Cryptography Reference
In-Depth Information
Target:
R
t
=r
i,t
i=1,,n
,
n
where
r
l,t
=1,
(9.5)
i=1
Corresponding
candidates:
P
t
(x, y)=p
i,t
(x, y)
i=1,,n
,
n
where
p
i,t
=1.
(9.6)
i=1
P
t
(x, y)andp
i,t
(x, y) denote a candidate located at (x, y) and the value
of its i
th
bin at time t, respectively; and r
i,t
represents the value of the i
th
bin at time t. The histogram with n bins of R and P are normalized by their
own total pixel numbers. Next, we employ a similarity function, called the
Bhattacharyya coe
cient [23], to calculate the degree of similarity between
the target and a candidate in the database. A Bhattacharyya coe
cient is
a divergence-type measure with a straightforward geometric interpretation.
It is defined as the cosine of an angle measured between two n-dimensional
unit vectors, (
√
√
√
√
√
√
r
n
)
T
. Detailed de-
finitions of the Bhattacharyya coe
cient can be found in [24]. The formal
definition of the distance between a target at time t and a candidate at time
t +1 is
p
n
)
T
p
1
,
p
2
,,
and (
r
1
,
r
2
,,
1−
n
d(x, y)=
p
i,t+1
(x, y)r
i,t
.
(9.7)
i=1
Therefore, to find the best match among a set of candidates located in the
subsequent frame, the candidate that has the smallest distance with the target
is chosen. We then use the color distribution of this chosen candidate to update
the color distribution of the target. The tracking procedure is iterated until
the target cannot find any further match. Since a color-based blob tracker may
generate more than one trajectory due to occlusion or the distinct movements
of different body parts, we now discuss how to merge these trajectories into
one representative trajectory.
Single out a Representative Trajectory from a Group
of Trajectories
Since the movement of an articulated object like a human being may cover
more than one trajectory due to occlusion or the movements of different body
parts, it is possible to derive more than one trajectory from a moving person.
Therefore, we adopt an algorithm proposed in our previous work [15] to single
out one representative trajectory from a set of derived trajectories. Initially,
we select a trajectory, a, that has the longest duration in a tracking sequence.
Suppose a starts from time t
i
and ends at time t
j
is the set of trajectories
