Agriculture Reference
In-Depth Information
ground truth where the vehicle is resting on. In addition, camera coordinates depend
on the inclination angle of the camera (
), so that distances to the vehicle from a
given obstacle will be different according to the camera tilt angle. Furthermore,
coordinates and scene renderizations taken by cameras set at different inclination
angles will be neither comparable nor miscible. To solve this problem, it is possible
to define an alternative coordinate system with the origin vertically aligned with the
camera but at ground level, with the
z
coordinates representing the height of objects
above the ground, and the
Y
axis providing the horizontal (parallel to ground) dis-
tances between the camera and the objects within its field of view, that is, the ranges.
The
X
-axis is perpendicular to the other two in order to form a Cartesian coordinate
system, and is therefore always perpendicular to the forward direction. The sche-
matic diagram shown in Figure 12.4a provides the
ground coordinate system
for an
agricultural vehicle equipped with a perception sensor affixed to the front end. After
both coordinate systems have been defined, the only step remaining is the transfor-
mation from the original camera coordinates to the operative ground coordinates.
This transformation has to be applied to every single point successfully correlated
from each pair of stereo images. Equation 12.2 provides the mathematical expression
to carry out the coordinate transformation, where (
x
,
y
,
z
) are the ground coordinates,
(
x
c
,
y
c
,
z
c
) represent the original camera coordinates delivered by the correlation soft-
ware,
ϕ
is the inclination angle of the camera, and
h
c
is the camera height measured
vertically above the ground. These parameters are graphically represented in Figure
12.4b for a generic point
P
. The transformation given in Eq. 12.2 is straightforward;
however, field experience has shown that small mistakes made in the estimation of
ϕ
ϕ
may result in significant errors in the 3-D representation of a scene. As a practical
check after the transformation from camera to ground coordinates has been per-
formed, it is always recommended to verify that the represented ground is horizontal
and establishes the origin of heights (
z
coordinates).
⎡
⎤
⎡
⎤
⎡
⎤
⎡
⎤
x
y
z
x
y
z
1
0
0
0
0
1
c
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎢
⎢
⎢
⎥
⎥
⎥
=
0
0
−
−
cos
φ
sin
φ
⋅
+⋅
h
(12.2)
c
c
φ
⎥
sin
φ
−
cos
⎣
⎦
⎣
⎦
⎣
⎦
⎣
c
⎦
The final destiny of 3-D information for surrounding awareness is normally data
processing rather than data visualization. Therefore, the way perception informa-
tion is extracted and managed is always critical to the successful implementation of
a stereo system. The raw output of a stereo camera is a discrete set of points, given
in camera coordinates, and directly generated by the correlation algorithm. This set
of independent points is called the
3-D point cloud
. After executing the transforma-
tion pointed out in Eq. 12.2, the 3-D data are still in a point cloud format, but now
expressed in ground coordinates. From this stage on, the particular analysis of the
point cloud must enhance the estimation of those perception parameters that best
fit the needs of the application developed. Generally speaking, the processing of
point clouds is complicated because of the occurrence of two negative facts: noisy
