JunThesisJune14

JUDGMENTS OF SPEED AND ALTITUDE: PERCEIVING OPTICAL INVARIANTS
IN OPTIC FLOW
A thesis submitted in partial fulfillment
of the requirements for the degree of
Master of Science
By
ASAD ALI JUNAID
M.S. (Electrical Engineering), Wright State University, 2003
B.E. (Electrical and Electronics Engineering), Bangalore University, 2000
2005
Wright State University

WRIGHT STATE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
DECEMBER 9, 2004
I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY
SUPERVISON BY Asad Ali Junaid ENTITLED Judgments of Speed and Altitude:
Perceiving Optical Invariants in Optic Flow BE ACCEPTED IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of
Science.
__________________________________
John M Flach, Ph.D.
Thesis Director
__________________________________
John M. Flach, Ph.D.
Department Chair
Committee on
Final Examination
__________________________________
John M. Flach, Ph.D.
__________________________________
Richard Warren, Ph.D.
__________________________________
Scott Watamaniuk, Ph.D.
__________________________________
Brian M. Kruger, Ph.D.
__________________________________
Joseph F. Thomas, Jr., Ph.D.
Dean, School of Graduate Studies

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ABSTRACT
Junaid, Asad Ali. M.S., Department of Psychology, Wright State University, 2005.
Judgments of Speed and Altitude: Perceiving Optical Invariants in Optic Flow
This study examines the influence of optic flow during self-motion on judgments of
speed and altitude. Optic flow is the apparent visual motion that we experience as we
move through the world. Participants in this experiment observed a series of trajectories
of self motion over three ground textures where altitude, speed or both changed smoothly
over their course. During the course of the trajectory, observer’s reaction time to changes
judged from the period when the change started was measured and the direction of
change – either increase or decrease – was recorded for changes detected in either speed
or altitude (as the case may be) over the ground textures. Catch trials which consisted of a
no change condition were judged by the subjects with a no button click. On looking at the
reaction time data, no useful information about human performance could be obtained. A
performance metric, the Direction Indicator, whose value was based on all three observer
responses, was used instead. A geometrical quantity – the angle of approach
(Langewiesche, 1944, Gibson, Olum & Rosenblatt, 1955) or the H-angle (Hasbrook,
1975) seems to provide a better explanation for the human performance data obtained
than the other geometrical quantities Global Optical Flow Rate (Warren, 1982; Ballard,
Roach & Dyre, 1998; Patrick, 2002; Patrick, Flach & Jacques, 2003; Junaid, Flach &
Warren, 2004) or Edge Rate (Denton, 1979, Warren, 1982; Ballard, Roach & Dyre, 1998;
Patrick, 2002; Patrick, Flach & Jacques, 2003; Junaid, Flach & Warren, 2004)

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TABLE OF CONTENTS
Page
I. INTRODUCTION………………………………………………………..…...1
a. Background..………………………………………………………………1
i. Perspective..……………….………………………………………4
ii. Angle of Approach..……………….………………………………5
iii. Glide..………………………...……………………………………6
iv. Motion Perspective..………………………………………………8
b. Global Optical Flow Rate (GOFR) ..……….……………………………10
c. Optical Edge-Rate..……...……………………….………………………14
d. Research on Speed Judgments: GOFR Vs Edge-Rate..……….…………17
e. Research on Altitude Judgments..…………………………..……………23
II. HYPOTHESIS..………………………………………...……………………27
a. Speed Perception..……………………………………..…………………27
b. Altitude Perception..………………………………..……………………30
III. METHOD..……………………...……………………...……………………32
a. Design..……………………………………..……………………………32
b. Procedure..……………………………….………………………………33
c. Display..………………………………….………………………………35
d. Apparatus..…………………………….…………………………………38
IV. ANALYSIS..…………………………………………………………………44
a. Percent Excluded Analysis..…………..…………………………………44
b. Reaction Time Analysis..……….…..……………………………………45
c. Percent Correct Analysis..…………..……………………………………45

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V. DIRECTION INDICATOR ANALYSIS……………………………………50
VI. H-ANGLE WITH DIRECTION INDICATOR ANALYSIS…....…………..56
VII. DARBY PATRICK DATA RE-ANALYSIS....…..…………………………61
VIII. PARTIAL ANALYSIS ASYMMETRIES..…....……………………………65
IX. SUMMARY..……………………………...…………………………………68
X. FUTURE RESEARCH..…………………..…………………………………71
XI. REFERENCES..………..…………………………….……...………………73

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LIST OF FIGURES
Figure Page
1. Use of perspective as a perceptual cue for aircraft landings……………………….5
2. Angle of Approach as a perceptual cue to aid approaches to landings ………..…..6
3. Glide as a perceptual cue while flying an airplane ………………………………...7
4. Plot of Judged speed change on the y-axis Vs %GOFR change on the x-axis to
indicate the GOFR strategy ……………………………………………….……12
5. An example of airplanes with different cockpit heights to illustrate perceptual
ambiguity in speed judgments ……………………………………………....….13
6. Denton’s research on approach to traffic intersections to give a perception of
increased speed which would facilitate immediate braking ……………...…….15
7. Judged speed change on the Y-Axis Vs GOFR change on the X-Axis for an edge-
rate strategy for constant texture spacing ………………..…………………..…16
8. Human performance data from Patrick (2002): Judged speed change Vs GOFR
change which does not follow either the GOFR or the edge rate strategy ……..19
9. Servo model showing speed judgment in presence of altitude disturbance …...….20
10. Predictions of speed judgments using the servo model with a gain equal to one (a
low value)……………………………………………………………….….…...21
11. Predictions of speed judgments using the servo model with gain equal to 100…...22
12. Predictions for the servo model with gain value of five ………………………..…23
13. Three types of texture that have been used to isolate components associated with
altitude change ……………………………………………………..……….…..24
14. Predictions of speed judgments using the servo model ……………………..…….28
15. Predictions of altitude judgments using the servo model …………………………30
16. Experimental setup ……………………………………………………………..…40
17. Grid or checkerboard texture simulated a checkerboard ground texture that included
both splay and depression lines ………………………………………………...41

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18. Splay or parallel texture which simulated vertical strips of texture parallel to the
forward direction of motion …………………………………………………...42
19. Depression or perpendicular texture simulated horizontal strips of texture
perpendicular to the forward motion path …………………………………….43
20. Angle of Approach (Langewiesche, 1944) or the H-Angle (Hasbrook, 1975)…..57

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LIST OF TABLES
Table Page
1. Trial layout using a Latin Square design, which indicates order of the trials over
different textures and conditions …………………………………….…34
2. Changes in GOFR as a function of speed and altitude manipulations ……………35
3. Instantaneous rates of change for this experiment and that of Patrick’s
experiment…………………………………………………………..... ..38
4. Percent exclusions over different conditions and textures …………………….....44
5. Percent correct out of 25 trials in each block (texture x judgment) for each subject …....46
5a. Average percent correct obtained by averaging over the 12 subjects …………….47
6. Percent correct out of 12 participants for each combination of speed and altitude
change when judging speed over grid texture …………………………..47
change when judging speed over depression texture……………………48
change when judging speed over splay texture………………………....48
9. Percent out of 12 participants for each combination of speed and altitude change
when judging altitude over grid texture…………………………………48
change when judging altitude over depression texture………………….48
change when judging altitude over splay texture………………………..49
12. Percent correct correlations over different conditions and textures……………….49
13. Direction Indicator (DI) correlations over different conditions and textures……...51
14. Correlations with DI and altitude, GOFR and Edge-rate for speed judgments
(human performance)…………………………………………………....53
15. Correlations with DI and altitude, GOFR and Edge-rate for altitude judgments
(human performance)……………………………………………………54

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16. H-Angle values for different speeds and altitudes and their corresponding final
vertical (due to final altitude values) and horizontal (due to final speed
values) distances……………………………………………………….58
17. H-Angle correlations with Altitude, GOFR and Edge-rate (not human
performance)…………………………………………………………...59
18. H-Angle, Altitude, GOFR and Edge-rate correlations with DI for speed judgments
(human performance).............................................................................60
19. H-angle for Patrick’s change rates……………………………………………...62
20. H-angle correlations for speed judgments for Patrick’s experiment (human
performance data)…………………………………………………...…63
21. H-angle correlations for altitude judgments for Patrick’s experiment (Human
performance data)………………………………………………….…..63
22. Partial analysis correlations (not human performance data)…………….………65
23. Partial analysis correlations for speed judgments (human performance data).…66
24. Partial analysis correlations for altitude judgments (human performance
data).........................................................................................................66

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Do you know what the scariest thing is?
It is to not know your place in this world
To not know why you’re here
That’s just an awful feeling
- Samuel L Jackson (Mr. Glass), Unbreakable

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Acknowledgments
Even before I express my gratitude towards anybody or anything else, my
acknowledgments to Rik Warren, for the ‘angle’, which showed a way, when all hope of
seeing a meaningful pattern in the data that was collected, appeared lost, and for his
insights and comments from the conception of this thesis idea till its culmination, and for
those long weekends spent looking over my data, and for the dinners with his family, and
everything else…
Scott Watamaniuk has been a very good critic and a great motivator. There have
been innumerable instances where I had to think more than twice about doing things a
certain way, formatting or presenting a certain way, with the thought about what Scott
would have to say about it. It has made me, if not anything, a much-improved self-critic.
Dr Kruger has been very supportive and has been always available whenever he was
needed for any work associated with the thesis.
Let me backtrack…
‘It’ all started when I came to WSU for my MS in Electrical Engineering. I also
began taking courses in psychology during the fall of 2001. I had been reading books on
psychology to satisfy my curiosity about what makes me ‘me’ and people ‘them’, but had
no formal education in it. I expressed my interest in psychology to Dr Nagy – who was
willing to listen - threw my fledgling interest in psychology a lifeline and gave me an
opportunity to work with him in his Visual Science lab. I spent a little more than a year,
until December 2002, working with him, understanding what I could about the part of
psychology that could not be learnt by reading books or taking classes.
Within the year, I was exposed to engineering psychology (Dr Flach) (bought a cell
phone – my first – for the course project), research methods (Dr Kruger), and cognition &
learning (Dr Flach again). Around this time, a suggestion by Dr Shebilske (then the Chair
of the Department) about applying for a MS degree in Psychology got me seriously
looking into the possibility that I could get a degree out of having a good time. I went
ahead and applied but I was denied admission then. Perhaps I had not expressed my
seriousness towards pursuing the psychology degree properly enough (“we did all we
could to keep him out...but he kept coming back” – Dr Flach mentioned later). It was
then, I decided that if it is worthwhile to work with anybody, it had to be Dr Flach – a
decision that I never had a second thought about.
I was given another chance (rather I “kept coming back”) and in the fall of 2002, I
was sitting through a 900 level course – ecological approach to man machine systems,
with Dr Flach. I was also in Val’s 701 – research methods and design. I was about to give
it all up after looking at all the statistical analysis that had to be done in Val’s class, but
on assurances from Dr Flach that psychology is not all about stats, I stuck around. Me
(who by then had become the ‘unofficial’ Dr Flach grad student) and Bmac (the ‘official’
Dr Flach grad student) started working on a Matlab project with Dr Flach, which was
officially supposed to be my ‘first year project’ though I was not officially into anything
yet. It was around then that I started to understand what Human Factors is and how it
cannot be not a part of engineering and design. Eco and Control theory asked questions

