IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 35, NO. 4, JULY 2005
505
The (In)Accuracy of Novice Rover Operators’
Perception of Obstacle Height From
Monoscopic Images
Arjun Kumar Kanduri, Geb Thomas, Member, IEEE, Nathalie Cabrol, Edmond Grin, and Robert C. Anderson
Abstract—Researchers have previously described a mobile
robot, or rover, operator’s difficulty in accurately perceiving
the rover’s tilt and roll, which can lead to rollover accidents.
Safe mobile robot navigation and effective mission planning also
require an operator to accurately interpret and understand the
geometry and scale of features in the rover’s environment. This
work presents an experiment that measures an observer’s ability
to estimate height of distant (5–15 m) obstacles given an accurate
local model (e.g., within 0–5 m of the rover), a panoramic image,
and a physical mock-up of the local terrain. The experimental
conditions were intended to represent a best-case scenario for a
stopped rover equipped with short base-line stereoscopic cameras.
The participants’ task was to extrapolate the well-modeled local
geometry to monoscopic images of the more distant terrain. The
experiment compared two estimation techniques. With the first
technique, each observer physically indicated his or her direct
estimates of the obstacle distance and height. With the second
estimation technique, which we call horizon analysis, the observer
indicated the position of the top and bottom of each rock on an
image and the height was calculated by measuring the visual
angle between the theoretical horizon and the points indicated by
the observer. The direct estimation technique overestimated the
height of the rocks by an average of 190%; the horizon analysis
technique overestimated by 80%. The results suggest that even
when provided with a rich set of supplementary and context information, rover operators have significant difficulty in vertically
perceiving the scale of distant terrain. The results also suggest that
horizon analysis is a more accurate method for determining the
height of distant rover navigation obstacles, when the local terrain
is nearly level.
Index Terms—Computer interface human factors, mobile robot
motion planning, mobile robots, spatial reasoning.
I. INTRODUCTION
M
OBILE robots, or rovers, are an important tool for
studying and operating in hazardous or remote environments. They are being used for police and military applications
Manuscript received August 1, 2004; revised March 14, 2005. This work was
supported by the NASA program Applied Information Systems Research under
Grant NAG5-11981 and Grant NNG05GA51G. This paper was recommended
by the Guest Editors.
A. K. Kanduri and G. Thomas are with the Department of Mechanical and
Industrial Engineering, University of Iowa, Iowa City, IA 52242 USA (e-mail:
[email protected]).
N. Cabrol and E. Grin are with the NASA Ames Research Facility,
Space Science Division, Moffett Field, CA 94035-1000 USA (e-mail:
[email protected]; [email protected]).
R. C. Anderson is with the Jet Propulsion Laboratory, California Institute
of Technology, Pasadena, CA 91109 USA (e-mail: Robert.C.Anderson@
jpl.nasa.gov).
Digital Object Identifier 10.1109/TSMCA.2005.850601
[1], search-and-rescue missions [2], as well as scientific explorations near volcanoes [3], in arctic environments [4], and on
Mars [5]. Two strategies for controlling rovers are telemanipulation and supervisory control. In telemanipulated systems,
operators navigate by sending motor and steering commands to
the rover. In supervisory-controlled systems, operators navigate
by interacting with the rover’s semiautonomous system, often
by suggesting intermediate goal locations or navigation tasks.
In either case, the operator primarily relies on imagery collected
by the rover’s cameras to perceive the remote environment and
make decisions about where the rover should go and how to
navigate there safely. The imagery may be provided by a live
video feed on a television monitor or as a series or collection of
still images in a specially designed operator interface [6].
Driving the rover remotely, however, is a difficult perceptual
task. The difficulty of accurately perceiving rover attitude (pitch
and roll) is described in [7] and [8]. However, few researchers
have investigated the difficulty of perceiving other features of
the environment from information provided by a rover. Estimating the height of distant obstacles is one such feature that
is both of immediate practical relevance for planning and navigation and is relatively unambiguous and is easily measured.
