Databases Reference
In-Depth Information
represents the time line, and each time interval represents the index where some
activities took place in each media, for example,
a
represents the time when Mr. X
spoke, and
b
represents the time when Mr. X appeared. Mr.X's talk is represented
with two time intervals, namely,
a
and
c,
because his voice was interrupted. Similarly,
Mr.X's appearance is represented as three time intervals, namely,
b, e,
and
e,
because
he disappeared from the screen due to the camera motion. Suppose we want to
retrieve video objects using that index. We would like to treat
b
and
d
as a video
object since his voice is continued even if he disappeared from the frame of the
motion picture. To this end, we introduce “joint” operation in addition to
conventional operations on time intervals such as intersection and union.
Figure 1: Simple indices
3.2
Operations on time intervals
In this subsection, we give formal definitions of time intervals and operations on
them.
Definition 1 (time intervals)
Let a
s
and a
e
be time instants such that a
s
< a
e
. Time
intervals are defined as (a
s
, a
e
).
In the next, we introduce three operations on time intervals, namely, union,
intersection, and joint operations.
Definition 2 (union)
Let
and
be time intervals. Union
(U)
of A and B is defined as
Note that intersection operation returns two time intervals if its arguments are
disjoint, that is, there are no overlapping interval between the arguments.
Definition 3 (intersection)
Let
and
be time intervals.
Intersection
(
)
of A and B is defined as