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that engineers never asked. I was still doing my MS in EE, ran into engineers ever so
often who could not comprehend that psychology “the study of crazy people” has
something to do with design and engineering. The fascination with psychology continued
to grow. Juggled an internship (another lifeline – was not funded yet!!) and coursework
(both EE and Psych) and also started looking into programming for my thesis – those
were some days.
And as they say, the rest is history.
Programming for my thesis was a major pain, finally managed to get it done, thanks
to Jeff and Rajitha (a CS student – another lifeline here).
The people who are in the department office have been good to me, especially Linda
(what would we grad students do without her!!!) who have shown tons of patience even
though “I kept coming back” (I simply had nowhere else to go….)
And my acknowledgments also to Bmac and April, who had their wonderful
insights and suggestions and were awesome lab mates and so were Kyle and Mei (sorry
Amy, we claim Mei as ours).
And to my awesome brother, Fahad, who has shown remarkable patience and
support from back home while I have perhaps sidestepped my responsibilities towards
him and my family in my pursuit of this degree.
And to Anu (my badi behen in the department), Shannon, Travis, Julio, Jen, Louise,
Lynn, Liza, Marjorie, Satomi, Pam, Candace, Kristin, Megan, Katie, Xiaofang, Joe, John,
Charlene, Markus, Esteban, Paul, Mark, Brad, BLee and Dan.
Thank you…
Asad Ali Junaid
“Now that we know who you are
I know who I am”
- Samuel L Jackson (Mr. Glass), Unbreakable
“Main Aisa Kyon Hoon, Main Aisa Kyon Hoon?
Main Jaisa Hoon, Main Vaisa Kyon Hoon?”
- Hritik Roshan (Karan), Lakshya

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I. INTRODUCTION
Controlled flight into terrain (CFIT) refers to situations where a pilot, usually on a
low altitude flight mission, flies his airplane into the ground without apparent mechanical
failure, bad weather conditions or a medical reason. Such accidents continue to happen
with alarming frequency (Junaid, Flach & Warren, 2004). This research is motivated by
the hypothesis that misperceptions associated with speed and altitude judgments may be a
contributing factor to some of these accidents. Amid questions involving CFIT accidents,
a fundamental question is how do people control self-motion through three-dimensional
space?
Background
The conventional approach for an answer to this question and more broadly to
questions regarding perception of motion assumes an abstract notion of space and bears
the imprint of the Cartesian metatheoritical framework developed centuries before the
formulation of evolutionary theory. The perception of three-dimensional space has been
explained by the conventional approach with the Newtonian concept in mind which
projects the view that space exists independently from the objects themselves and that
three-dimensional space perception and locomotion is indirectly mediated by an internal
representation of space.
A contrasting viewpoint to the conventional Newtonian approach was suggested
by James Gibson with his radical "ecological approach" which came to a culmination
with his book on ecological psychology titled “The ecological approach to visual
perception” in 1979. Gibson wrote:

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I am (also) asking the reader to suppose that the concept of space has
nothing to do with perception. Geometrical space is a pure abstraction.
Outer space can be visualized but cannot be seen. The cues for depth refer
only to paintings, nothing more. The visual third dimension is a
misapplication of Descartes’ notion of three axes for a coordination
system.
The doctrine that we could not perceive the world around us unless we
already had the concept of space is nonsense. It is quite the other way
around: We could not conceive of empty space unless we could see the
ground under our feet and the sky above. Space is a myth, a ghost, a
fiction for geometers. All that sounds very strange, no doubt, but I urge the
reader to entertain the hypothesis. For if you agree to abandon the dogma
that “percepts without concepts are blind,’ as Kant put it, a deep
theoretical mess, a genuine quagmire, will dry up. (p. 3)
In place of the classical framework of “space” perception, Gibson (1979) offered
the theory of “direct perception.” To explain the visual control of locomotion, Gibson
(1958, 1966) described how a moving observer could perceive his own motion (self-
motion) based on patterns of structure that exist in the optical flow field. Gibson went on
to explain that the human perceptual system is tuned to these optical patterns, which form
a predictable or invariant structure that specifies both the layout of the environmental
surfaces and the motion of the observer with respect to those surfaces.
Before Gibson formulated notions of direct perception and optical flow,
Langewiesche (1944) provided an account of how a person flying an airplane might use

3
properties of an optical flow field as a guide for approaches to landing. In his analysis,
Langewiesche first looked into how a beginner lands his airplane using a set of static cues
for his approach:
A beginner depends on memory relative to fixed landmarks to help him land. He
remembers that, if he is to hit it right, he must glide past that certain tree at about
twice the tree’s height. In order to do so, he must cross a certain road at about the
height of a fifth-floor window, with the grass in the fields looking thus-and-thus.
And he knows that, in order to have the right altitude over the road; he needs
about 500 feet on his altimeter when he crosses over a certain farmhouse. (p. 265)
This system of memorizing and theorizing where to begin a descent is based on
simple heuristics and local-rules. The beginner pilot at this stage has not yet learned the
higher order perceptual invariants that could be available in the environment to aid
approach to landings.
Langewiesche dismisses the use of learning such static cues by the beginner pilot
by saying that:
This kind of judgment, by absolute heights and absolute distances, is all wrong. It
will not work except on one’s home field, in one’s familiar ship, under familiar
conditions of wind. Obviously it can’t work on a strange field or if the altimeter
isn’t set to zero for the field if there is a strong wind or no wind at all or if the
pilot switches to a cleaner ship that has a shallower glide or, for that matter, if
someone chops down that tree. (p. 265)
This indicates the brittleness of local rule based solutions and the ineffectiveness
of the use of memory of fixed landmarks for perceptual learning.

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Perspective
As an alternative to the local cues, Langewiesche described a set of “visual tricks”
(p. 264) (which are similar to “optical invariants” as described by Gibson) to aid
approaches to landings. These tricks provide a more general strategy for successful
navigation in flight. Among his cues or tricks, the perspective in which a field appears to
the pilot seemed to be one of the most important (Figure 1). He explained the use of
perspective by saying:
A better clue is the perspective in which the field appears; its foreshortened
appearance as it lies before and underneath the pilot. This clue is used consciously
by many pilots and unconsciously probably by all. In bringing a ship at night into
a field that has only boundary lights or only a flare path down the runway, it is
sometimes the only clue, especially if the field is far away from towns or other
lights and surrounded by darkness. (p. 266)
Assume the field is square. Then if it appears radically foreshortened, then it lies
‘in front’ of the pilot much more than ‘below’ him (Figure 1a). If it looks ‘about
right’ (Figure 1b) to the pilot, then he can probably glide into it. If the field
appears almost square to the pilot in his approach, then the pilot would know that
he is high above it (Figure 1c). (p. 266)
It (perspective) is a fairly reliable clue. It will work from any altitude, regardless
of the absolute heights and distances involved; you get the same degree of
foreshortening of a square as long as you view it from the same angle. (p. 266)

5
Figure 1. Use of perspective as a perceptual cue for aircraft landings (a) landing field looks
radically foreshortened – lies in front of the pilot much more than below him, (b) landing field
looks about right – pilot can fly into it easily, (c) landing field appears almost square to the pilot
and the pilot would know that he is too high above it. From Langewiesche, W. (1944). (p. 265)
Angle of approach
The horizon – a perceptual invariant as stated in Gibsonian terms – according to
Langewiesche is:
The line where the earth and sky appear to meet. What the flyer finds as he goes
up (or goes down in the case of a landing) is that the horizon does not stay below
(or above): it goes up (or down) with him…the horizon is (practically) always as
high as your eye. The line from your eye to the horizon is always horizontal.
(p.267)
The angle of approach as you come into land is a constant for a predetermined
landing spot with reference to the horizon – another perceptual invariant, as stated in
Gibsonian terms. The pilot should learn to use the angle of approach as a perceptual cue
to aid him in landing an airplane. Langewiesche goes on to illustrate the usefulness of the
angle of approach with reference to the horizon as shown in Figure 2. Also shown in the
figure is the fixed point of reference to the ground.
(a) (b) (c)

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Figure 2. Angle of Approach as a perceptual cue to aid approaches to landings (a) airplane 3000ft
above the ground, (b) airplane 1000ft above the ground. From Langewiesche, W. (1944). (p. 276)
Langewiesche writes that, consciously or unconsciously, the experienced flyer
would be interested in mostly angles at which things would lie under (or above) him
rather than absolute distances and heights for making judgments and inferences during a
flight or while coming into land. This effect of using the horizon as a perceptual cue is
further illustrated with respect to the glide.
Glide
The visual effect that the horizon is always as high as our eye also comes in handy
when flying near radio towers, mountaintops, or other airplanes. It gives us the
information that, while flying, those objects which appear to us above the horizon, are
higher than where we eventually would end up and those which appear to us below the
(a)
(b)

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horizon are lower than where we will eventually end up. Those, which appear “on” the
horizon, are at our altitude.
Figure 3. Glide as a perceptual cue while flying an airplane. (a) approach during a Glide as seen
from quite a distance, (b) approach during a Glide as seen from a nearer distance, (c) approach
during a Glide just before landing. From Langewiesche, W. (1944). (p. 274 – 275)
This effect is as shown in Figure 3. Figure 3a shows approach during a glide as
seen from a distance, Figure 3b shows approach during the glide as seen from a nearer
(a)
(b)
(c)