Misperceiving the height of obstacles is important because it
can lead to inefficient and frustrating rover operations. While
misperceiving rover attitude leads to rover rollover accidents,
misperceiving obstacle height leads to a more subtle operation
problem. If the operator underestimates the size of an obstacle,
he or she may drive the rover along a particular course only to
find the path blocked when the obstacle turns out to be unexpectedly large. If the rover operator overestimates the size of an
obstacle, he or she may avoid a particular path, even though that
path may be more efficient or productive. A more concerning
aspect of the obstacle height problem, however, is that a misperception of obstacle height suggests a more general lack of
veridical perception of the scale of the remote environment, for
how can an operator misperceive one aspect of the environment,
yet maintain a consistent, accurate representation of the other
particulars?
Many different factors may have a profound effect on the
operator’s perception of the remote environment. Differences
in camera resolution, field of view, camera height, image update
rate, and rover velocity are all likely to affect the operator’s
ability to accurately perceive the remote environment. Many
other relevant factors are related to the environment and the
operator, such as the presence of familiar objects, regular
texture patterns, lighting conditions, operation training, and
1083-4427/$20.00 © 2005 IEEE
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operator experience. The exhaustive experimental analysis of
each combination of these factors is beyond the scope of this
work. Instead, we have designed the experiments reported here
to demonstrate the need for greater study and understanding of
this particular feature of rover operations.
To that end, we have emphasized relatively simple techniques
that favor experimental repeatability, focused on a well-known
rover paradigm (Mars exploration) using a widely available
data set, and relied on naïve research participants rather than
trained rover operators. Although well-trained operators may
have better performance than the participants reported here,
the point of this work is to demonstrate that rover interface
designers and mission planners can not assume that operators
accurately perceive the remote environment, even when they
are provided with a relatively rich set of information. Their
ability to interpolate information to construct an accurate gestalt
model may be severely limited.
Furthermore, rather than simply report the estimates of the
participants, we seek to explain how the observer made (or did
not make) these estimates. Finally, we propose an estimation
scheme that, although not without limitation, appears to be more
effective than the default approach. In this manner, we hope to
report a quantitative performance benchmark by which other
rover systems may be compared and to begin to provide a theoretical framework within which this particular perceptual challenge may be addressed and eventually resolved.
II. BACKGROUND
People are not good at judging the heights of unfamiliar objects. When judging the height of unfamiliar targets in a broad,
open field, people overestimate the height of the targets by as
much as 225% [9]. Height estimate variability depends on the
distance between the observer and the target and as well as the
availability of pictorial depth cues, such as the presence of familiar objects or a clear horizon.
When comparing the size of 5–15-cm targets placed on a
nearby table with similar targets placed on a lawn at distances of
5, 24, and 98 m, research participants overestimated the size of
the more distant targets by 25% [10]. In another experiment, participants verbally estimated the height of 30–350-cm targets at
distances of 25–400 m. When the visual angle subtended by the
objects was large, approximately 25 visual degrees, the participants underestimated target size by as much as 10%, but when
the visual angle was small, they overestimated the target size by
as much as 225% [9]. When participants were asked to compare the height of a 107-cm target placed at 30 m with similar targets placed at distances of 30–1200 m on a long runway,
the participants overestimated the height of the stimulus by between 6.41% and 34.04%, depending on the target distance [11].
The presence of familiar objects and conspicuous depth cues
in the environment can greatly enhance the accuracy of height
judgments [12], possibly because a different processing mechanism is used when familiar objects are present [13]. Because
the experiments described here use stimuli from the surface of
Mars, the participants are not expected to be familiar with the
size of any of the features, beyond those presented in the experiment’s physical mock-up. However, if a rover is operating
in a familiar domain, which might be the case with an urban
search-and-rescue rover, for example, more accurate size estimates would be expected when familiar objects are available.
