speed
was expected for the splay texture, because there should be
no optical effect of the increasing speeds. However, the data
show that the asymptote was lowest for the splay texture
when the speed was lowest.
The interaction pattern for the rate of approach (see
Figure 13) was more consistent with our expectations. For
all textures containing depression information (grid, dot, and
31 T
Dot
29— - __ _o Depression
27-
_ 25- •
£
2 23 +
Grid
E
"* 21 • •
19- •
17- •
15
35
70
Speed (ft/s)
Figure 12. Significant interaction between texture type (grid, dot, depression, or splay) and flow
rate (0, 35, or 70 ft/s) [0,10.7, or 21.3 m/s]) for the asymptote (in feet; 1 ft = 0.3048 m) of approach
in Experiment 3.
ALTITUDE CONTROL
0.26 T
0.25-
Splay
0.24 •
0.23 - •
0.22-Depression
0.21
35
70
Speed (ft/s)
Figure 13. Significant interaction between texture type (grid, dot,
depression, or splay) and flow rate (0, 35, or 70 ft/s [0,10.7, or 21.3
m/s]) for the rate of approach to asymptote in Experiment 3.
depression), the rate of approach was highest for the lowest
flow rate and lowest for the higher flow rate. Again, this may
reflect the signal-to-noise ratios. At the higher flow rates,
"noise" from the optical changes that are due to forward
motion results in a more cautious approach toward the
ground. For the splay texture, the variation across flow rates
was smaller and the'trend was in the opposite direction.
Because speed has no optical consequences for the splay
texture, it should not influence the ability to discriminate
changes in altitude.
General Discussion
The pattern of results across the three experiments was
generally consistent with the signal-to-noise hypothesis of
Flach et al. (1992). The hypothesis was that performance on
the altitude regulation task depended on the ratio of the
optical activity due to altitude (signal) to the optical activity
arising from other sources (noise). Table 1 shows how the
four textures affect the signal and noise components of optic
flow. The specific prediction derived from this hypothesis
was an interaction between texture and forward flow rate
(i.e., global optical flow rate) such that control would
deteriorate for the depression texture with increasing flow
rates but would be good and independent of flow rate for the
splay texture. The reason for this prediction is that the
forward flow rate is visible with the depression texture and
thus is an increasing source of noise (i.e., optical activity
unrelated to changes in altitude) with increasing forward
speeds. Forward flow is invisible for the splay texture, and
thus no increase in noise results with increased forward flow
rate. Such interactions were found in all three experiments.
1779
The results of these experiments have important implications for an examination of the visual system within the
framework of ideal observer theory (see Crowell & Banks,
1996). The differential performance found for the splay and
depression textures seems to reflect differences in the quality
of the information (signal-to-noise ratio) and not differential
attunement or sensitivity of the visual system to a specific
component of the optical expansion pattern (i.e., splay angle
or depression angle). Thus, when information is most
nearly equivalent for the two components (0 forward flow
and equivalent initial angular positions in the field of view),
near equivalent performance is observed. This is most
clearly illustrated in Figure 8, which shows equivalent levels
of CCP for the splay and depression textures, and in Figure
9, which shows similar levels of RMSE for the splay and
depression textures for zero forward flow rate.
Although performance is equivalent when the signal-tonoise ratios for the two textures are similar, there are a
number of factors that contribute to an information bias in
favor of the splay texture. First, as shown in Figure 2, the
complete range of splay angles is normally visible in the
field of regard, whereas only a limited range of depression
angles is normally visible. Also, the range of visible splay
elements will normally include the points of maximal
absolute optical change (±45°), whereas this will seldom be
the case with depression texture.
A second factor that contributes to an information bias in
favor of the splay texture as information for altitude change
is the ubiquitous forward (or fore-aft) motion associated
with locomotion. Such motion is a source of noise for
depression texture but is not visible in splay texture.
Whenever significant forward motion is present there is a
decline in the ability to regulate altitude with the depression
texture. No such decline is evident for the splay texture.
A final factor that contributes to an information bias in
favor of splay texture is a distinction in the symmetry of
effects that are due to lateral motion and altitude change on
splay angle. Changes in altitude have symmetric effects on
splay angle. That is, a change in altitude has equal and
opposite effects for splay textures equal distances from the
right and left of the forward motion path. Lateral motion has
an asymmetric effect on splay angle. Splay angle decreases
for texture elements in the direction of the motion and
increases for texture elements in the direction opposite that
of the motion. Similar differences in symmetry are also
present for depression angle; however, because of limits in
the field of view, these asymmetries in depression angle are
generally not visible. The difference in symmetry that is
visible for splay is information that observers can use to
distinguish optical activity associated with change in altitude from optical activity associated with lateral motion.
There is an important caveat with regard to the optimal
observer framework and the signal-to-noise hypothesis used
here. Generally, the noise in the optimal observer framework
reflects resolution of the visual processing system (e.g.,
different resolutions of the central and peripheral retina—
Crowell and Banks, 1996). However, in the context of our
experiments, the distinctions between signal and noise arise
from the specific experimental task used. Optical changes
1780
FLACH, WARREN, GARNESS, KELLY, AND STANARD
arising from forward or lateral motion are only noise relative
to the goal of discriminating changes in altitude. A strong
case could be made that this task is not representative of
natural locomotion. In natural locomotion, all disturbances
(altitude, fore-aft, and lateral) are important signals. In fact,
it might be further argued that higher order relational
properties of these components are the true signals that
guide locomotion. For example, with a fixed-wing aircraft,
altitude depends on airspeed. Increased airspeed results in
increased lift (a gain in altitude); reduced airspeed results in
a reduction in lift (a decrease in altitude). Thus, we should be
careful in generalizing the results from the experiments
reported here to the general problem of control of locomotion. This caveat applies equally well to all of the studies on
altitude control that have been reviewed in the introduction.
