Environmental Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
FIGURE 6.6
Results of roof detection by RANSAC.
3
To repeat Steps (1) and (2)
M
times. In each one, it compares
the obtained result with the last one. If the new result is better,
then it replaces the saved result with the new one.
4
To exclude the points belonging to the best plane from the
building data when the best plane
P
is found.
6.2.3.4
Building boundary refinement
by aerial imagery
By comparisonwith its vertical accuracy, the planimetric accuracy
of lidar data is relatively lower due to the errors in the global
positioning system (GPS), inertial measurement unit (IMU),
mirror angles, and range measurements. However, lidar data
cannot provide the linear edges of buildings because it is a set
of sample points about the Earth's landscape. The aerial image
compensates the weakness of lidar data. Locations of linear
features of roofs within building boundaries are not affected
by the distribution of points because they are estimated from
intersection of two extracted roof planes. Thus, aerial image
can be utilized to improve the quality of building boundary
refinement.
The procedures of boundary refinement can be listed as
follows:
In order to detect all roof surfaces within an individual building,
the above process has to be repeated several times until the
number of points is smaller than the given threshold
δ
(in
this study,
δ
=
20). Namely, if the number of points within a
plane is below 20, these points are treated as noisy points and
ready to be rejected. Defining a minimum number of points per
surface helps to remove small surfaces that are not of further
interest, e.g., chimneys. Beside the distance threshold
τ
and the
minimum number of points
δ
, the RANSAC algorithm also
uses the following three variables to control the plane model
estimation process:
1
To extract edge line segments from aerial image.
2
To project the building boundaries extracted from lidar data
into the aerial image; see Fig. 6.7 for an example of a 2D
projected boundary
{
B
1
,
B
2
,
B
3
,
B
4
}
.
3
To determine a buffer zone for each line segment of the
boundaries- such as buffer of the segment
B
1
B
2
in Fig. 6.7.
The buffer zone of the line segment of the building boundary
is formed by expanding to its perpendicular direction.
4
To search for edge line segments extracted in a buffer zone
and construct the new boundary by replacing the old line
●
ε
, the probability that any selected data agrees with the plane
model,
●
α
, ranging from 0.90 to 0.99,the minimum probability of
finding at least one good set of observations in
M
trials, and
M, the number of iterations,
M
, which can be defined as:
●
1
−
(1
−
(1
−
ε
)
m
)
M
=
α
(6.13)
Taking the logarithm of both sides of Equation 6.13, we have
M
=
log(1
−
α
)
/
log(1
−
(1
−
ε
)
m
)
(6.14)
The RANSAC algorithm uses a pure mathematical principle to
detect the best planes from a 3D point cloud. That means it looks
for the maximum number of points which represent statistically
the best planes without consideringwhether those building points
are consecutive in 3D space or not. In other words, it detects
a set of points which represents several roof planes or belongs
to several planes. Therefore, we use a simple region-growing
algorithm to find consecutive roof surfaces. It is necessary to
build a TIN structure to search neighborhood for points within
each individual building. Randomly starting from a point, a roof
surface grows until it cannot find any neighbor point. Points
being part of this roof surface are removed from the available
points and the algorithm continues until all potential points
are used. As shown in Fig. 6.6, several rooftop structures are
successfully extracted from building points using the RANSAC
algorithm.
FIGURE 6.7
Refinement of building boundary.
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