There are at least two competing theories about how people
perceive the size of objects. The first, called the Size Distance
Invariance Hypothesis (SDIH), assumes that an observer estimates height as the product of distance to the object and the
vertical angle subtended by the object [14]. The alternative
theory assumes that people interpret the texture gradient and
other invariant visual characteristics to infer the three-dimensional (3-D) structure of the environment. The observer then
estimates size to be consistent with the larger 3-D structure
[15]. One invariant visual characteristic useful in the estimation
of object height is the angle between the target object and the
horizon.
A. Size Distance Invariance Hypothesis
The SDIH [16] states that an observer estimates the height of
an object as the product of the visual angle represented by the
retinal projection of the object , and the distance between the
observer and the object
(1)
This hypothesis is supported by an experiment [17] that
showed that height estimates covary with estimated distance
and estimated visual angle. In particular, the experiment
showed that (1) predicts height estimation if is taken as the
estimated distance rather than the actual distance. In [16] an
experiment tested the invariance hypothesis independent of any
distance estimate. Participants compared visual stimuli to a set
of reference objects, where both references and stimuli were
displayed without distance cues. The authors argue that in the
absence of distance cues, participants will perceive the stimuli
and references to be at the same distance. The participants
estimated the objects to be the same size when they subtended
the same visual angle, consistent with the assumptions of the
SDIH. Holway and Boring [17] measured stimuli sizes with
four different sets of distance cues. When distance cues were
completely eliminated, size estimates varied with the visual
angle; when distance cues (such as binocular cues) were available, size estimates varied with stimulus height. This indicates
that perception of the size of unfamiliar objects depends on both
the visual angle and the perceived distance, again consistent
with SDIH.
Many other experiments validating the SDIH [18]–[20] have
been conducted with physical stimuli, but relatively few test the
SDIH with image stimuli. This may be a result of the theoretical
complexity introduced by presenting a photograph rather than a
physical stimulus. The SDIH research suggests that height estimation depends on distance estimation; it is not clear, however,
how accurately people can estimate distance with an image
B. Horizon Analysis
Gibson [15] argued that people observe spatial relations
through invariant structures in an optic array. Gibson favored
the invariant structures present in texture gradients. For example, a monoscopic image of a homogeneously textured
KANDURI et al.: (IN)ACCURACY OF NOVICE ROVER OPERATORS’ PERCEPTION OF OBSTACLE HEIGHT
Fig. 1. Angles used in Sedgewick’s horizon analysis, where the observer is
represented by a camera mounted on a mast.
surface provides a clear cue to a surface’s geometry (but not its
scale).
Sedgwick [21] explored the utility of the horizon in determining object height, where horizon is defined as an infinitely
distant great circle of the optic array located at the height of
the observer and perpendicular to the direction of the plane
upon which the observer rests. Sedgwick proved that when
an object rests on a perfectly flat plane, or ground, its height
may be determined from the angles between the horizon and
the top and bottom of the object. This height estimate does
not directly depend on the distance between the object and the
observer.
Sedgwick’s theory, which we refer to as horizon analysis,
calculates the height of an object resting on the ground as a
function of , the height of the camera focal point or observer’s
eye, , the angle between the horizon and top of the object, and
, the angle between the horizon and bottom of the object (see
Fig. 1)
(2)
The principle advantage of this approach is that these parameters do not require a depth estimate. The principle limitation is
that the model assumes that the ground is flat.
Sedgwick [21] applied horizon analysis to the perception of
both physical objects and images of objects. The extension to
images, however, requires that the observer must correctly estimate the camera height and angles and . The conversion
from vertical lengths in an image to a visual angle also depends
on the image’s vertical field of view.
Rogers and Costal [22] investigated the ability of artists and
university students to use a horizon to estimate relative size in
simple line drawings. Their stimuli consisted of a horizontal line
representing the horizon and a vertical line representing a target
extending upward from the ground plane. Their research participants drew a vertical line to indicate how large the target would
appear if it were located at the designated reference position.
