Graphics Reference
In-Depth Information
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
/ω
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
(ω
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
(ω
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