Cryptography Reference
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whose start or end times are within the duration. We merge b (b is a member
ofB) with a, if it satisfies the following condition:
(a(t)−a(t s ))−(b(t)−b(t s ))
t e
<ǫ,
(9.8)
−t s
t∈[t s ,t e ]
where t s and t e are respectively the start and end times of trajectory b.Let
a(t)andb(t) be the spatial positions of a and b at time t, respectively; and
let a(t s )andb(t s ) be the spatial position of a and b at time t s , respectively. If
the average of the relative spatial distances between a and b is smaller than a
threshold, ǫ, we consider b a highly correlated trajectory of a. Therefore, the
trajectory a is updated by the average position of trajectories a and b using
Eq. (9.9),
b(t),
if a(t)∩b(t)∈φ
a(t)=
t∈[t s ,t e ] ,
(9.9)
1
2 (a(t)+b(t)),
otherwise
where φ represents an empty set. We consider a as the representative trajec-
tory ofBand store it temporally. Next, we select the longest trajectory from
the remaining trajectories, and repeat the above process. If the trajectory un-
der consideration is longer than the temporary one, we replace it; otherwise, it
is removed. This process continues until all trajectories inBare processed.
Here, we only consider trajectories with duration longer than three seconds
in order to avoid the effects of noise. The trajectory that survives until the
last moment is chosen as the representative trajectory.
Fig. 9.3 explains how the above algorithm works. Figs. 9.3(a)9.3(c) show
three discontinuous frames indicating a man climbing a stairway. Due to the
occlusion of the handrail, the person is split into three blobs in Figs. 9.3(a)
and 9.3(b), and two blobs in Fig. 9.3(c). From the blob-moving sequence, our
algorithm detects several trajectories, as illustrated in Fig. 9.3(d), and singles
out a representative trajectory as shown in Fig. 9.3(e).
9.2.3 Representing a Trajectory and Matching
After obtaining a trajectory calculated by a real-time tracking process, we
need an e cient algorithm that can compare the degree of similarity between
this trajectory and the trajectories stored in the local database.
We adopt the Douglas-Peucker algorithm [25] to select the necessary con-
trol points from a trajectory. The algorithm starts by using a straight line
segment to connect the start and end points of the trajectory. If the perpen-
dicular distance between any intermediate point to the anchor line is larger
than a threshold, we split the trajectory into two segments via the farthest
intermediate point. This process continues until all perpendicular distances
are smaller than the preset threshold. The selected points and the two end
points form the set of control points of the trajectory.
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