The artist’s estimates were within –6% and 15% of the height
predicted by horizon analysis, whereas the university students
varied between –21% and 23%. This suggests that the ability to
effectively use horizon information is a skill that varies among
individuals.
Rogers [23] sought to further understand whether observer
height estimates were consistent with horizon analysis by
manipulating the position of the horizon line in simple line
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drawings. When the location of the horizon line was raised
or lowered, the consistency of observer estimates ranged from
approximately 30% overestimation to 20% underestimation,
with most of the estimates consistent within approximately
5%. The results suggest that the accuracy of height estimates
from images follows the pattern predicted by horizon analysis,
particularly when the horizon appears near the center of the
image.
The evidence for SDIH is generally drawn from direct observations of test stimuli in natural environments, but not from
images of these scenes, while the evidence for horizon analysis is generally from experiments with simple line drawings.
The experimental evidence in both cases suggests that in some
conditions people can significantly overestimate height. However, the evidence with the horizon analysis suggests that with
very little information, observers can make surprisingly accurate height estimates. Neither theory defines the process an observer would use to estimate object height using all of the information provided by a rover, nor does either theory predict how
accurate such estimates might be.
C. Rover Operator Obstacle Height Estimation
Because consistently overestimating obstacle heights limits
an operator’s ability to plan rover actions beyond the range
of locally modeled terrain, it is useful to consider strategies
that would allow the analyst to make more accurate estimates
of the height of distant obstacles. This paper compares two
estimation strategies: direct, physical height estimation and
a horizon analysis-based estimation. The first, which follows
current estimation strategies, provides the analyst with a 3-D
model of the local terrain and then requires the operator to
extend this model to provide scale for more distant objects.
This approach tends to support SDIH, because it emphasizes
information related to distance. The second approach supports
horizon analysis. The analyst need only indicate the position
of the top and bottom of the object in an image, because the
position of the camera, horizon and visual angles may all be
calculated automatically.
D. Objectives and Hypothesis
The objective of the following experiment is to compare
the accuracy of two methods of estimating the height of rocks
5–10 m from the camera in monoscopic images of a natural
environment containing no familiarly sized objects. The first
estimation method, direct estimation, is the operator’s direct
physical indication of the height of the object made by marking
a similar distance and height in a hallway. The second method,
horizon estimation, is based on the operator’s indication of
the top and bottom of the feature in an image. In all cases the
operator is provided with a 3-D model of the local terrain (less
than 5 m), a panoramic image, and a simple physical mockup
of the environment including the position of the camera and
several prominent features.
The experimental hypothesis is that horizon estimation is
more accurate than direct estimation because it avoids the
inaccurate process of estimating distances from monoscopic
images.
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distance and height of each target rock was calculated from the
unmodified, 3-D model.
Obstacle height is defined as the length of the vector that
passes through the highest point of the rock, downward in the
direction of gravity, to the base. The base is defined as the plane
parallel to the viewing direction that intersects the local region
of the ground on the left and right side of the rock. In each
image, the position of the horizon was assumed to be horizontal
and positioned above the image center by an angle equal to the
camera’s tilt.
C. Apparatus and Procedure
Fig. 2. Screen shot of the original VRML model constructed from stereoscopic
images taken by the IMP camera. A geometric model of the landing craft is
located at the center of the image. The rover is above and to the left of the
landing craft.
III. METHOD
A. Participants
Eight members of the university community (five male,
three female) aged between 18 and 60 years with normal or
corrected-to-normal vision participated in the experiment. Each
participant completed the experiment within 1.5–2 h.
B. Stimuli
The panoramic mosaic image, individual camera images,
and the 3-D model used in this experiment are from the Mars
Pathfinder data archive [24]. The experiment also employed
a simple, full-scale, physical mock-up of a portion of the
Pathfinder Landing Site terrain based on the objects and dimensions represented by the 3-D model.
The 3-D model of the landing site was adapted from [25].