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distance, and Figure 3c shows approach just before landing. Along with the horizon
appearing at constant eye height, the angular distance to the horizon from the fixed point
on the runway also looks constant – a perceptual invariant. Langewiesche explains the
invariance of the horizon and the point of landing during a glide by saying that our glide
will touch the ground at the one spot which does not move. It will always undershoot any
spot which moves ‘upward’, toward the horizon and it will always overshoot any spot
which moves ‘downward’, away from the horizon.
It is important to note here that, Langewiesche’s observations anticipated the later
work of Gibson. Langewiesche was describing properties of optical flow fields even
before Gibson coined the term “optical invariants” to describe these very properties.
Motion Perspective
Gibson, Olum and Rosenblatt (1955) came up with the concept of motion
perspective to explain linear self-motion. Motion perspective refers to the systematic
changes in a visual scene during self-motion. Motion perspective is based on the
continuous transformations of either a portion or the entire visual scene. These
transformations are specific to the relative direction of one’s locomotion as well as
information about the surface itself. This information about transformations in the visual
array is contained in the optic flow field, which forms the stimulus for an ocular system.
Gibson et al. (1955) introduced the concept that there was a lawful structure in the
environment that exists in the dynamics of an optical flow field. They further explained
that the flow of objects in a visual scene was useful for the perception of self-motion and
could provide a motion perspective that provided detailed information about the states of
self-motion, including speed and height. In other words, speed and height judgments may

9
be judged based on how the visual scene changes or flows as an observer moves through
the world. To come up with the mathematical analysis, Gibson et al. (1955) reduced the
eye to a geometrical point, the earth to a plane and the texture of the earth to points on the
plane.
The general statement of the Law of Motion Perspective by Gibson et al. (1955) is
given by the equation:
dδ/dt = V/h (sin δ cos δ + sin^2 δ cos θ cot β) (1)
Where dδ/dt is the angular change associated with a texture element,
V is the speed of self-motion; h is the distance above the ground,
δ is the angular separation between the point of heading and any other point on the
surface (e.g. the angular distance of something above the horizon),
θ is the angular separation between the perpendiculars to the line of heading. It can
also be referred to as the azimuth (horizontal direction expressed as the angular distance
between the direction of a fixed point (as the observer's heading) and the direction of the
object),
β is the angle of approach from a fixed point on the ground which can vary from
0° (parallel locomotion) to 90° (perpendicular locomotion).
The trigonometric relations within the parentheses specify how the flow rate
depends on the specific location of a texture element. Elements at different positions
within the field will flow at different rates. For example:
For an aim point directly ahead, the trigonometric relations within the parentheses
reduce to zero. Therefore, substituting zero for the trigonometric relations in Gibson’s

10
equation, motion is given by dδ/dt = V/h (0) = 0 i.e. the aim point is a fixed position in
space which specifies zero self-motion.
For a point directly below, the trigonometric relations within the parentheses
reduce to negative one. Therefore, substituting -1 for the trigonometric relations in
Gibson’s equation, the 90° point motion is given by dδ/dt = V/h (-1) = -V/h, which
signifies the fastest moving point on the surface. It is the fastest moving point because the
flow is equal in magnitude and in the exact opposite direction as the direction of self-
motion.
Global Optical Flow Rate (GOFR)
The global index of motion perspective depends mainly on the ratio of speed of
the flight to the distance above the ground as is given by V/h in the above equation. The
V/h term specifies how the flow rate depends on the distance of the eye point from the
surface (h) and the speed of motion (V).
Gibson had defined optic flow as the transformations in perspective due to
observer movements which specifies both the layout of surfaces and the motion of the
observer relative to those surfaces.
Continuing with Gibson’s tradition of direct perception, Warren (1982)
introduced the construct of Global Optical Flow Rate (GOFR) as a hypothesis to explain
altitude dependencies that had been noted in reports of judgments about the speed of self-
motion. Warren identified global optical flow rate as an extension of the analysis of the
optic flow field performed by Gibson et al., (1955). Global optical flow rate is the global
index of motion perspective (V/h) as used by Gibson et al. (1955). It is the ratio of speed

11
over altitude with units of eye heights per second. Global optical flow rate may play an
important role in perception of speed (and altitude).
In a strict interpretation of Warren’s (1982) GOFR hypothesis, the impact of
speed and altitude on judgments of either speed or altitude, the ratio of V/h in the
equation of the law of motion perspective (1) should be equivalent. That is, increasing
speed or decreasing altitude by the same proportion should result in equivalent judgments
of speed increase. Likewise, increasing speed and increasing altitude by the same
proportion should cancel out each other resulting in a perception of no change in speed.
The GOFR strategy can be better understood using an analysis space where
percentage global optical flow rate change is plotted on the X-axis and magnitude of
judged speed change is plotted on the Y-axis. As one would recall, GOFR is simply the
ratio of speed over altitude. An actual increase in speed or decrease in altitude, according
to the GOFR hypothesis, will result in an increase in the value of judged speed. Similarly,
an actual decrease in speed or increase in altitude will result in a decrease in the value of
judged speed.
The plot for such judgments would be a straight line passing through the origin
and this would look like what is shown in Figure 4.

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Figure 4. Plot of Judged speed change on the y-axis Vs %GOFR change on the x-axis to indicate
the GOFR strategy
Owen and Warren (1982) recounted an example of misjudgments of speed that they
attributed to judging speed based on GOFR. Shortly after the Boeing 747 (B-747) entered
service, a series of dangerously high taxi speeds that led to landing gear damage were
observed. The excessive taxi speeds were unanticipated since most of the pilots involved
were highly experienced Boeing 707 (B-707) and Boeing 727 (B-727) pilots.
G O F R C h a n g e
Speedjudgment

13
Figure 5. An example of airplanes with different cockpit heights to illustrate perceptual
ambiguity in speed judgments. At the same taxi speeds the GOFR will be proportionally lower in
the aircraft with the higher cockpits.
It was hypothesized that the high taxi speeds were a result of the pilots
experiencing a perceptual ambiguity in the optical flow field consistent with GOFR.
Apparently, pilots experienced in other jets had learned to set their taxi speeds based on
global optic flow rate. The B-747 (tail height 19.33 m) is much taller than either the B-
707 (tail height 12.8 m) or B-727 (tail height 13.56 m). The cockpit height is roughly half
the tail height and pilots did not anticipate the effect of the change in the out-of-the-
window view from the cockpit while taxiing. It was suggested that because of the
unexpected influence of height on optical flow, pilots taxied at higher speeds to maintain
optical flow rates that were consistent with safe speeds in the B-707 and B-727. Flow
rates that were acceptable for the planes with shorter heights were not appropriate for the

14
taller B-747. Owen and Warren (1982) pointed out that, “Eventually pilots were
instructed to use an instrument to determine actual taxi speed.”
Optical Edge-rate
At about the same time that Owen and Warren (1982) were studying speed
perception related to aviation, Denton (1980) was studying speed perception related to
highway safety. He was concerned with the instability of the relationship between
objective and subjective speeds as experienced by the driver of a motor vehicle. He
outlined a number of factors that might contribute to the instability in a driver to
differentiate between objective and subjective speeds. One of these factors has come to
be known as optical edge or discontinuity rate. Optical edge rate can be described as a
measure of how frequently edges flow past a fixed visual reference point during self-
motion in the observer’s field of view. These edges that flow past a fixed visual reference
point during horizontal self-motion will not be influenced by change in altitude (vertical
self-motion).
Again in line with Gibson’s tradition of direct perception, Denton (1979), in his
experiment, attempted to answer whether it was possible to create a speed illusion which
could counteract the influence of adaptation. Denton, tried to influence the driver to adopt
a slower and safer speed when leaving high-speed roads by manipulating the structure of
the visual field presented to him while driving. Denton hypothesized that by a process of
integration with respect to some metabolic time base we are able to compute relative rates
of movement. Denton then applied the knowledge of the influence of edge-rate on speed
perception to reduce vehicle speed at an intersection in Scotland.

15
Denton decreased spacing between the stripes painted on the road (as shown in
Figure 6.) at an exponential rate to give a perception of increased speed. On doing so, as
cars approached the intersection in Scotland, the discontinuity rate would accelerate. The
“illusion” of increased speed due to the acceleration in discontinuity rate resulted in
earlier, harder braking. This led to safer speeds for the approach towards the intersections
and thereby reduced the incidents of accidents.
Based on these results Denton concluded that relative-speed judgments in a
driving situation are highly dependent on the geometry of the visual field presented to the
driver, and that the driver’s sense of speed could be considerably modified by
manipulating the pattern of the visual field.
Figure 6. Denton’s research on approach to traffic intersections to give a perception of increased
speed which would facilitate immediate braking. (a) example of stripes painted on a road, (b)
exponential rate of edge decrease
(b)
(a)

16
Figure 7 illustrates how performance might look if judgments of speed were based
on edge-rate as Denton’s work suggests. Figure 7 uses the same coordinate system used
to illustrate performance based on GOFR (Figure 4). If the ground texture has a constant
distance between edges (or is at least stochastically regular) then perception based on
edge-rate should be proportional to the actual speed, independent of any change in
altitude. The flat functions in Figure 7 would represent constant judgments to conditions
of constant speed change, but different conditions of altitude change (to account for the
different values of GOFR change). Thus, the flat functions with respect to GOFR for each
different speed change indicate that judgments are independent of the associated altitude
changes.
Figure 7. Judged speed change on the Y-Axis Vs GOFR change on the X-Axis for an edge-rate
strategy for constant texture spacing
G O F R C h a n g e
Speedjudgment

