In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009
Yarlagadda et al„ (2008) has applied a spoke model to vehicle
database in a parking lot scanned by airborne LiDAR for 3D
classification task of vehicle category. The point cloud of single
vehicle is fitted with multiple connected planes being similar to
spokes, which are used to describe the vehicle shape via two
controlling parameters for each spoke, namely the orientation
and radius of it. For the purpose of our task, it is desirable that
the original vehicle form and motion artifacts are able to be
captured by a unified geometric model. Due to flexibility and
efficiency, the spoke model for vehicle point sets is selected
here as general framework for vehicle shape parametrization.
Being subject to minor modifications towards the analysis
objective, the spoke model could consistently encode geometric
information used for robust classification of vehicle motion.
Based on the moving vehicle model, which is focused on the 2-
d deformation of vehicle form, the 3D spoke model of vehicles
can be projected onto 2-d plane to deriving the shape
parameters, thereby avoiding unnecessary complexities. Instead,
the angle of shear and radius of projected 2-d point sets have to
be estimated as controlling parameters of modified spoke model
for vehicle parametrization. Due to the limited point sampling
rate of ALS data, the number of spokes in the model is flexible
to be determined depending on the point density or vehicle
category, despite that the vehicles in our test data are frequently
modeled with only one spoke.
To obtain the geometric features of extracted vehicles, the
shape analysis is to be performed on the projected point sets of
the spoke model. The whole procedure mainly consists of two
steps: boundary tracking and parallelogram fitting.
A modified convex-hull algorithm (Jarvis, 1977) is used to
determine the boundary of a set of points, namely the spoke
model of extracted vehicles. The modification is to constrain
the searching space of a convex hull formation to a
neighborhood. The study showed that the approach can yield
satisfactory results if the point distribution is consistent
throughout the dataset. Such condition could be fulfilled, as
only one-path ALS data are considered for moving object. The
boundary tracing method for a point set B using a modified
convex hull analysis starts also with a randomly selected
boundary point P. Then, we use the convex hull algorithm to
find the next boundary point P k within the neighborhood of P,
which is defined as rectangle with two dimensions
corresponding to the point spacing in along and across-track
directions of ALS data. Finally, the approach will proceed to
the newly selected boundary point and repeat the step
mentioned above until the point P is selected as P k again, as
depicted in the left column of Fig.4.
Since the sampling irregularity and randomness are generally
assumed to be present in the LiDAR data, the traced boundary
cannot be directly used as shape description for single vehicle
instances, based on which the shape analysis is performed to
parameterize the vehicle point sets. Consequently, a boundary
regularization process aided by analytic fitting operations is to
be introduced for tackling these problems. It is noticed that
most vehicles have mutually parallel directions. We can find
these directions from the boundary points and fit parametric
lines.
The first step in regularization is to extract the points that lie on
identical line segments. This is done by sequentially following
the boundary points and locating positions where the slopes of
two consecutive edges are significantly different. Points on
these edges are grouped to one line segment. Therefore, a set of
line segments {/,, l 2 , ..., I„,n> 4} from which four longest line
segment {!,, L 2 , I,, I 4 } are selected. Each of the selected line
segments is modeled by equation A,x -t-5,.y + l = 0 . Based on the
slope M t =-AjB,., line segments are sorted into different groups,
each of which contains line segments being parallel within a
given tolerance. As we know from the defined vehicle models
(Yao et al., 2008b), the vehicle point sets generally appear as a
parallelogram and have only two groups of line segments, i.e.
vertical and horizontal.
The next step is to determine the least squares fitting to these
line segments, with the constraints that the lines segments are
parallel to each other within one group, namely parallelogram
fitting. The solution consists of sets of parameters required to
describe four line segments, which are formed as following line
equations:
A,x + + 1 = 0 /=1,2,3,4; j =y(i) =1,2,3,... m i
A/, = M,
with the condition: <=> L, ( ) and L ( L, ) are
M 2 = M 4 -
opposite sides.
where m i is the number of points on the line segment i.
However, there are no specific constraints on the line segments
belonging to different groups.
Once the spoke model of vehicle point sets is constructed and
parameterized (Fig.4, right column), two controlling parameters
can be derived, which measure the accordance of 2-d point sets
to parallelogram (non-rectangularity) and dimension scale,
respectively. The angle of shear 9 S4 of parameterized vehicle
point set:
9 sa = arctan
M, -M.
1 + M,-M 2
The extent E of parameterized vehicle point set:
E = L, • Lj -sin^
where M 2 , A/, are slopes of line segments belonging to two
groups respectively and | | indicates the length of corresponding
line segment.
Figure 4. Two examples for vehicle parametrization: boundary
tracing, shape regulation (parallelogram fitting). Top row:
moving vehicle; bottom row: vehicle of ambiguous movement
with abnormal laser reflections. Green points marks the borders
of extracted vehicle, red lines indicate the non-parallel sides of
a fitted vehicle shape.
Two basic cases have to be distinguished in view of vehicle
movement, based on the geometric features derived above for
each extracted vehicle. However, they occasionally emerge