The original model indicated the scaled geometry of the terrain
features from the lander location to a distance of approximately
14 m from the lander. However, for the purpose of this experiment, the model was modified by removing all features beyond
the distance of 5 m. Fig. 2 presents a screen shot of the modified model as it appeared when rendered by a VRML browser
plug-in.
The color panoramic image, which showed all the features of
the landing site terrain visible from the lander cameras, was also
used in the experiment. The panoramic image has a resolution
of 6230 1075 pixels, a horizontal field of view of 360 and a
vertical field of view of 62 . A portion of this color mosaic is
displayed in Fig. 3.
The five training and nine experimental image stimuli each
had a resolution of 258 246 pixels, with a vertical and horizontal field of view of 13.6 degrees. The five training stimuli
were selected to indicate prominent rocks within 5 m of the
lander, which were clearly identifiable in both the panoramic
and 3-D model. The nine experimental stimuli (see Fig. 4) were
selected to provide clearly identifiable rocks at distances between 5 and 10 m from the rover, which were also evident in
the panoramic image. The target rocks provided a range of distances, heights and elevations from the ideal ground plane. The
Each participant completed each portion of the experiment
in the same order. First, each participant was taught how to
use an interactive VRML browser window displayed on a 21-in
monitor to navigate and explore the 3-D model. Then he or
she was shown how objects in the full-scale, physical mock-up,
which was located in the same room as the monitor, represented
the physical scale of the model. The physical mock-up consisted of five boxes that represented the actual height, width,
and relative position of five prominent rocks pictured in both the
3-D model and the panoramic image. A tripod positioned near
the boxes represented the height and position of the Pathfinder
lander camera. Each box was labeled with an image of the corresponding rock in the panorama.
Next, each participant observed the panoramic image in
a Photoshop window displayed on the monitor. The proctor
again demonstrated the correspondence between rocks in the
panoramic image and the boxes in the physical mock-up.
Finally the participants observed the five training images, each
of which corresponded to one of the boxes in the physical
mock-up.
The main experimental session consisted of showing each
participant one of the nine experimental stimulus images and
asking the participant to estimate the distance and height of one
of the features indicated in the image. The participants were encouraged to look at the indicated stimulus image as well as the
panoramic image and 3-D model. With each stimulus image,
the participants were told the coordinates of the corresponding
feature in the panoramic image and were permitted to study the
available information until they were prepared to estimate the
size of the indicated feature.
To estimate the object height, the participant directed the experimenter to move forward or backward until the experimenter
stood at a distance that the participant estimated to be the distance between the landing camera and the target. To help with
this estimation, the origin for the estimate was a tripod set to
the height of the lander camera. A tapemark on the floor indicated where the bottom of the image would theoretically intersect with the floor, given the camera field of view and camera
tilt for each stimulus image. Although the tapemark represented
a useful reference point given the geometric information available regarding the imaging conditions, each participant was reminded that the terrain in the image may not be level and that
they should estimate the absolute distance between the camera
and the rock.
Once the participant was satisfied that the experimenter stood
at the target distance, the participant instructed the experimenter
KANDURI et al.: (IN)ACCURACY OF NOVICE ROVER OPERATORS’ PERCEPTION OF OBSTACLE HEIGHT
Fig. 3.
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Portion from the color panoramic mosaic image of the Pathfinder landing site, reproduced here in black and white. The original image is available in [24].
Fig. 4. Examples of stimuli used in the experiment. Target rocks are in dictated with a white cross.
to indicate the height of the target rock with a marker on a
meter stick. Once the participant was satisfied with the estimate
position, the experimenter recorded the estimated distance and
height. Finally, the participant indicated the precise pixel locations on the stimulus image that corresponded to the top and
bottom of the rock. The experimenter recorded the pixel coordinates of these points.
D. Experimental Design
In each experimental block, a participant estimated the
height, distance, and pixel coordinates of the top and bottom of
the rock for each of the nine stimuli. Each subject participated
in three successive, randomized blocks.
