Figure 3). The direction difference should be lower than
a threshold for the two road segments to be connected.
•
Circular Intersection (
CI
)
Based on this criterion, which is proposed in this
research, a circle of radius
R
with center at each road
key point is considered. Circular intersection is defined
as the intersection area between two circles of corre-
sponding road key points. The distance (
d
) between the
centers of the circles (distance between two road key
points) affects the size of the intersection area. Consid-
ering two circles with the same radius (
R
) and different
values for
d
, these three situations are introduced:
1. If
d = 0
: two circles are completely overlapped.
2. If
d
≥
2R:
two circles are tangential or may not intersect
at all, so the area of intersection is 0.
3. If
d <2R:
two circles intersect in two distinct points.
In this paper circular intersection in the case
d
<
2R
is
selected to investigate the connection condition between dif-
ferent road key points. In that, overlapping of the intersection
area between two circles centered at two road key points with
the corresponding road patches in the binary road image is
considered as a fundamental connection criterion. Based on
this criterion, as the number of road pixels in the circular in-
tersection area increases (higher
CI
), the connection probabil-
ity of the corresponding road key points is raised (Figure 4).
In general, the distance and the direction difference values
should be low and the circular intersection value should be
high to correctly connect the road key points.
All the defined criteria are categorized into quantitative
variables. To make various criteria of different alternatives
comparable, they are normalized using the
maximum score
procedure (Malczewski, 1999). Table 1 summarizes the range
of criteria values and their corresponding normalization
functions. Among the criteria,
d
and
DD
are cost criteria.
CI
is
a benefit criterion which is subtracted from one to be compa-
rable to other cost criteria. In Table 1,
d
max
is the maximum of
road key points distance in the data set,
DD
max
corresponds to
the maximum of direction difference, and
CI
max
represents the
maximum sum of the number of road pixels in two corre-
sponding road patches.
Figure 2. DRPCPSO algorithm to obtain optimized road key points.
Figure 3. Definition of direction difference.
Figure 4. Circular Intersection with binary road image: (a) CI = 0,
(b) Small CI, and (c) Large CI.
T
able
1. R
ange
of
C
riteria
V
alues
and
T
heir
N
ormalization
F
unctions
Criteria
Range of
values
Normalization function
Distance(
d
)
[0
∞
)
N(D)= d/d
max
Direction Difference (
DD
)
[0
π
/2]
N(DD) =DD/D
Dmax
Circular intersection (
CI
)
[0
∞
)
N(CI)= 1- CI/CI
max
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
February 2016
109
