Cryptography Reference
In-Depth Information
Fig. 9.3. An example showing a representative trajectory is singled out from a
group of trajectories. (a)-(c): tracking of a person whose body is split into three
parts due to occlusion of the handrail; (d) the group of calculated trajectories; and
(e) the representative trajectory derived by applying the proposed algorithm.
Conventionally, (x, y) is used to denote the position of a point in the spatial
domain. In contrast, we use five positive real numbers (x + ,x ,y + ,y ,d)to
represent the position of a control point. Here, d denotes the cumulative length
of the trajectory from the first control point to the current control point,
and +/−denotes the cumulative positive/negative movement along the x-
or y-axis from the first control point. Now, let Q and D be the trajectories
of the query and a model in the database, respectively. We normalize the
length of both trajectories into a unit length before making a comparison.
This technique guarantees the requirement of scale invariance. Therefore, the
parameters d, x+, x−, y+, and y−of each control point on the two trajectories
must be normalized by dividing them by the length of Q and D, respectively.
We align both Q and D by calculating the length d from the first control
point. For each control point on Q(D), we interpolate a corresponding point
that has the same cumulative length onto D(Q). The d value is used as the
basis of the alignment task, because we only consider the similarity between Q
and D in the spatial domain. The control points and the corresponding points
are labelled by circles and triangles, respectively (Fig. 9.4). The insertion of
the corresponding points on Q and D is dependent of d. Now, for each control
point on the trajectory Q(D), we can interpolate a corresponding point located
on D(Q). Assume the total number of control points and their corresponding
points located on Q and D are both N .LetQ
:Q
1 ,Q
2 ,,Q
N
and D
:
N
D
1 ,D
2 ,,D
be the set of points including the control points and the
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