IV. RESULTS
The data from the three repetitions of each subject on each
stimulus were averaged to produce 72 independent pairs of distance and height estimates from the direct estimates and 72
height estimates from the horizon analysis. Fig. 5 compares the
direct and horizon height estimates for each stimulus.
The average direct estimates varied from 126% to 579% and
were, on average, 192% of the actual target height. The average
horizon estimate for each stimulus ranged from 61% to 279%
of the actual stimulus height, with an average overestimation of
79%.
Height estimate error is the difference between each estimate
and the actual value. Both the horizon estimate errors (0.14 m,
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Fig. 7. Inferred visual angle (degrees) derived from the direct estimates as a
function of true visual angle (degrees). The error bars represent one standard
deviation of the averaged estimates.
Fig. 5. Comparison of the horizon estimation and direct perception techniques
for estimating heights. The error bars represent one standard deviation of the
averaged estimates across the subjects. Perfect estimates would lie on the lower
dotted line.
Fig. 8. Direct height overestimation as a function of true visual angle in
degrees. The estimates are the average of each participant for each stimulus.
The error bars represent one standard deviation of the estimates.
m
m
Fig. 6. Estimated distance ( ) as a function of true distance ( ). The error
bars represent one standard deviation.
SD 0.22 m) and the direct estimate errors (0.30 m, SD 0.13 m)
,
,
were significantly greater than zero (
,
, respectively).
and
Fig. 6 presents the direct estimates of stimulus distance versus
true distance. Ideally the slope of a regression of this data would
be equal to one with an intercept of zero. However, a regression
value of
yields a slope of 0.2, an intercept of 7.3, and an
value suggests that the true distance was not
0.03. The low
a reliable predictor of estimated distance.
Fig. 7 presents the estimated visual angle, which is the estimated height divided by the estimated distance, as a function of
true visual angle. A regression of these parameters provides a
value of 0.17.
slope of 0.78, an intercept of 2.4 and an
Fig. 8 presents height overestimation (directly estimated
height divided by true height) as a function of the true visual
angle of the stimulus. A regression of these two parameters has
value of 0.53. Stimuli with a small visual angle tend to
an
be overestimated more than larger stimuli.
V. DISCUSSION
The results suggest that novice observers tend to overestimate the height of distance objects, at least with the viewing
conditions similar to those used for Mars exploration. Even
when provided with a physical mock-up of the height of the
camera and several objects within 5 m of the rover, a 3-D
model of the nearby terrain, and references that indicated the
physical tilt of the camera for each stimulus, the participants
overestimated the height of targets by 126% to 579%. When
using horizon analysis, the overestimation was still significant,
but smaller in magnitude. Consequently, the results support
the assertion that horizon estimation is the more accurate and
precise method for estimating obstacle height. Not only is the
average error significantly smaller, but the average standard
deviation is also smaller.
The observations in this experiment are consistent with and
extend previous results. The average direct observation overestimation of 126% is similar to the height overestimation range of
10%–235% reported in previous field studies [10]. The average
to 23%
horizon overestimation of 79% is larger than the
range for nonartists looking at simple line drawings [22]. However, the stimuli in this experiment are different from line draw-
KANDURI et al.: (IN)ACCURACY OF NOVICE ROVER OPERATORS’ PERCEPTION OF OBSTACLE HEIGHT
ings in at least two important ways. First, the real images do not
always contain the horizon within the viewing area, so angles
and in Fig. 1 are larger than those used in the line drawings.
Second, the simple line drawings assume that all the features
lie on a uniform ground plane, whereas the terrain in the images
naturally undulates, violated the assumption of horizon analysis
and introducing error. The two most overestimated stimuli also
had bases farther above the ground plane (0.15 and 0.25 m) than
any of the other stimuli. Unfortunately the experiment was not
designed to differentiate between these two possible sources of
error.
As a bellwether for the observer’s capability to interpret the
geometry of the remote environment, the experimental results
displayed in Fig. 4 suggest that there are important challenges.