17
Research on speed judgments: GOFR Vs edge-rate
In a review, Warren (1982) identified two geometrical (perceptual) aspects of the
optic array that may affect the perception of ego speed: optical edge-rate and global
optical flow rate (GOFR). This set the context for future research on speed perception
that has been framed to measure the relative contributions of edge-rate and GOFR.
In experiments done by Owen and Wolpert (1984) and Larish and Flach (1990),
eye height was manipulated with edge spacing kept constant. Results showed additive
effects of GOFR and edge-rate with edge-rate dominating speed perception. Edge-rate
was directly proportional to the true speed, where as GOFR varied with both speed and
altitude change.
Dyre (1997) manipulated discontinuity rate (edge-rate) and flow rate
independently by varying velocity and texture density, which produced a perfect
correlation between flow rate and ego speed and a zero correlation between edge-rate and
ego speed, the exact opposite of Larish and Flach’s (1990) design. Dyre’s (1997)
manipulation of edge-rate was therefore independent of proximal flow rate (optic flow
rate). Dyre (1997) showed an additive effect of GOFR and edge-rate with GOFR
dominating speed perception. He proposed that
Discontinuity rate (edge-rate) effects on ego speed found by Denton (1980);
Owen et al. (1984); and Larish and Flach (1990) have been overestimated due to
methodological artifacts in the displays used by Denton (1980) and Owen et al.
(1984). Effects attributed to discontinuity rate may have resulted from changes in
proximal flow rate, resulting in an overestimation of the discontinuity rate (edge-
rate) effect on ego speed. Larish and Flach’s (1990) manipulation of discontinuity

18
rate –independent of changes in altitude and speed –was independent of proximal
flow, however other methodological factors might have accounted for the
dominance in discontinuity rate found. All of these factors may have contributed to
the dominance of discontinuity rate over flow rate.
Ballard, Roach and Dyre (1998) found that relative use of edge-rate and flow rate
was related to the validity of sources of information. They showed that dominant use of
either edge-rate or GOFR varied based on ground texture type. They suggested that the
visual system is sensitive to multiple sources of information for perceiving speed and
adapts to the more valid source.
Patrick (2002) tried to better understand the judgment of height and speed as a
function of GOFR. He hypothesized that judgments of either speed or altitude would be a
function of changes in GOFR. He was investigating whether manipulations of speed and
altitude can be combined additively to influence judgments about either speed or altitude.
Therefore, Patrick (2002) in a simulated flight task manipulated five levels of speed
change and five levels of altitude change and asked people to judge magnitudes of speed
and altitude change. The visual scene was a virtual world, which replicated the vicinity of
a rural airport.
The first ten seconds of the flight sequence was a preview period during which the
airplane flew at a constant speed and altitude. The next ten seconds contained changes in
speed or altitude or both. The last ten seconds of the simulated flight were a post view
period where he asked the participants to judge the magnitude of speed and altitude
changes. In addition, the path of flight in the virtual environment was varied. One path
was parallel to the airport the other path was perpendicullar to the runway. The different

19
paths impacted the availability and salience of certain sources of information (e.g., the
changes relating to, seen, or represented in perspective in the runway – the perspectival
changes in the runway).
Figure 8 shows results from Patrick (2002) for speed judgments. Note that the
pattern falls between the predictions of the strong GOFR hypothesis (Figure 4) and the
edge-rate hypothesis (Figure 7). Consistent with the GOFR hypothesis, judgments of
speed change do vary with changes in altitude. However, the impact of altitude change on
judgments is small relative to the impact of speed changes. This result is similar to most
of the human performance data obtained over the years suggesting that neither a simple
GOFR hypothesis nor a simple edge-rate hypothesis can account for human performance.
Figure 8. Human performance data from Patrick (2002): Judged speed change Vs GOFR change
which does not follow either the GOFR or the edge rate strategy.

20
In an attempt to explain this adaptability of human performance, an “observer” in
the form of a servo model that embodied Flach et al.’s (1992) signal to noise hypothesis
was proposed by Patrick, Flach and Jacques (2002).
Figure 9. Servo model showing speed judgment in presence of altitude disturbance.
The signal-to-noise hypothesis suspected that performance on an active task
(speed detection) depended on the ratio of the optical activity due to the signal (speed) to
that arising from other sources of variation (effectively noise or disturbance - e.g. altitude
change).
The servo model consists of a single parameter, gain (G), that indexes the impact
of the altitude disturbance on speed judgments. High gain results in a small effect of the
altitude disturbance on speed judgments. Similarly, low gain results in a large effect of
the altitude disturbance on speed judgments. Mathematically, the servo model can be
represented as
J = S [G/ (1+G)] + A [1/ (1+G)] (2)
Where J is the judgment of speed, S is the reference (the speed change signal) and A is
the altitude change (the disturbance). For low values of Gain, for e.g. when gain = 1, we
have, J = S (1/2) + A (1/2). This results in equal contributions of both change in speed
G
Speed (S) Change
Speed
Judgment (J)
Altitude
(A)
change

21
and altitude to the judgment of speed change. Figure 10 shows what this model would
predict using the same values for speed and altitude change that Patrick (2002) used in
his experiment. Essentially, judgments of speed change are proportional to the change in
GOFR.
Figure 10. Predictions of speed judgments using the servo model with a gain equal to one (a low
value). The predictions were computed for the five levels of speed and altitude change used by
Patrick (2002). Points connected represent conditions with a constant speed change with different
levels of altitude change.
For high values of gain, for example when gain equals a value of 100, we have
judgment, J = S (100/101) + A (1/101). In this case, the altitude disturbance will have
almost no impact on judgments of speed. Figure 11 shows the predicted change in speed
judgments for the speed and altitude changes used by Patrick (2002). Note that the
pattern of results is very similar to the predictions for an edge-rate hypothesis as
illustrated in Figure 7.

22
Figure 11. Predictions of speed judgments using the servo model with gain equal to 100. The
predictions were computed for the five levels of speed and altitude change used by Patrick
(2002). Points connected represent conditions with a constant speed change with different levels
of altitude change.
For a gain value of 5, we have judgment, J = (5/6) S + (1/6) A. The resultant
relationship suggests that there are noticeable altitude dependencies on judgments of
speed change. However, the impact of altitude change is small relative to the impact of
speed change. Thus, as with the results of most of the studies of speed judgments, the
pattern of performance is somewhere between the predictions of the GOFR hypothesis
and the discontinuity rate hypothesis. Figure 12 shows the prediction for the intermediate
level of gain, plotted against the results obtained by Patrick (2002). At least qualitatively,

23
the servo model seems to provide a way to account for performance that falls between the
two alternative hypotheses.
Figure 12. Predictions for the servo model with gain value of five are shown as dashed lines with
open symbols. The functions with solid lines and filled symbols show performance obtained by
Patrick (2002). Points connected by the lines represent a constant speed change with varying
levels of altitude change.
Research on Altitude Judgments
Use of local static cues like object size, object detail and relative heights for
judging altitude have been described earlier in the context of space perception
(Langewiesche, 1944; Coran, Porac & Ward, 1979). In the current study, the focus was
on dynamic changes within optical flow fields. To isolate these dynamic changes,
artificial textures as illustrated in Figure 13 were used.

24
Figure 13. Three types of texture that have been used to isolate components associated
with altitude change. From Flach, J. M, & Warren, R. (1995). (p. 85)
The three textures that have been used in previous studies to isolate optical
changes associated with altitude change are a) splay or parallel texture which simulates
vertical strips of texture parallel to the forward direction of motion (it isolates splay angle
(Flach et al. 1997) as a source of information for altitude and has no texture flow
associated with changes in forward speed), b) depression or perpendicular texture
simulates horizontal strips of texture perpendicular to the forward motion path (it isolates
depression angle (Flach et al. 1997) as a source of information for altitude and edge-rate
as a source of information for speed), and c) combination of splay and depression
textures – grid or checkerboard texture which simulates a checkerboard ground texture
which includes both splay and depression angles.
Early interest in the relative information for altitude change provided by the
different textures was stimulated by some conflicting results in early studies. For a
forward velocity task performed by Wolpert (1988), performance in judging altitude
change was found to be best with splay texture; where as for a hover task (constant
position above the ground with up-down movement) done by Johnson et al. (1989)

25
performance was found to be best with depression texture. Flach et al. (1992, 1997) tried
to explain these ambiguities by suggesting that information value of particular ground
textures varied as a function of task constraints, i.e., those textures that have the least
noise (or in other words that isolate the optical changes that are specific to altitude
change) for a task are typically best suited for that task.
Flach et al. (1992) theorized that the ratio of optical activity from altitude change
relative to the optical activity arising from other aspects of the motion (e.g., fore-aft and
side-to-side motions) might be the critical factor while making altitude judgments. In a
series of three experiments Flach et al. (1997) sought to find the optimal texture for
altitude control at different forward speeds. They showed that the different performance
levels for altitude control across the three experiments were consistent with the signal-to-
noise hypothesis of Flach et al. (1992).
Flach et al. (1997) predicted that the interaction between texture and forward flow
rate (i.e., GOFR) was such that control would deteriorate for the depression texture with
increasing GOFR but would be good and independent of GOFR for the splay texture.
They reasoned that GOFR was visible with the depression texture and thus was an
increasing source of noise (i.e., optical activity unrelated to changes in altitude) with
increasing forward speeds. GOFR was invisible in the splay texture, and thus there was
no increase in noise with increased GOFRs.
Fore-aft motion (forward/backward motion at a constant height above the ground)
is a source of noise with depression texture, but is not visible in splay texture. Whenever
significant fore-aft motion is present there is a decline in the ability to regulate altitude
with the depression texture. No such decline was evident for the splay texture.

26
In all three of Flach et al.’s (1997) experiments, forward speed was the key
component that determined optimal ground texture type. Splay texture was best for
controlling altitude during forward motion, while depression texture was best for
controlling altitude during a hover task. Flach et al.’s (1997) key contribution was the
support for the idea that the information value of particular ground textures depends on
the self-motion of the observer.

27
II. HYPOTHESES
Hypotheses were based on earlier results that have shown that some textures are
superior for either speed or for altitude judgments (Wolpert 1988, Johnson et al. 1989,
Flach et al. 1992, 1997). A goal for this work was to test whether human judgments
would behave in a consistent way with Flach’s (1992) signal to noise hypothesis and also,
whether the data obtained could be modeled using the single parameter servo model used
earlier to explain adaptations in the judgment of speed (Patrick et al., 2003; Junaid, Flach
& Warren, 2004).
Speed Perception
Consistent with Warren (1982), it was hypothesized that when a GOFR strategy is
used to judge speed changes, altitude change will be the significant disturbance. When
edge-rate is used as the strategy to judge speed changes, the performance would be
independent of altitude changes. The strategy for judging speed would be dependent on
whether the ground texture would allow for an edge-rate strategy to be used. Previous
research has found some ground textures better suited for the usage of the edge-rate
strategy than other textures (Wolpert, 1988; Johnson et al., 1989). When there is no
information within the textures themselves for the use of an edge-rate strategy, then
GOFR strategy would be used.
The servo model for speed judgments (Figure 9), which is a control theoretic
model based on Flach’s (1992) signal to noise hypothesis, has speed change as the
reference, altitude change as the disturbance, and has speed as the quantity that is being
judged.

