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independent of frame-rate. The latter increases with frame-rate, i.e. prediction er-
ror may decrease when frame-rate decreases. The reason for this difference is as
follows. When the shutter open interval increases, relative noise power decreases
because of the increase in light intensity. This relative decrease in noise can lead to
a decrease in inter-frame prediction error. Therefore, we understand that the third
term of equation (14) decreases as the frame-rate decreases. On the other hand, that
of equation (10), the relative noise power is independent of frame-rate, since this
model assumes that the shutter open interval is fixed.
3
Evaluation of Proposed Models
3.1
Captured High Frame-Rate Video Signal
The original sequences in the following experiments consisted of 480 frames at
1000 [frames/sec]. Sequences taken with a high speed camera at 1000 [frames/sec]
were output in 24 bit RGB format. The frame interval equaled the shutter speed of
1/1000 [sec]. The video signal was not gamma corrected. We converted the color
format from RGB data to YCbCr data. Y-data with 8 bit gray scale were used in
the rate evaluation experiments. The following three sequences were used; “golf”
was the scene of a golf player swinging his club. “tennis” was the scene of a tennis
player hitting a ball with her racket. “toy” was the scene where the rings of a toy
rotated independently. All sequences were captured without camera work.
In order to identify the relationship between frame-rate and bit-rate, the se-
quences with different frame rates were generated by two down-sampling meth-
ods; temporal sub-sampling and temporal down-sampling. Temporal sub-sampling
is frame-rate conversion using frame-skip as shown in Figure 2, and temporal down-
sampling means frame-rate conversion using the mean filter described in equation
(11). The temporally sub-sampled sequences were utilized for evaluating the model
described by equation (10). The temporally down-sampled sequences were utilized
for evaluating the model described by equation (14).
3.2
Regression Analyses of the Proposed Models
We performed regression analyses in order to verify the validity of the above-
mentioned models. In Figure 3, the dot symbols show the results of rate evaluation
experiments on the original sequences and the temporally sub-sampled sequences
generated by frame-skip, while the solid lines plot the results of the proposed model
given by equation (10). The horizontal axis is the frame-rate [frames/sec] and the
vertical axis is the bit-rate [bits / pixel] which is the entropy of inter-frame predic-
tion error. The parameters (
α
3
) were obtained by least-squares estimation. In
Figure 4, the dot symbols show the results of rate evaluation experiments on the origi-
nal sequences and the temporally down-sampled sequences generated by mean-filter,
while the solid lines plot the results of the proposed model given by equation (14).
α
1
,
α
2
,