The observers’ estimates of stimulus distance are nearly independent of the actual distance. This suggests that the observers
may have had difficulty in interpreting the pictorial depth cues
in the image to infer much useful depth information.
The pattern of results for direct estimation conflicts with the
SDIH. As Fig. 5 illustrates, the participants’ indication of position and height is inconsistent with the visual angle presented
in the stimulus. In all cases the participants’ recreation of the
scene overestimated the visual angle presented in the image.
One possible explanation for this pattern is that the participants
misunderstood the camera’s vertical field of view. If the participants consistently underestimated the camera’s vertical field
of view, they would consistently overestimate the visual angle
of the stimulus. This misperception should lead to consistent,
linear relationship between the estimated visual angle and the
true visual angle. In this experiment, the regression was signifvalue of just 0.17,
icantly different from zero, but had an
which is not a reliable, predictive pattern. However, Fig. 5 suggests that with the exception of two outliers, there may be a reliable linear trend between true and estimated visual angle. Consequently, although the experiments generally refute SDIH as
the sole estimation strategy, it may be that the observations are
consistent with SDIH plus some other factor or combination of
factors.
The strongest trend in the experimental results was the overestimation of stimulus height as a function of the visual angle
value of 0.53. As Fig. 6 inof the stimulus, which had an
dicates, direct estimates of the stimulus height were within a
factor of two when the stimulus presented a visual angle of just
over 1 degree. This is similar to the pattern observed in [9]. If
confirmed by other rover experiments, this factor-of-two relationship may provide a useful operational guideline, because it
frames the accuracy of perception in a manner that is relatively
easy to remember. However, this relationship is less useful to designers because it does not suggest how to improve operator’s
perception of stimulus height, because the absolute visual angle
presented by a target can not be manipulated.
A practical application of height estimation during rover operations is to allow an operator to decide if a distant object poses
a navigation threat to the rover. The Pathfinder rover was able
to safely traverse obstacles less than 0.25 m [26]. Based on this
criterion, seven of the nine stimuli represented obstacles that
did not pose a threat to rover navigation. However, with direct
estimation, all of these objects would have been perceived as
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a threat. With horizon estimation, only one stimulus would be
classified as a threat, three would be classified as not a threat,
and the other three would have been classified as a threat by
some analysts and not a threat by others. Consequently, although
horizon estimation is still not a perfect solution for long-range
rover obstacle estimation, it provides a practical improvement
over current estimation techniques.
Accurate estimation of obstacle height with a rover still
poses a significant challenge for rover operators. Generally,
current rover designs have addressed this by equipping rovers
with stereoscopic camera systems. In cases where the ground
is reasonably level or when a terrain model is available and the
rover is aware of its position within the terrain, horizon analysis
may provide an effective alternative to stereoscopic imagery.
We speculate that adding graphical enhancements to provide a
horizon-analysis reference may help rover operators to perceive
obstacle height with reasonable accuracy, even accurate depth
information is not available. Testing this speculation, however,
will be the subject of future research.
VI. CONCLUSION
Naïve observers are not reliable judges of the height of distant objects pictured in still, monoscopic images under conditions similar to those used in Mars rover exploration. In these
conditions, horizon analysis provides a more accurate and precise height estimate than direct estimation. With the conditions
tested here, which included providing information to support an
accurate physical understanding of the local
m geometry
of the camera and local terrain, observers overestimated stimulus height by an average of 192%. Direct estimation is not consistent with the SDIH or with any single source of error, such
as a consistent misestimation of target distance, camera field of
view, or camera height. Horizon estimation, on the other hand,
is a more reliable technique, so long as the terrain is generally
flat. For the conditions investigated here, horizon analysis yields
a superior estimation when the bottom of the obstacle is within
10 cm of the ideal ground plane.
These results suggest that designers and operators should
be aware that the operator’s perception of the geometry of
the rover’s environment may differ substantially from the true
environment. The operator may tend to overestimate both the
height and the distance of objects in the remote environment.