A second caveat concerns the use of the term noise to
characterize the optical effects that are due to movements in
axes other than the vertical axis. Two types of disturbances
were used. One type of disturbance was a sum-of-sines
disturbance. This disturbance was applied to both the
fore-aft and lateral axes. In zero forward flow conditions
this was the only type of noise present. This was noise in the
sense that the effects were variable and not easily predicted
by the actor. The other type of disturbance was that due to
the forward flow rate. This was noise in the sense that the
optical effects were irrelevant to the problem of controlling
altitude. However, the effects of forward flow rate were
constant within a trial. It has been suggested by W. W.
Johnson (personal communication, March 1995) that the
effect of flow rate might be better understood in the context
of a Weber fraction. That is, the ability to see changes in the
optical activity (i.e., that are due to change in altitude) may
depend on the base level of optical activity. In this sense,
global optical flow rate is not noise in the sense of being an
unpredictable or quasi-random disturbance. Rather, it establishes the baseline from which observers are sensitive to
fractional changes. Thus, with increasing flow rate, proportionally greater changes in altitude are required to yield the
same perceptual effect.
A third caveat concerns the notion of equating information. Splay and depression angles are qualitatively different
kinds of angles as they appear in the field of view. Thus,
equating them in terms of optical rates of change does not
necessarily mean that they are psychophysically equivalent.
It will be important to test the psychophysical equivalence of
these two sources of information directly. A psychophysical
program is needed to evaluate the relative sensitivities to the
various optical changes.
To end the discussion, we raise a final puzzle for future
research. In terms of distinguishing optical changes in
depression angle that are due to a change in altitude from
those that are due to a change in fore-aft position (e.g.,
global optical flow rate), what is the ideal field of view? Or
what is the ideal field of regard—where should the observer
look, out toward the horizon or further down in the field of
view? The maximum change in depression angle for a given
change in altitude will occur at 45°. Will performance
improve when this peak is included in the field of view?
Early on we would have said yes to this question. This
thinking was part of the rationale for equating the textures
(splay and depression angles) for peak rates of change in
Experiment 2. However, discussions with W. W. Johnson
(personal communication, March 1995) have caused us to
reassess our position. Figure 14 illustrates the puzzle. Figure
14 shows the components of optical change in a forward
field of view including 50° below the horizon. The dotted
line shows optical change that is due to a 5-ft (1.5-m) change
in altitude from a height of 25 ft (7.6 m). The solid line
shows absolute optical change that is due to movement
forward at 1 eyeheight/s (25 ft/s at 25 ft). Note that a
crossover occurs at an angle of 78.7°. Below this crossover,
changes that are due to forward flow are larger than changes
that are due to altitude. Above this crossover, the opposite is
true. Perhaps relative change is the critical factor determining sensitivity. Thus, the observer should look near the
horizon, where rates of change due to altitude are relatively
large compared to rates of change due to forward motion. If
it is the relative change that is critical, then does discriminability depend on the relative peaks within the field of regard or
on an integral function over the two curves (e.g., the average
change over the field of regard)?
If relative change is the critical variable for discriminating
altitude change from forward flow, then the crossover point
shown in Figure 14 is critical. The crossover point can be
computed by equating the formulas for the two components
of optical change and solving for the angle:
cos 8 sin 8 =
cos2 8
8 = tan'1 -
u
The crossover point is a tangent function of the ratio of
forward speed to rate of change of altitude. In Figure 14, the
forward flow rate was five times faster than the rate for
change in altitude. If the average change in altitude was
equal to the average flow rate (i.e., 8 = tan"1 1), then the
crossover point would be at 45° (as shown in Figure 2) and
the maximum advantage for altitude change relative to
forward motion would occur at about 67.5°. Important
psychophysical questions remain about how field of regard,
field of view, texture, and task dynamics interact to determine optimal strategies for extracting control-relevant information from optic flow.
In conclusion, the performance differences that have in
the past been attributed to different textures (splay or
depression texture) seem to result from differential rates of
optical change specific to altitude change, relative to the
rates of optical change resulting from other motions. The
visual system does not appear to be differentially tuned to
one component of the expansion pattern (splay angle) or the
other (depression angle). There appear to be a number of
ALTITUDE CONTROL
1781
0.45 n
8,
I
0.15- •
50
60
70
Optical Position In Field of View
Figure 14. The angular change in depression angle as a function of optical position for two
movements. The dotted line shows optical change due to a 5-ft (1.5-m) change in altitude at an
altitude of 25 ft (7.6 m). The solid line shows optical change resulting from a 25-ft change (i.e., 1
eyeheight) in fore-aft position.
important factors that create a general information bias in
favor of splay angle as a more robust and salient source of
information for specifying altitude change. However, many
psychophysical questions remain to be addressed before we
can fully specify the limiting factors for extracting information from optic flow and the implications for the control of
locomotion in general and the control of low-altitude flight
in particular.
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Received March 20, 1995
Revision received August 2, 1996
Accepted October 22, 1996
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