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(a) Original sequence
(b) Sequence sub-sampled to 1/2 frame-rate
(c) Sequence sub-sampled to 1/4 frame-rate
Fig. 2
Conversion of frame-rate (Shaded rectangles are frames at each frame-rate. Rectangles
enclosed by dotted-lines are down-sampled frames)
2
Relationship between Frame-Rate and Inter-frame
Prediction Error
In deriving temporal sub-sampling and temporal down-sampling, this section con-
siders a one-dimensional signal for simplicity. The former is derived in 2.1, and
the latter in 2.2. It is trivial matter to extend the following work to cover two-
dimensional signals.
2.1
Mathematical Model for Temporal Sub-sampling by Frame
Skip
This subsection establishes a mathematical model of the relationship between
frame-rate and bit-rate for temporally sub-sampled sequences generated by frame
skip. Let
f
t
(
x
) denote a one-dimensional signal at position
x
in the
t
-th frame with
X
pixels. Let
B
[
i
](
i
= 1
,
2
,
,
X
/
L
) be the segment which is a one-dimensional
region with
L
pixels and the
i
-th segment in
f
t
(
x
). When segment
B
[
i
] in
f
t
(
x
) is
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