The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008
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adjustment, the points in interval A i 2 + i+A i/ (past, present, and
future data points) are used, 2) the value (y,) and the slope (m,)
at x=t are computed; these values are used as fixed constraints
in the curve fitting for the next segment, and 3) step 1 is
repeated to process the next segment. Additional details can be
found in (Toth et al., 2007). Curves fitted to pavement
markings’ and GPS-surveyed points are shown in Figure 8; the
LiDAR scanlines are readily visible.
Figure 8. Curve fitting, LiDAR and GPS-surveyed points (blue
and magenta) and fitted curves (red and cyan)
5. MATCHING CURVES
The objective of curve matching is to find the spatial
relationship between two data representations of the pavement
markings, the curve-fitted pavement markings and the GPS
surveyed points. Assuming that the two representations, such as
the curve fitted ones, provide an adequate description of the
same shape, the free-shape curve matching techniques can be
applied. Since the pavement markings’ descriptions in both
original and curve-fitted representations for both LiDAR and
GPS-surveyed points are spatially close to each other, the well-
known Iterative Closest Point (ICP) algorithm (Besl and
McKay, 1992; Madhavan et al., 2005) was selected to perform
this task.
Iterative registration algorithms are increasingly used for
registering 2D/3D curves and range images. Due to its
consistent performance, the ICP algorithm was adopted here to
match curves describing pavement markings obtained from
LiDAR intensity and GPS measurements. The ICP algorithm
finds the best correspondence between two curves (point sets)
by iteratively determining the translations and rotations
parameters of a 2D/3D rigid body transformation.
min (,r)lK-(^, + r)|| 2
Where R is a 2x2 rotation matrix, T is a 2x1 translation vector,
and subscript i refers to the corresponding points of the sets M
(model) and D (data). The ICP algorithm can be briefly
summarized as follows:
1. For each point in D, compute the closest point in M
2. Compute the incremental transformation (R, 7)
3. Apply incremental transformation from step (2) to D
4. If relative changes in R and T are less than a given
threshold, terminate, otherwise go to step (1)
ICP can be applied to individual pavement markings or to a
group of pavement markings. Figure 9 shows an intersection
where four lines were matched.
Figure 9. Curve matching based on four curves; magenta:
curves fitted to control points, red: GPS control points, cyan:
curve points derived from LiDAR, and blue: transformed curve
points after ICP.
The ICP algorithm was implemented in Matlab and space-scale
optimization was incorporated to reduce execution time.
6. EXPRIMENTAL RESULTS
Initial performance tests of the proposed method were
performed using typical intersection and freeway ramp data
from a recently flown LiDAR survey, where GPS-surveyed
pavement markings were available, both were provided by the
Ohio Department of Transportation. The LiDAR point spacing
varied in the 1-3 pts/m range, and the horizontal accuracy of the
GPS-surveyed points, provided by a VRS system was 1-2 cm.
In the curve fitting process both data representations were fitted,
with a point spacing of I cm, and various combinations were
processed by the ICP-based curve matching in 2D and 3D. In
order to assess the accuracy of the transformation, the
correspondence between the LiDAR-derived curve and the
control curve was established. Since the two curves, in general,
are not entirely identical, even after the final ICP iteration, the
transformed LiDAR point-derived curve is close but not
necessarily falls on the control curve. However, the location of
the transformed LiDAR-derived points represents the best fit to
the control curve in the least squares sense. Therefore, these
points are projected to the closest points of the control curve,
and then they are considered as conjugate points. Figure 10