Providing a 3-D model of the local environment does not appear to eliminate this overestimation tendency. Generally, when
direct sensor measurements are not available and until better
analysis techniques are developed, rover operators should avoid
making navigation decisions based on the perceived height of
distant objects. When operators must make such judgments,
they should use horizon analysis rather than direct estimation,
particularly if the terrain is generally level.
ACKNOWLEDGMENT
The authors would like to thank the participants of the experiment and Z. Xiang and the members of the GROK Laboratory,
University of Iowa for their technical help and encouragement
throughout the project.
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Arjun Kumar Kanduri is currently pursuing the M.S. degree at the University
of Iowa, Iowa City.
His current research interests include actuarial science and finance. He is also
exploring areas that include the modeling of uncertainty events using probabilistic actuarial concepts in engineering.
Geb Thomas (M’96) received the B.S. degree in
physics from the State University of New York,
Stony Brook, in 1991 and the M.S. and Ph.D.
degrees in industrial engineering from Pennsylvania
State University, University Park, in 1995 and 1996,
respectively.
Since 1997, he has served as an Assistant
Professor in the Department of Mechanical and
Industrial Engineering, University of Iowa, Iowa
City. His research interests include human factors,
human computer interaction, and robotics. He has
published over 50 journal articles and conference papers in this and related
areas.
Nathalie Cabrol received the M.S. and Ph.D. degrees in planetary science from Sorbonne University,
Paris, France, in 1986 and 1991, respectively.
She was a Postdoctorate Researcher with the
NASA Ames Research Center, with the Association
Française pour L’Avancement des Sciences (Actualités de l’Hydrologie) from 1994 to 1995, then as
a National Research Council Associate from 1996
to 1998. Since 1998, she has continued her work at
NASA Ames through a cooperative agreement with
the SETI Institute. She has participated in many
large projects involving robotics for planetary exploration. Most notably, she
is a Co-investigator and Science Team Member of the NASA/JPL Surface
Science Operation, Moffett Field, CA, on the 2003 Mars Exploration Rover
(MER) Spirit and Opportunity Missions since 2002. She has published over 120
journal articles relating to planetary geology and robotic planetary exploration.
Edmond Grin received the M.S. degree in geography and geology from the University of Neuchâtel,
Neuchâtel, Switzerland, in 1983, the M.S. degree in
theoretical physics from the University of Lausanne,
Lausanne, in 1942, the M.S. degrees in geography
and land development and quantitative geography
modeling from the University of Sorbonne, Paris,
France, in 1985 and 1986, respectively, and the Ph.D.
degree in civil engineering from the Swiss Federal
Polytechnicum Institute, Zurich, Switzerland, in
1947.
After a successful career as a Hydraulics Engineer from 1948 to 1975, he
turned his attention toward Mars in 1987, working first as a Research Associate
in planetary sciences at the Paris-Meudon Observatory, Laboratoire de Physique
du Système Solaire, France, from 1987 to 1994. He then was with the NASA
Ames Research Center in 1994, first as a Research Associate (1994–1998), then
under a cooperative agreement with the SETI Institute. In addition to his interests in Martian hydrology, he has participated in a large number of rover field
tests, often serving as the geology team’s ground truth geologist, assessing the
geologic history of the site in person for comparison with the remote science
team’s assessment. He has been a Collaborator with the Mars Exploration Rover
Science Team since 2002.
Robert C. Anderson received the B.S. and M.S.
degrees in geology from Old Dominion University,
Norfolk, VA, in 1979 and 1985, respectively, and the
Ph.D. degree in geology and planetary science from
the University of Pittsburgh, Pittsburgh, PA, in 1995.
Since receiving his Ph.D., he has been with the Jet
Propulsion Laboratory, Moffett Field, CA, where he
specializes in Mars exploration first with the Mars
Pathfinder Mission and more recently with the Mars
Exploration Rovers.