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The superiority of the proposed model over the conventional one is due to the
following reasons. The conventional model is constructed based on the assumption
that the information of inter-frame prediction error converges to zero at infinitely
large frame-rate, i.e. an asymptotic characteristic. The inter-frame prediction is the
frame difference and does not consider motion compensation. Furthermore, the con-
ventional model does not consider the above-described noise elements caused by
thermal noise in the imaging device. Therefore, the fitness of the model degrades
when blocks have large displacements and the effect of the noise elements grows.
From Figure 4(b)(c), we can confirm that the bit-rate of prediction error may de-
crease as the frame-rate increase to approach 500 [fps]; above this frame-rate, the
bit-rate increases. For the case of the temporal down-sampling using the mean filter
described in equation (11), the shutter-open interval increases with the decrease in
the frame-rate. The increase in the shutter-open interval leads to the suppression of
the noise elements caused by the thermal noise in the imaging device and the reduc-
tion of the spatio-temporal high frequency components of down-sampled sequences.
This is why the bit-rate of the sequences generated by the temporal down-sampling
may decrease as the frame-rate increases.
4Conluion
In this chapter, we analytically derive two mathematical models that quantify the
relationship between frame-rate and bit-rate. The first model supports temporal
sub-sampling through the frame skip approach. The second one supports temporal
down-sampling realized by a mean filter; it incorporates the integral phenomenon
associated with the open interval of the shutter. By using these models, we can
describe the properties associated with frame-rate, that have not been clarified in
previous studies. We can confirm that the derived models well approximate our ex-
perimental results. These evaluation results support the validity of the assumptions
used in deriving our models.
Acknowledgements.
We would like to thank Dr. T.Nakachi, NTT Network Innovation Lab-
oratories, for his useful suggestions and his valuable advice. We also appreciate the members
of video coding group of NTT Cyber Space Laboratories for their cooperation.
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