28
For judgments of change of speed, Figure 14 illustrates the predictions of reaction
time for the GOFR and edge-rate hypotheses as shown in Figures 4 and 7. The solid lines
illustrate the predictions for the GOFR hypothesis. When the percent change of GOFR is
low, then it should take the participants more time to judge change in speed. When the
percent change of GOFR is higher, then the changes in speed should be judged earlier.
The dashed lines illustrate the predictions for an edge-rate hypothesis. Reaction times for
judging speed change should be faster (should have a lower value) when the magnitude
of speed change is larger independent of any change in altitude.
-100 -80 -60 -40 -20 0 20 40 60 80 100
%GOF change
ReactionTime
High altitude
Medium altitude
Low altitude
Figure 14. Predictions of speed judgments using the servo model
Based on earlier research (Wolpert 1988, Johnson et al. 1989, Flach et al. 1992,
1997) depression or perpendicular texture should be well suited for speed judgments
because this texture would have salient signal and little noise for speed judgments. The
depression texture would be facilitating horizontal strips of texture perpendicular to the
forward motion path, which would facilitate the edge-rate strategy to be used. The
hypothesis would then be that, a person judging speed change when depression texture is

29
used would behave as a high gain adaptive controller. Altitude would have little impact
on speed judgments. Also, splay or parallel texture should be worst suited for speed
judgments because it would have low signal and high noise for speed judgments. The
splay texture simulates vertical strips of texture parallel to the forward direction of
motion, which would not facilitate the edge-rate strategy to be used. Therefore the
hypothesis when flying over a splay texture would then be that a human judging speed
change when splay texture is used would behave as a low gain adaptive controller.
Altitude should then have a significant impact on speed judgments. Finally, grid or
checkerboard texture should give rise to speed judgments, which are in between that for
depression and splay textures because grid texture has higher noise than depression
texture but still has higher signal than splay texture. Grid texture simulates a
checkerboard texture that includes both splay and depression lines. The depression lines
in the texture would facilitate an edge-rate strategy to be used for judging speed but the
presence of splay lines would introduce perceptual disturbance in the use of the edge-rate
strategy for judging speed. Therefore speed judgments should take longer over the grid
texture than depression texture indicating that altitude change is having an impact on
speed judgments but the magnitude of this impact is not as much as it had been over
splay texture.
Altitude Perception
For altitude perception, it was hypothesized that when there is rich information in
the ground texture for perceiving speed changes, speed change will be a very high noise
source. When the ground texture is devoid of information for perceiving speed change,
speed change will then become a non-significant noise source for perceiving altitude

30
changes. Previous research has found some types of ground texture better suited for
perceiving altitude change when there is little or no information from the ground textures
for perceiving speed changes (Wolpert 1988, Johnson et al. 1989, Flach et al. 1992,
1997). The servo model for altitude perception would be similar to the model shown in
Figure 9, with the exception that altitude change would be the reference, speed change
would be the disturbance, and the output (judgment) would be of altitude change.
For perceptions of change in altitude, Figure 15 shows the predictions for the
strong forms of the GOFR and splay angle hypotheses. The solid lines show the
predictions for the GOFR hypothesis. When the percent change of GOFR is small it
should take longer to detect a change in altitude, than when the percent change in GOFR
is larger. The dashed lines show the predictions for a splay angle hypothesis. With splay
angle, judging altitude change should take less time when the changes in altitude are
larger, independent of any changes in speed.
-100 -80 -60 -40 -20 0 20 40 60 80 100
%GOF change
ReactionTime
High speed
Medium speed
Low Speed
Figure 15. Predictions of altitude judgments using the servo model

31
Based on earlier research (Wolpert 1988, Johnson et al. 1989, Flach et al.
1992, 1997) splay or parallel texture should be well suited for altitude judgments because
this texture would have salient signal from the splay angle element and little noise from
other sources for altitude judgments. The hypothesis would then be that, a person judging
altitude change when splay texture is used would behave as a high gain adaptive
controller. Speed would have little impact on altitude judgments. Depression or
perpendicular texture should be worst suited for altitude judgments because it would have
low signal and high noise. The hypothesis would be that, a human judging altitude
change when depression texture is used would behave as a low gain adaptive controller.
Speed should then have a significant impact on altitude judgments. Finally, grid or
checkerboard texture should give rise to altitude judgments, which are in between that of
splay and depression textures because grid texture has higher noise than splay texture but
still has higher signal than depression texture for altitude judgments. Speed should have
lower impact on altitude judgments than with depression texture.

32
III. METHOD
Design
This experiment is a logical follow up of Patrick (2002). In Patrick’s experiment,
participants were flown through a flight trajectory in which speed, altitude, or
combinations of the two were smoothly changed. The participants’ task in Patrick’s
experiment was to estimate the magnitude of speed and altitude change. Independent
variables used in his experiment were speed change, altitude change, flight direction and
block ordering. Dependent measures were magnitude estimates in which observers
specified their judgments of the degree of change in speed and altitude on a scale from –
100 to +100. Patrick’s results showed that, consistent with previous studies, judgments of
speed change were affected by the presence of altitude changes. Patrick’s study also
showed that altitude judgments were affected by the presence of speed changes. In both
cases, the changes were in a direction that was consistent with the change of GOFR.
Increases of GOFR were associated with increasing speed and/or decreasing altitude.
Decreases of GOFR were associated with decreasing speed and/or increasing altitude.
In the present experiment, as in Patrick’s experiment, participants observed a
series of trajectories where altitude, speed or both changed over the course of the
trajectory. The observer’s reaction time and the direction of the change were measured to
changes detected in speed or altitude depending on the trial sequence. This procedure was
repeated over surfaces with different texture gradients.

33
Independent variables for this experiment were speed change, altitude change, and
type of ground texture. The dependent variables for this experiment were reaction time
and direction of speed/altitude judgments.
A reason to look at reaction time (as opposed to just magnitude change), as a
dependent variable was to get a better understanding of the strategy adopted to detect
speed and altitude changes. Some participants in Patrick’s study reported basing their
judgments on not having seen speed and altitude changes while they occurred, but basing
their judgments on the differences observed in the initial and final flight conditions. In
this experiment, the goal was to test whether observers could perceive changes as they
happened.
Also using artificial ground textures namely splay, depression and grid (as
opposed to a naturalistic setting) tried to prevent participants from using static, local cues
such as runway edge markings, width of the runway or the dashed runway centerline,
which were reported to have been used by participants in Patrick’s (2002) study.
Procedure
A trial consisted of a preview period followed by a “change” period. The preview
period could vary randomly between three and seven seconds. The “change” period was
at most fifteen seconds, but could be shorter if a subject indicated a response by clicking
a mouse button prior to the end of the “change” period. There was no post-view period.
“Change” is in quotes to indicate that some trials were catch trials and had a zero rate of
change.
Each trial consisted of a maximum 22 s of total flight time over splay, depression
or grid textures. The participant did not have any control over the flight scene. Heading,

34
pitch and roll did not change at anytime during the flight. The first few seconds of the
flight was a preview period and then randomly, any time between the third and the
seventh second, manipulations in altitude or speed or both were made to the trajectory.
The participants signaled the detection of speed/altitude change by a mouse button click.
A left mouse button click signified an increase in speed/altitude, and a right mouse button
click signified a decrease. At the instant of the button press, the time elapsed since the
change occurred was recorded. On the button press, the trial ended and a new trial was
ready to begin which the observer initiated. The new trial again had the obligatory initial
preview period and continued as described previously. During one block which consisted
of three sets of 25 trials each over a different ground texture, participants were asked to
detect only changes in speed, and during another block which again consisted of three
sets of 25 trials over different ground textures, only changes in altitude. The order of the
blocks used a Latin-Square design as shown.
TABLE 1. Trial layout using a Latin Square design, which indicates order of the trials over
different textures and conditions.
Participant Speed Judgments Altitude Judgments
1 Grid Depression Splay Splay Depression Grid
2 Splay Grid Depression Grid Splay Depression
3 Depression Splay Grid Depression Grid Splay
4 Splay Depression Grid Grid Depression Splay
5 Grid Splay Depression Splay Grid Depression
6 Depression Grid Splay Depression Splay Grid
Participant Altitude Judgments Speed Judgments
7 Grid Depression Splay Splay Depression Grid
8 Splay Grid Depression Grid Splay Depression
9 Depression Splay Grid Depression Grid Splay
10 Splay Depression Grid Grid Depression Splay
11 Grid Splay Depression Splay Grid Depression
12 Depression Grid Splay Depression Splay Grid

35
There were a total of twelve participants. Each participant ran each of the six
conditions once. The first six participants did the speed block first and the altitude block
next, while the next six did the altitude block first and the speed block next. There were a
total of 25 trials per block. There were three blocks for each judgment type (speed or
altitude) and one block with each texture type. This resulted in a total of 150 trials.
Display
All experimental trials began at the same initial speed, altitude and GOF rate. The
initial values for these state variables were cruising speed of 180 knots, altitude of 600
feet, and therefore the GOFR equaled 0.506 eye height/sec. Participants did not have any
control over the flight trajectory.
TABLE 2. Changes in GOFR as a function of speed and altitude manipulations.
The speed of 180 knots was chosen because it is a common cruising speed and is
within the range of landing approach speeds of many airplanes. Large changes in airspeed
below 180 knots would lead to an engine stall in the aircraft and large changes over 180
knots would lead to aircraft over speed during landing. The initial altitude of 600 feet was
chosen since it is a common altitude for low-level flight and allows ground detail to be
seen. A suitable height at which ground texture was visible was important in this
experiment since ground texture was one of the independent variables manipulated. The
initial GOFR is the ratio of initial speed in feet/sec to the initial altitude in feet, which
equals 0.506 h/s. Assuming a trial lasted its full length of the 15 s “change” period,
percentage changes in airspeed and altitude were based on these initial values and were
% Change in Altitude
+33(800) +17(700) 0(600) -17(500) -33(400)
+33(240) 0(0.506) +14(0.579) +33(0.675 +60(0,810) +100(1.013)
+17(210) -12(0.444) 0(0.506) +17(0,591) +40(0.709) +75(0.886)
0(180) -25(0.380) -14(0.434) 0(0.506) +20(0.608) +50(0.760)
-17(150) -38(0.317) -29(0.361) -17(0.422) 0(0.506) +25(0.633)
-33(120) -50(0.253) -43(0.289) -33(0.338) -20(0.405) 0(0.506)
% Change in
Speed

