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from aerial LiDAR data, while Dick et al. [ 120 ] addressed how to fit architectural
primitives (walls, roofs, columns) to image sets taken at ground level. Golovinskiy
et al. [ 172 ] trained a system to recognize objects like lampposts, traffic lights, and
fire hydrants in large-scale LiDAR datasets, while Vasile and Marino [ 511 ] addressed
the detection of military ground vehicles from foliage-penetrating aerial LiDAR. Kim
et al. [ 238 ] discussed how salient regions could be automatically detected in co-
registered camera and laser scans of an outdoor scene. Huber et al. [ 208 ] proposed
an algorithm for part-based 3D object classification (e.g, types of vehicles) based on
spin images. More generally, Chen and Stamos [ 87 ] discussed how to segment range
images of urban scenes into planar and smooth pieces, which can be of later use in
registration and object detection.
8.7
HOMEWORK PROBLEMS
8.1 A LiDAR scanner reports that a point at azimuth 60 and elevation 20
is
located 100m away. Convert this measurement into an
(
X , Y , Z
)
Cartesian
coordinate system in which the scanner is located at (0,0,0).
8.2 Compute the time resolution required, in picoseconds, for a pulse-based
LiDAR's receiver electronics if we want the system to have
2mm accuracy.
8.3 Compute the distance to a scene point for which 500 nanoseconds was
recorded for the time-of-flight of a LiDAR pulse.
8.4 Prove the relationship between the phase shift
±
ψ
and the time of flight t in
Equation ( 8.2 ).
8.5
Show that the restriction on the range ambiguity in a phase-based LiDAR
scanner, 0
<ψ<
π
π
2
, imposes a maximum range of
c
, where c is the
is the frequency of the modulating sinusoid in radians.
8.6 A phase-based LiDARwith carrier frequency 1.3
speed of light and
ω
10 7 radians/sec is used to
scan a scene. Compute the distance to a scene point for which a
×
π/
3 radian
phase shift was recorded.
8.7
Some flash LiDAR systems estimate the phase of an amplitude-modulated
signal using four samples. Suppose the transmitted signal is f
(
t
) =
cos
t
)
and the received signal is g
B , where A is the attenuated
amplitude of the signal and B is a constant offset. Show that the phase shift
ψ
(
t
) =
A cos
t
+ ψ) +
can be recovered as
arctan g 3
g 1
ψ =
(8.24)
g 0
g 2
g i 2 ω
.
where g i =
8.8 We can interpret the triangulation process for a stripe-based structured
light sensor as the intersection of a 3D line (corresponding to the ray from
the camera center through the observed image coordinates
(
x , y
)
on the
stripe) with a 3D plane aX
0 (corresponding to the light
plane from the laser). Determine a closed-form formula for this line-plane
intersection as the solution of a 3
+
bY
+
cZ
+
d
=
×
3 linear system. (Hint: write the line as
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