In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009
those points on the road surfaces and computes their elevations.
Chen and Lo (2009) assumed that the local relief of road
surfaces should be continuous for traffic. They then analyzed
the elevation histogram and extract the candidate points on the
roads to fit surfaces. The proposed scheme contains two parts:
(1) initial modelling and (2) profile refinement. The initial
process calculates the surface elevations from discrete points
along each produced centerline. Those original road surfaces
then are modified their elevations to keep the model continuities
in elevation and slope.
2.3 Initial Modelling
Those existed airborne laser scanning data describe accurate
elevations with considerable quantities of points. The laser
beam also has the opportunity to penetrate canopies to detect
elevations in occluded areas. However, this kind of data has no
distinct boundaries. To directly use discrete points for surface
modelling is a difficult work. Chen and Lo (2009) proposed a
two-way method to extract road points. They assume that the
road surface profile is smooth and continuous in a local area so
that the maximum number of elevation histogram of road points
may locate within a certain interval. One process, thus, extracts
points with a designed threshold to fit surfaces at each vertex of
centerlines. The used equations, i.e. linear and quadratic
polynomial functions, are shown in Equation (1) and (2). The
unknown parameters are the sll~ s26. Those two hypotheses
are automatic selected according to the analysis of the standard
deviation during the fitting procedure. In some conditions, road
surfaces may be interfered by cars or canopies, this threshold
may lead to remove too many points to calculate surfaces. The
other process then selects the locally lowest point to be the
surface elevation. In the first way, the cross-section is a curve to
represent the reality of horizontal profiles by surface fitting. On
the other hand, the second way provides a flat road surfaces.
S l {Z) = s u+ s i2 X + s l3 Y (1)
S,(Z) = .s 2l + s 22 X + s, 3 T + s 24 XY + s 25 Y 2 +s 26 T 2 (2)
where X, y,and Z are coordinates of the LIDAR points; and
Sii~S 2 6 are parameters of the surface function.
2.4 Profile refinement
This investigation describes each road segment with two nodes
and several vertices, i.e. conjunction points of networks and
consecutive center points, respectively. In the previous step, we
independently derive the elevation of each vertex from original
point clouds. Nevertheless, some parts of each vertical profile
may be discontinuous, erroneous, and empty. The following
process then transforms the coordinates (X, Y, Z) to mileages
(Stations) and fine-tunes the vertical profiles with three
mathematical models. The linear, quadratic, or cubic functions
are used to refine its vertical profile. The mathematical models
are formulated in Equation (3), (4), and (5), respectively. The
modification process would select an optimal function
according to the minimum standard deviation. Those errors and
empty values of each road segment are detected and re
computed.
After vertical refinements, the continuities of horizontal profiles
may be interfered. In this process, the surface fitting then
includes those consecutive vertices to smooth their elevations.
Equation (1) and (2) are considered in the smoothing process.
However, if a road segment is too long, the used models may be
insufficient to describe the characteristics of vertical profiles.
Chen and Lo (2009) considered that road systems are designed
and organized by low-ordered polynomial models everywhere
so that the theoretical models can easily represent each sub part
of one vertical profile. They created some pseudo nodes for
each road segment and smooth the geometry of cross-sections
with Equation (1) or (2). The profile refinement is an iterative
process until the elevation change of each road segment is
smaller than the designed tolerance.
L ] {H) = Pu + P U M (3)
L 2 {H) = p 2l + p 22 M + p 2: M 2 W
L 3 i H ) = Pi| + Pi2 M + Pl3 M ' + PuM' ^
where pn~Pi4 are parameters of the line function; M is the
mileage of each road segment; and H is vertex height.
2.5 Network surface fitting
This study focuses on the modelling procedure with multiple
roads using different data and keeps the results continuous in
elevation and slope. For this purpose, we propose to use B-
spline surface fitting to modify all conjunction points of road
networks. The elevation correction of each road segment is then
re-arranged to its internal vertices. In this step, we simplify the
format of those produced road models for surface fitting. The
conjunction points are selected and computed their new
elevations using B-spline curve function, i.e. Equation (6), to
maintain the continuities in elevation and slope. After the fitting
process, all the conjunctions have new height values, and
elevation changes then bring to each road segment and modify
the elevations of internal vertices. The iteration stops when the
elevation change of all road systems is smaller than the
threshold. In short, the proposed scheme makes the capability to
reconstruct three-dimensional road models combining different
data sources.
c(«)=Y.fMP, < 6 >
i=0
where P, are control points and fj is a basis function.
3. EXPERIMENTAL RESULTS
The scheme was validated using data for single and multiple
layer road systems in Taipei City of northern Taiwan. The area
has the coverage of 3,200m*6,600m. The test site includes
arterial streets, local streets, expressways, and mass rapid transit
in an urban area. The test datasets include topographic maps,
airborne scanning data, and three-dimensional boundaries. The
scale of the topographic maps is 1:1000. They contain several
feature layers, such as buildings, roads, power lines, etc. In
Taiwan, road boundaries are recorded as independent
planimetric polylines without topology or transportation
attributes, as shown in Figure 2. As shown in Figure 3, the
LIDAR data was derived from a Leica ALS50 system in March
2007. The flight altitude ranged from 1200 to 1500 m. The laser
pulse rate was 70 kHz, and the point density was about 10
points/nr. The random error of laser points in elevation is better
than 0.15m (ITRI, 2006). The third type dataset is the three-
dimensional road boundaries which were digitized from aerial
images. The spatial resolution of used DMC images is about 17
cm. Figure 4 shows edited road boundaries in aerial images.