36
manipulated for five levels of speed change and five levels of altitude change. These
values are shown in Table 2.
The five percentage changes in speed and altitude were a 33% increase, a 17%
increase, no change, a 17% decrease, and a 33% decrease. GOF rate would vary based on
speed and altitude changes. The values of each combination of these state variables are as
shown in Table 2. All trials started at cruising speed of 180 knots and an initial altitude of
600 feet. Over 15 s, the final speeds could change from 180 knots to any one of the 4
values: 240 knots, 210 knots, 150 knots, 120 knots or would remain at 180 knots as
shown. Over the same 15 s, the final altitudes could change from 600 feet to any one of
the 4 values: 800 feet, 700 feet, 500 feet, 400 feet or would remain at 600 feet as shown.
If the trial ended at any point before the change period of 15 s is up, then speed/altitude
final values would not be reached. For e.g., a +33 percent change in speed, would
indicate that speed would change from an initial value of 180 knots to a final value of 240
knots if the trial goes through the change period of 15 s. A -17% change in altitude would
indicate that altitude has changed from an initial value of 600 ft to a final value of 500 ft,
again, if the trial goes through the entire change period of 15 s. A no change condition
would indicate no change in either altitude or speed or both over 15 s. The final values
for each speed, altitude and resulting GOF rate are in parentheses. For example, a 17%
final increase in speed over 15 s (210 kts final speed) combined with a 17% decrease in
altitude over 15 s (500 ft final altitude) would result in a 40% increase in GOF rate (0.709
h/s final GOF rate).
Changes in the independent variables were fractional changes based on the initial
values of these variables. State changes were smooth and evenly stepped transformations

37
from the initial to the final values. Equations 3 through 6 are the equations of motion
used to accomplish the changes in the experimental variables.
Equations 3 and 4 were used to calculate the current speed for each point along
the flight path during manipulation phase of the trial. These equations were as used by
Patrick (2002) for his experiment.
SCurrent = SInitial * exp (RSpeed * TElapsed) (3)
Where RSpeed = (1/ TTotal) * ln (SFinal /SInitial) (4)
Where SInitial is the initial speed (180 knots always for this experiment)
SCurrent is the current speed
SFinal is the final speed
RSpeed is the rate of change in speed
TElapsed is the time elapsed in the manipulation phase of flight in seconds
TTotal is the total time in the manipulation phase of flight in seconds (15 s always
for this experiment)
Equations 4 and 5 were used to calculate the current altitude for each point along
the flight path during the manipulation phase of the trial.
ACurrent = AInitial * exp (RAltitude * TElapsed) (5)
Where RAltitude = (1/ TTotal) * ln (AFinal /AInitial) (6)
Where AInitial is the initial altitude (600 feet always for this experiment)
ACurrent is the current altitude
AFinal is the final altitude
RAltitude is the rate of change in altitude for each data point
TElapsed is the time elapsed in the manipulation phase of flight in seconds

38
TTotal is the total time in the manipulation phase of flight in seconds (15 s always
for this experiment)
Together these equations determined the movement of the observer along the
flight path during the manipulation phase of the flight. Note from Equations 3 and 5 that
speed and altitude varied exponentially over the length of the trial. Exponential control of
the flight trajectories provided a uniform change in GOF rate, as specified by changes in
speed and altitude, over the length of each flight.
An important difference between this experiment and Patrick’s (2002) was the
length of the change period. A 10 s change period was used in Patrick’s study where as a
change period of 15 s was used for this one. Thus, the values for the instantaneous rates
of change were different in the two experiments. Table 3 shows a comparison between
the instantaneous rates of change used in the two experiments.
Hence, while the total change in both speed and altitude was the same for both the
experiments, the rate of change was slower for this experiment as compared to Patrick’s.
TABLE 3. Instantaneous rates of change for this experiment and that of Patrick’s experiment
Apparatus
Speed Rate (Junaid) Rate (Patrick)
240 0.0192 0.0288
210 0.0103 0.0154
180 0.0000 0.0000
150 -0.0122 -0.0182
120 -0.0270 -0.0405
Altitude Rate (Junaid) Rate (Patrick)
800 0.0192 0.0288
700 0.0103 0.0154
600 0.0000 0.0000
500 -0.0122 -0.0182
400 -0.0270 -0.0405

39
Another significant difference between this study and Patrick’s (2002) study was
that Patrick did his experiment with a 3-D view in the CAVE, a virtual-reality
environment with a panoramic view, which provided a visual simulation of self-motion
experienced during a flight. The current experiment was simulated on an Alienware
Personal Computer (Miami, FL) workstation with a Sony monitor. Also Patrick’s study
used a refresh rate of 19-24 Hz where as a refresh rate of 55 Hz was used for this
experiment. The program was designed and run using Multigen-LynX-Prime (Ver 1.2)
simulation software and individual elements like ground textures were built using
Multigen-Creator (Ver 2.6).
A mounted frame with a chin rest maintained viewing distance at 18 inches from
the screen. This viewing distance created a horizontal field of view for the simulation of
45 degrees of visual angle. A black oval border was placed over the monitor so that the
participant could not see the edges of the monitor. The experiment was conducted in a
small room painted black. Arrows indicating judgment of increase/decrease were pasted
on the mouse itself as a reminder to observers. Before the beginning of the trial block for
a specific condition, it was made sure the participant knew that it was either
speed/altitude that was being judged. At the end of the condition, feedback was obtained
whether there were any judgment reverses that happened during the trial block. There
was not a single instant when a participant stated having made a judgment reversal during
any of the trials.
Earthy colors like green and brown (better visible in the grid texture) were chosen
as colors for the textures in the simulation to make the setting more naturalistic.

40
The experimental setup is shown in Figure 16 and the three different textures used
are shown in Figures 17, 18, and 19.
Figure 16. Experimental setup shown includes a Sony monitor, chin rest, and an oval frame to
hide screen edges. Note that the visible screen edge in the picture is due to the camera angle. It
was not visible to participants.

41
Figure 17. Grid or checkerboard texture simulated a checkerboard ground texture that included
both splay and depression lines.

42
Figure 18. Splay or parallel texture which simulated vertical strips of texture parallel to the
forward direction of motion

43
Figure 19. Depression or perpendicular texture simulated horizontal strips of texture
perpendicular to the forward motion path

44
IV. ANALYSIS
As stated in the procedure, there were three valid responses a participant could
have made. A participant indicated an increase in speed/altitude by clicking the left
mouse button, indicated a decrease in speed/altitude by clicking the right mouse button
and the participant indicated the no change condition by letting the trial time out (by not
clicking any mouse buttons). A fourth possible response was when a subject clicked even
before the change began to take place. Out of possible 1800 trials, participants clicked
early even before the change started a total number of 287 times over all the trials. These
responses were excluded from later analysis. Percent exclusion over different conditions
is as shown in Table 4.
Percent Excluded Analysis
TABLE 4. Percent exclusions over different conditions and textures
As seen in Table 4, there were fewer percentage exclusions over splay texture (6%
and 3% for speed and altitude judgments respectively) than grid (24% and 12%) and
depression (26% and 24%) textures. While judging over splay texture, participants
seemed to have a lesser degree of confusion while compared to grid and depression
textures, about when the change started and for most of the time were judging changes
after the trial got well into the “change” time when there were manipulations in
speed/altitude taking place. This could also indicate that visible changes over the splay
texture were very subtle and the participants could see these changes only when they get
well into the trial.
Task Grid Depression Splay
Speed Judgment 0.24 0.26 0.06
Altitude Judgment 0.12 0.24 0.03

45
Reaction Time Analysis
In choosing reaction time as the dependent variable, it had been assumed that
participants would generally respond either consistently with the actual changes in speed
or altitude or at least with the changes in GOFR. It was assumed that reaction time would
index the difficulty of the judgments, with longer reaction times indicating more difficult
judgments. However, it was found that this assumption was not correct and was perhaps
confounded by various methodological errors, which are being investigated and debated.
Based on these investigations, suggestions for further research have been made in a later
section. However the performance metric, namely judgments of increase/decrease of
speed/altitude for speed/altitude judgments was looked into, to investigate and understand
the strategy used by the participants for making judgments.
Percent Correct Analysis
While judging speed change, if there was an actual increase/decrease in speed
during the trial, the judgment of that trial would be correct if the participant indicated that
there has been an increase/decrease in speed by clicking the designated mouse button,
independent of change in the value of altitude. Similarly, while judging altitude change, if
there was an actual increase/decrease in altitude during the trial, the judgment of the trial
would be correct if the participant indicated that there has been an increase/decrease in
altitude by clicking the designated mouse button, independent of change in the value of
speed. For a no change condition during speed judgments (final speed remained equal to
the initial speed of 180 kts), the trial was counted as correct only when the participant had
indicated a no change in speed by letting the trial time out by not clicking any mouse
buttons, again independent of change/no-change in the value of altitude. Similarly, for a

