Biomedical Engineering Reference
In-Depth Information
FIGURE 9.23
The simplest case of an optical-flow measurement from an aircraft: a downward-looking camera, a for-
ward-moving aircraft, over a flat surface.
world around it as patterns of optical flow. For
the simplest case of a downward-looking per-
spective-projection camera mounted on a for-
ward-moving aircraft flying over flat ground,
as shown in
Figure 9.23
, the optical-flow vector
f
is given by
at any significant height, optical flow induced
by rotation of the head will be the primary
measurement produced by the optical-flow
system. In a
strap-down
system
[38]
, rotation
can be canceled by measuring the rotation
using gyroscopes and subtracting the effect
from the optical-flow field. Unlike the effect of
translation, rotation induces an optical Flow
pattern that does not vary with distance to the
surface viewed.
In all experiments and equations that fol-
low, rotation was removed by software com-
pensation of the optical-flow vector using gyro
measurements from the attitude reference in
the aircraft.
f
=−
k
v
(9.14)
r
,
where
v
is the velocity,
r
is range to the ground,
and
k
is the camera constant that scales world
coordinates to image coordinates. Note that
f
is a 2-dimensional vector on the perspective-
projection camera's imaging plane. From this
simple equation, it is also clear that if
k
,
v
, and
f
are known, then
r
can be computed. There is a
substantial literature debating the exact means
used by insects to compute optical flow
[2, 39]
;
however, it is well established that insects use
optically detected relative movement of the
world extensively for flight control.
Rotation in pitch and roll in the case of a fly-
ing insect or vehicle will also appear as optical
flow. If
f
is optical flow in pixels per second,
then
9.5.2 Height
The difficulty faced by aircraft navigation sys-
tems is that there is no absolute instantaneous
measure of inertial-frame velocity. Airspeed is a
measure of dynamic pressure relative to the air-
mass in which the aircraft is flying. True airspeed
(
v
TAS
)
is the airspeed measure compensated for
the barometric pressure and temperature. Veloc-
ity is the resultant of the
v
TAS
along the well-
calibrated and compensated magnetic heading
unit vector
(
m
)
and the wind
(
w
)
, as shown in
Figure 9.24
; thus,
f
=−
k
ω,
(9.15)
where
ω
is a rotation orthogonal to the direc-
tion of view. The effect of rotation is not signifi-
cant for insects if they stabilize their heads (in
dragonflies, using the ocelli), so rotation angles
do not always enter the visual system. If not,
m
|
m
|
+
w
.
(9.16)
v
=
v
TAS
