Cryptography Reference
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and b t s denote the spatial position of a and b at time t s respectively. If the
average of the relative spatial distance between a and b is lower than a given
threshold ǫ, we consider b to be a sub-segment of a.Asb can be retrieved from
a by a partial matching process, it is redundant and can be removed.
We then consider a as the representative of the motion flow removed from
Band store it in the database. Next, we again select the motion flow with
the longest duration from the remaining motion flows, and repeat the above
process until all motion flows are either stored or removed. Here, we only
consider motion flows longer than 3 seconds in order to avoid the effects of
noise and reduce the size of the database.
Fig. 9.11(b) shows different representative motion flows of the video clip
shown in Fig. 9.11(a). The original motion flows (with ǫ =0)areshownon
the left-hand side, and the motion flows after applying the removal process
using different thresholds are shown in the middle and on the right-hand side,
respectively. It is obvious that the redundant motion flows have been success-
fully removed, and that the number of representative motion flows is controlled
by the value of ǫ. Fig. 9.12 shows another example of representative motion
flows derived from a video sequence containing multiple moving objects and
global camera motion. Since the movement of each object is different, several
representative motion flows are generated concurrently to represent the way
the objects move. The extraction of motion flows is therefore much faster and
easier than deriving a trajectory, but there still exist two problems when we
construct motion flows from motion vectors. First, the occlusion of multiple
moving objects can cause a macroblock to be intra-coded, which means we
could miss motion information. Thus, a complete motion flow for each moving
object may not be derived. The region surrounded by dotted lines in Fig. 9.12
illustrates the above situation. The sudden termination of motion flows is ap-
parently caused by the occlusion of two of the football players. Second, since
we remove the camera motion before extracting the local motion from a video,
the motion flow will break off if a moving object stops temporarily.
9.3.2 Coarse-to-Fine Trajectory Comparison
Having constructed the motion flows from each shot, we propose a new al-
gorithm that compares the degree of similarity between a query trajectory
and the trajectories formed by the motion flows in a database. Since we are
looking for similar clips in the database, some geometric transformation, such
as scaling or translation, should be handled. Here, we do not consider rota-
tion invariance because the direction, that is, up-and-down or left-and-right,
usually has semantic meaning in a video. For example, if one wants to query a
jump motion, the trajectory should start from a lower position, pass through
a higher position and then return to the lower position. Also, the issue of par-
tial matching must be handled if a user provides an incomplete query. In the
following, we propose a simple, but fast, algorithm for comparing two distinct
trajectories (motion flows). To reduce the time complexity and minimize the
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