Cryptography Reference
In-Depth Information
however, that all the elements that form the vector of a check-point on a
trajectory are positive and their magnitudes are accumulated from the begin-
ning. Therefore, if we choose an intermediate check point, Q
′
′
k
,inQ
and its
′
′
corresponding check point, D
k
,inD
, we can be sure that
Dist
Q
′
,D
′
i,j
Dist
Q
′
,D
′
i,k
Dist
Q
′
,D
′
k,j
≤
+
.
(9.12)
Eq. (9.12) shows that a coarse-to-fine search strategy is appropriate for
a trajectory-based query. In the first step of the comparison between Q
′
and
Dist
Q
′
,D
′
1,N
′
D
, we simply check the value of
. This step only needs to consider
′
′
′
′
four check points Q
N
. Since the value of TDist(Q, D) must
be equal to or larger than that of, we can quickly determine that trajectory
D is not similar to Q if the returned value of
1
, D
1
, Q
N
,andD
Dist
Q
′
,D
′
1,N
is greater than a
predefined threshold δ.
Once the value of
Dist
Q
′
,D
′
1,N
<δ, we seek the second check points on
Q
′
and D
′
, respectively, by checking Q
2
and D
2
.IfQ
2
is chosen as Q
′
2
,we
′
can insert D
2
into the right position between D
1
and D
2
and vice versa.
Furthermore, Q
′
′
′
and D
can be divided into four sub-trajectories by Q
2
and
Dist
Q
′
,D
′
1,2
′
D
2
. Under these circumstances, we only compute the sum of
Dist
Q
′
,D
′
2,N
and
as the distance between the sub-trajectories. If the distance
between two distinct sub-trajectories is still larger than a predefined threshold
δ, D will be filtered out. Otherwise, we insert Q
′
3
and D
′
3
to further compute
Dist
Q
′
,D
′
2,3
Dist
Q
′
,D
′
3,N
and
. The above newly computed distances replace
Dist
Q
′
,D
′
2,N
the value of
, and the process is executed repeatedly until the
computed distance is larger than δ, or there are no more intermediate check
points within each sub-trajectory. Since most of the trajectories would be
filtered out by checking the first few control points, our proposed algorithm
is very e
cient.
9.2.4 Experiment Results
In order to test the effectiveness and e
ciency of our real-time event detec-
tion method, we tested our algorithm on the proposed surveillance systems
with monitors placed at eight different locations. These indoor/outdoor en-
vironments included a parking lot, the area in front of an elevator, and a
stairway. The corresponding background views taken at these locations are
shown in Fig. 9.5. To demonstrate the performance of the proposed color-
based blob tracking algorithm, the tracking results of the outdoor and indoor
environments are demonstrated in Figs. 9.6(a)(b) and Fig. 9.6(c), respec-
tively. Moving objects in Figs. 9.6(a)(b) were successfully tracked because
adaptive mixture Gaussian model is advantageous under changing illumina-
tions. In addition, the color histograms provide e
cient computation and