46
no change condition during altitude judgments (final altitude remained equal to the initial
altitude of 600 ft), the trial was counted as correct only when the participant had indicated
a no change in altitude by letting the trial time out by not clicking any mouse buttons,
again independent of change/no-change in the value of speed.
Table 5 shows the percent correct judgments by subject and block (texture by
judgment type). Tables 6 through 11 show the percentages over the twelve participants
who judged correctly in each of the 25 combinations of speed and altitude change. This
task turned out to be much more difficult than had been anticipated. Many of the
participants were responding at less than chance levels, especially when judging speed. A
chance level for the way this experiment has been set up would not be 50% as normally
expected, but would be around 33% since the participant had three possible options that
he could respond to.
TABLE 5. Percent correct out of 25 trials in each block (texture x judgment) for each subject.
Table 5 gives us percent correct values out of 25 trials per subject. This analysis
included the excluded trials and these trials were counted as incorrect responses. The
average values obtained from Table 5 were included in Table 5a for further analysis.
Participant Speed (Grid) Speed (Depr) Speed (Splay) Altitude (Grid) Altitude (Depr) Altitude (Splay)
1 0.32 0.36 0.36 0.64 0.48 0.44
2 0.64 0.36 0.52 0.60 0.40 0.64
3 0.40 0.32 0.44 0.52 0.32 0.80
4 0.08 0.00 0.40 0.20 0.16 0.80
5 0.40 0.32 0.56 0.72 0.64 0.76
6 0.24 0.40 0.28 0.84 0.20 0.96
7 0.32 0.12 0.40 0.56 0.12 0.32
8 0.32 0.48 0.36 0.76 0.16 0.92
9 0.48 0.44 0.44 0.64 0.28 0.76
10 0.56 0.32 0.32 0.44 0.20 0.76
11 0.20 0.16 0.40 0.60 0.20 0.20
12 0.24 0.20 0.40 0.24 0.48 0.24
Average 0.35 0.29 0.41 0.56 0.30 0.63

47
TABLE 5a. Average percent correct obtained by averaging over the 12 subjects
Table 5a gives us average values of percent correct over the 12 subjects. The overall
average correct for altitude judgment was higher than that of speed judgments by about
15 percentage points. This seems to indicate that altitude judgments were easier to make
than speed judgments.
Also from Table 5a, we see that depression texture had a very low average percent
correct for both speed and altitude judgments. This seems to indicate that judgments over
the depression texture were the toughest among the three textures.
Table 6, 7 and 8 show percent correct for speed judgments, and tables 9, 10 and 11
show percent correct for altitude judgments, over the 12 participants for each
combination of speed and altitude. For this analysis, the trials where subjects responded
even before the change started were excluded. On looking at the tables, there seem to be
trends that would indicate that participants seem to obtain a higher number of percent
correct values when there are simultaneous increases/decreases with both speed and
altitude.
TABLE 6. Percent correct out of 12 participants for each combination of speed and altitude
change when judging speed over grid texture
Task Grid Depression Splay Average
Speed Judgment 0.35 0.29 0.41 0.35
Altitude Judgment 0.56 0.30 0.63 0.50
Average 0.46 0.30 0.52
Altitude
Speed 800 700 600 500 400
240 0.80 0.60 0.30 0.55 0.70
210 0.70 0.78 0.33 0.44 0.44
180 0.40 0.11 0.22 0.25 0.11
150 0.33 0.28 0.50 0.50 0.44
120 0.11 0.55 0.38 0.80 0.63

48
change when judging speed over depression texture
change when judging speed over splay texture
TABLE 9. Percent out of 12 participants for each combination of speed and altitude change when
judging altitude over grid texture
change when judging altitude over depression texture
Altitude
Speed 800 700 600 500 400
240 0.50 0.50 0.00 0.10 0.30
210 0.80 0.60 0.29 0.33 0.43
180 0.33 0.33 0.10 0.50 0.40
150 0.63 0.42 0.13 0.22 0.64
120 0.45 0.25 0.33 0.40 0.50
Altitude
Speed 800 700 600 500 400
240 0.73 0.50 0.30 0.60 0.75
210 0.77 0.44 0.50 0.60 0.73
180 0.80 0.45 0.45 0.30 0.80
150 0.82 0.80 0.55 0.80 0.90
120 0.82 0.82 0.36 0.60 0.75
Altitude
Speed 800 700 600 500 400
240 0.88 0.71 0.50 0.25 0.20
210 0.63 0.75 0.67 0.20 0.11
180 0.10 0.40 0.13 0.11 0.22
150 0.11 0.22 0.56 0.64 0.64
120 0.29 0.50 0.20 0.90 0.25
Altitude
Speed 800 700 600 500 400
240 0.75 0.58 0.00 0.45 0.73
210 0.83 0.55 0.00 0.64 0.91
180 0.09 0.08 0.55 0.10 0.00
150 0.33 0.67 0.27 0.45 0.45
120 0.36 0.64 0.17 0.83 0.33

49
change when judging altitude over splay texture
To further investigate the trends and whether there was any meaningful pattern in
the data so parsed, a correlational analysis with GOFR change was done. Table 12 shows
the correlations for percent correct with GOFR and across the different textures and
judgment conditions. There were no significant correlations between percent correct
values and GOFR over the different textures for either speed or altitude judgments.
However, there were significant correlations for percent correct with the grid texture and
the other two textures, depression and splay while judging speed changes. This suggested
the possibility that a common criterion, that the GOFR strategy was not able to account
for, might be used for making speed judgments. There were still no trends observed to
indicate any strategy being adopted by the participants for judging altitude at this stage of
the analysis.
TABLE 12. Percent correct correlations over different conditions and textures.
** Correlation is significant at the 0.01 level (2-tailed).
Junaid_Data GOFR Speed (Grid) Speed (Depre) Speed (Splay) Altitude (Grid) Altitude (Depre) Altitude(Splay)
GOFR 1.000 0.119 - 0.170 0.122 - 0.081 - 0.184 0.187
Speed (Grid) 1.000 0.574** 0.640** 0.130 0.252 - 0.063
Speed (Depre) 1.000 0.245 - 0.041 0.167 - 0.199
Speed (Splay) 1.000 0.367 0.304 0.023
Altitude (Grid) 1.000 0.373 0.073
Altitude (Depre) 1.000 0.118
Altitude(Splay 1.000
Altitude
Speed 800 700 600 500 400
240 0.45 0.33 0.66 0.55 0.83
210 0.66 0.75 0.66 0.50 0.83
180 0.45 0.58 0.64 0.75 0.64
150 0.58 0.66 0.64 0.66 0.82
120 0.75 0.64 0.75 0.64 0.83

50
V. DIRECTION INDICATOR ANALYSIS
To examine the possibility that some specific strategy has been used by the
participants, while at least making judgments about speed change as was indicated in
significant correlations obtained within the textures themselves for speed judgments in
the percent correct analysis, another performance metric, the Direction Indicator, was
evaluated. It is given by the formula
Direction Indicator, D.I= (#inc-#dec) / (#legitimate responses) (7)
Where #inc indicated the number of participants (out of a possible 12) who saw an
increase in speed/altitude, #dec indicated the number of participants (again out of a
possible 12) who saw a decrease in speed/altitude. The #legitimate responses included
judgments for no change (no_response) and excluded responses where participants
clicked the mouse button before a change actually took place. Therefore,
Number of legitimate responses = (#inc+#dec+#no_response) (8)
The direction indicator is a value which indicates what most participants are
seeing. If the Direction Indicator (DI) value is close to +1, it indicates most participants
among the 12 saw an overall increase. If the DI value is close to –1 it indicates most
participants among the 12 saw an overall decrease. Finally, if the DI value is close to 0, it
indicates most participants among the 12 saw a no change or that the number of
participants who saw an increase was about the same as the number of participants who
saw a decrease.
Here are some examples of how the DI value was computed:

51
a. Out of 11 legitimate responses from the 12 participants, 9 said there was an increase, 1
said there was a decrease, 1 did not see a change, then from (7), DI = +0.7.
DI value of +0.7, which is close to +1, indicates that most participants saw an
increase in speed/altitude.
b. Out of 12 legitimate responses from the 12 participants, 2 said increase, 9 said
decrease, 1 did not see a change, then from (7), DI = -0.58.
DI value of -0.58, which is closer to -1, than a zero or +1, indicates that most
participants saw a decrease in speed/altitude but to a lower extent
c. Out of 10 legitimate responses from the 12 participants, 3 said increase, 2 said
decrease, 5 did not see a change, then from (7), DI = 0.1.
DI value of 0.1, which is closer to zero than +1 or -1, indicates that most
participants saw a no change in speed/altitude.
TABLE 13. Direction Indicator (DI) correlations over different conditions and textures
* Correlation is significant at the 0.05 level (2-tailed).
Table 13 shows the pattern of correlations using the DI measure (rather than
percent correct as was done in Table 12). As with percent correct, there were no
significant correlations with GOFR for speed judgments. However, there were significant
correlations with GOFR for altitude judgments over grid and splay textures. The negative
correlations are consistent with expectations of the GOFR hypothesis: an increase in
JunaidData GOFR Speed(Grid) Speed(Depre) Speed(Splay) Altitude(Grid) Altitude(Depre) Altitude(Splay)
GOFR 1.000 0.138 -0.316 0.318 -0.746** 0.130 -0.698**
Speed(Grid) 1.000 0.613** 0.494* 0.305 0.263 0.346
Speed(Depre) 1.000 0.213 0.540** 0.226 0.564**
Speed(Splay) 1.000 -0.119 -0.041 -0.117
Altitude(Grid) 1.000 0.107 0.865**
Altitude(Depre) 1.000 0.231
Altitude(Splay) 1.000

52
GOFR should correspond with a decrease in the DI (most people should see a decrease in
altitude).
As with the correlations for percent correct (Table 12), there were significant correlations
for the DI measures for speed judgments between grid and the depression and splay
textures as shown in Table 13. In addition, there were significant positive correlations
between speed judgments with depression texture and altitude judgments with grid and
splay textures. This suggests that people may have been using the same criterion for
judging speed change with depression texture as they were using for judging altitude with
the grid and splay textures, and once again GOFR was not able to account for judgments
so made.
For altitude judgments, even though GOFR accounted for high significant
correlations with the grid and the splay textures, there were higher significant correlations
with the two textures themselves as shown in Table 13. Also, as mentioned earlier, there
were significant positive correlations between the speed judgments with depression
texture and the altitude judgments with grid and splay textures. This suggests that there is
some common criterion that is being followed by the participants which has not surfaced
yet with the GOFR/DI analysis. It seems that, there definitely is another property or
invariant in the optic flow field that participants are basing their judgments upon which
has not been an emergent property of the current analysis.
In an attempt to learn more about what factors might be influencing judgments
about speed and altitude, the variables altitude and speed (edge-rate) were included in the
correlational analysis. Altitude and edge-rate were correlated with the human

53
performance measure – Direction Indicator for both speed (Table 14) and altitude (Table
15) judgments.
TABLE 14. Correlations with DI and altitude, GOFR and Edge-rate for speed judgments (human
performance)
Table 14 shows correlations between the three variables GOFR, altitude and edge-
rate and the human performance indicator, DI, for speed judgments over the three ground
textures. There were no significant correlations between GOFR and DI with any of the
three ground textures for speed judgments as seen earlier in Table 13. But there were
significant positive correlations between DI and the manipulated variable, altitude over
grid and depression textures. These positive correlations between DI and altitude are
surprising because, according to the GOFR hypothesis, an increase in altitude should give
rise to a perception of a decrease in speed and a decrease in altitude should give rise to a
perception of an increase in speed, and therefore negative correlations are what should be
expected. The correlations suggest that the participants perceived an increase in altitude
as an increase in speed and a decrease in altitude as a decrease in speed.
There was also a significant positive correlation between the manipulated variable
speed (edge-rate) and DI for the grid texture. The direction of this correlation is
consistent with the edge-rate hypothesis of speed judgments, which would indicate that
increased edge rates lead to increased values for the DI measure and vice versa. It should
be noted, however, that the correlation for depression texture was not significant. In terms
of the signal-to-noise hypothesis, the salience of edge-rate should be greater with the
Speed Judgments Speed (Grid) Speed (Depre) Speed (Splay)
GOFR 0.138 -0.316 0.318
Altitude 0.417* 0.628** 0.007
Speed/EdgeRate 0.563** 0.234 0.324

54
depression texture. There were no significant correlations seen with splay texture for
speed judgments with any of the manipulated variables. This is consistent with the fact
that there is essentially no optical information to specify speed change with the splay
texture.
The correlations with speed judgments seem to indicate that the manipulated
variable, altitude, is playing a significant part in influencing judgments of speed over the
grid and the depression textures. Information about whether altitude as a manipulated
variable is influencing judgments of altitude is investigated in using the correlations
obtained in Table 15.
TABLE 15. Correlations with DI and altitude, GOFR and Edge-rate for altitude judgments
(human performance)
Table 15 shows correlations between the three variables GOFR, altitude and edge-
rate and the human performance indicator: DI for altitude judgments over the three
ground textures. Significant correlations are seen with GOFR over grid and splay textures
as seen earlier in Table 13. Very strong positive correlations are seen between the DI
measure and the manipulated variable altitude over grid and splay textures. This suggests
that splay angle might be the optical variable driving judgments about altitude change, at
least over the grid and splay textures. It is possible that the correlations with GOFR (seen
earlier in Table 13) simply reflect the negative correlation of altitude change and GOFR.
This cannot be taken as unambiguous support for the GOFR hypothesis with respect to
altitude judgments.
Altitude Judgments Altitude (Grid) Altitude (Depre) Altitude(Splay)
GOFR -0.746** 0.130 -0.698**
Altitude 0.910** 0.231 0.897**
Speed/EdgeRate -0.185 0.464* -0.112

55
Speed (edge-rate) showed a significant positive correlation with DI for depression
texture while judging altitude. This correlation seems to suggest that participants were
using a strategy based on speed for judging altitude over the depression texture. This
correlation is surprising for two reasons. First, it is in the opposite direction of what
would be expected given an optical analysis. Increasing speed should lead to judgments
of decreasing altitude and vice versa. Second, the correlation between speed and DI was
not significant for judgments of speed (Table 14). It is curious that participants were
more sensitive to edge-rate when judging altitude than when judging speed.
The DI analysis came up with a few curious correlations that warrant further
investigation. For speed judgments, there were significant positive correlations of DI with
the manipulated variable altitude over grid and depression textures (Table 14). These
positive correlations were inconsistent with the GOFR hypothesis. For altitude
judgments, there was a significant correlation with edge-rate and DI over depression
texture, which again is inconsistent with the GOFR strategy. Also altitude on its own is
not a perceptual variable. Altitude has to be specified from properties in the optical flow
field. To find that functional property of altitude that participants seem to use for basing
their altitude/speed judgments we go back to the Law of Motion perspective (1), given by
Gibson et al. (1955).
Looking at the equation of the law of motion perspective (1), it has been shown by
earlier research that the ratio V/h in the equation leads to speed/altitude misjudgments,
when judgments are made using the GOFR strategy (Warren, 1982; Ballard et al., 1998;
Patrick, 2002; Patrick et al., 2003; Junaid et al., 2004). It is also known that V: speed of
self-motion can be judged optically using the edge-rate strategy (Denton, 1979, Warren,

56
1982; Ballard et al., 1998; Patrick, 2002; Patrick et al., 2003; Junaid et al., 2004). But it is
not known for sure which strategy is being adopted to judge h: the change in vertical
distance during self-motion. It was earlier shown that it is the GOFR strategy (Warren,
1982; Ballard et al., 1998; Patrick, 2002; Patrick et al., 2003; Junaid et al., 2004), which
is being used to make judgments about altitude, but the correlations seen in earlier
analysis seem to indicate that this assumption perhaps might not be correct.
An astute participant could observe subtle changes in pixels at the edges of the
display during a trial. This effect was more pronounced in the splay texture, than the grid
texture and was not visible in the depression texture. The pixels either sped up or slowed
down as the altitude decreased or increased correspondingly. Participants could have
perhaps used these pixel effects, which could be an important display artifact, to make
judgments of speed and altitude. This effect could perhaps explain why some basic
assumptions of GOFR did not hold good here. Whether this potential artifact can explain
our results is still unclear. However, it is important to acknowledge the possibility that the
patterns in our data reflect some artifact in the graphical presentation.
To further explore the possibility that there could be another property of the optical
flow field that might account for the correlations with altitude, the angle of approach
(Langewiesche, 1944, Gibson, et al. 1955) or the H-angle (Hasbrook, 1975) was
examined.

57
VI. H-ANGLE WITH DI ANALYSIS
Figure 20. Angle of Approach (Langewiesche, 1944) or the H-Angle (Hasbrook, 1975)
Langewiesche (1944), as mentioned earlier, in his book Stick and Rudder set about
describing a set of “visual tricks” for successful navigation while flying and to aid
approaches to landing.
Among the cues, or “visual tricks”, Langewiesche illustrated the use of what he
called the angle of approach with respect to a glide path to a landing spot with reference
to the horizon as shown in Figure 20. He said that the angle cue with reference to the
horizon could be used to judge self-motion and navigate during flight. Langewiesche and
later on Gibson advocated the idea that it is not absolute heights and distances a pilot
judges, but angular distances with respect to different points in the field of view.
Hasbrook in 1975 referred to the angle of approach as the H-Angle with respect to the
horizon. For the purpose of this analysis, the angles above the optical horizon are referred
to as positive H-Angles and below as negative H-Angles.

58
For five levels of speed “change” and five levels of altitude “change” 20 different H-
Angles are obtained. The H-Angle remains zero when the final altitude remains at 600.
The H-Angles so obtained are as shown in Table 16.
TABLE 16. H-Angle values for different speeds and altitudes and their corresponding final
vertical (due to final altitude values) and horizontal (due to final speed values) distances
To calculate the H-Angle, final vertical distance covered (ft) is first computed. The
final vertical distance covered is simply the difference of initial altitude (ft) and final
altitude (ft). The final horizontal distance covered (ft) is then computed. The final
horizontal distance is obtained by integrating Equation 3 within the limits 0 to 15 s. On
Altitude (Ft)Speed (Kts) Vertical Distance (Ft) Horizontal Distance (Ft)H-Angle
800 240 200.00 5280.25 2.17
800 210 200.00 4927.17 2.32
800 180 200.00 4557.15 2.51
800 150 200.00 4166.00 2.75
800 120 200.00 3696.06 3.10
700 240 100.00 5280.25 1.08
700 210 100.00 4927.17 1.16
700 180 100.00 4557.15 1.26
700 150 100.00 4166.00 1.37
700 120 100.00 3696.06 1.55
600 240 0.00 5280.25 0.00
600 210 0.00 4927.17 0.00
600 180 0.00 4557.15 0.00
600 150 0.00 4166.00 0.00
600 120 0.00 3696.06 0.00
500 240 -100.00 5280.25 -1.08
500 210 -100.00 4927.17 -1.16
500 180 -100.00 4557.15 -1.26
500 150 -100.00 4166.00 -1.37
500 120 -100.00 3696.06 -1.55
400 240 -200.00 5280.25 -2.17
400 210 -200.00 4927.17 -2.32
400 180 -200.00 4557.15 -2.51
400 150 -200.00 4166.00 -2.75
400 120 -200.00 3696.06 -3.10

59
integrating Equation 3, the total horizontal distance traveled within the time interval
specified is obtained. On obtaining the total vertical and horizontal distances, H-Angle in
radians is then obtained by the trigonometric relation,
H-Angle (radians) = Arctan (final vertical distance) / (final horizontal distance) (8)
H-Angle in degrees is obtained by multiplying the conversion factor 57.286 with the H-
Angle (radians) value.
TABLE 17. H-Angle correlations with Altitude, GOFR and Edge-rate (not human performance)
To investigate if H-Angle is the functional property of altitude that people infer from the
environment for judging speed/altitude, the scalar quantity altitude, and the optical
quantities H-Angle, GOFR and edge-rate were correlated and compared among
themselves (see Table 17). On correlating the optical variable H-Angle with altitude, a
high significant correlation is seen. This correlation could be just because of the way the
variables used to find the H-Angle were manipulated with altitude having the most
influence on these manipulations. An important point to note is that altitude and the
perceptual variable H-Angle have similar correlations with the other two perceptual
variables, namely, GOFR and edge-rate. For example, both altitude and H-Angle have
zero correlations with edge rate. These zero correlations are because of the way the
variables altitude and speed were manipulated in this experiment and not because of any
other coupling they have in the real world. H-Angle obtains a high negative correlation
Junaid Data Altitude H_Angle GOFR EdgeRate
Altitude 1.000 0.992** -0.703** 0.000
H-Angle 1.000 -0.677** 0.000
GOFR 1.000 0.675**
EdgeRate 1.000

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