Rate-distortion modeling of scalable video coders

指導教授：許子衡 教授學生：王志嘉

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Introduction (i)

R-D models can be classified into two categories based on the theory they apply: models based on Shannon's rate-distortion theory and those derived from high-rate quantization theory

These two theories are complementary , converge to the same lower hound D~ e-αR when the input block size goes to infinity.

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Introduction (ii)

Block length cannot be infinite in real coding systems, it is widely recognized that classical rate-distortion theory is often not suitable for accurate modeling of actual R-D curves.

Adjustable parameters are often incorporated into the theoretical R-D models to keep up with the complexity of coding systems and the diversity of video sources

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Introduction (iii)

Recall that most current R-D models are built for images or non-scalable video coders.

In this paper, we complete the work and examine R-D models from a different perspective.

We first derive a distortion model based on approximation theory and then incorporate the ρ-domain bitrate model into the final result.

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Introduction (iv)

We also show that the unifying ρ-domain model is very accurate in both Fine Granular Scalability (FGS) and Progressive FGS (PFGS) coders.

Our work demonstrates that distortion D can be modeled by a function of function of both bitrat R its logarithm log R:

variance of the source

constants

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Motivation (i)

A typical scalable coder includes one base layer and one or more enhancement layers.

We examine the accuracy of current R-D models for scalable coders. with R representing the bitrate of the enhancement layer.

Without loss of generality, we use peak signal-to-noise ratio (PSNR) to measure the quality of video sequences.

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Motivation (ii)

With the PSNR measure, it is well-known that the classical model becomes a linear function of coding rate R:

Fig. I shows that PSNR is linear with respect to R only when the bitrate is sufficiently high and also that model (6) has much higher convexity than the actual R-D curve.

constants

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Fig.1

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Motivation (iii)

This bound is specifically developed for wavelet-based coding schemes. Mallat extend it to transform-based low bitrate images:

constant

parameter

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R-D Model For Scalable Coders—Preliminaries (i)

Uniform quantizers are widely applied to video coders due to their asymptotic optimality.

We show the lower bound on distortion in quantization theory assuming seminorm-based distortion measures and uniform quantizers.

If X, are k-dimensional vectors and the distortion between X and is d(X, ) = || X- ||τ, the minimum distortion for uniform quantizers is

XX X X

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R-D Model For Scalable Coders—Preliminaries (ii) 2

Gamma function

△ is the quantization step.

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R-D Model For Scalable Coders—Preliminaries (iii) When r= 2, k = 1. we obtain the popular MSE formula fo

r uniform quantizers:

β is 12 if the quantization step is much smaller than thesignal variance

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Distortion Analysis (i)

In the transform domain, distortion D consists of two parts:

1) distortion Di from discarding the insignificant coefficients in (- , )△ △

2) distortion Ds from quantizing the significant coefficients

Given this notation, we have the following lemma. Lemma 1: Assuming that the total number of transform c

oefficients U is N and the number of significant coefficients is M,MSE distortion D is:

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Distortion Analysis (ii)

In Fig. 2, the left side shows an example of actual distortion D and simulation results of model (10) for frame 3 in FGS-coded CIF Foreman, and the right side shows the average absolute error between model (10) and the actual distortion in FGS-coded CIF Foreman and Carphone sequences

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Fig.2

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R-D Modeling (i)

To improve the unsatisfactory accuracy of current R-D models in scalable coders. we derive an accurate R-D model based on source statistical properties and a recent ρ domain model.

Bitrate R is a linear function of the percentage of significant coefficients z in each video frame.

We extensively examined the relationship between R and z in various video frames and found this linear model holds very well for scalable coders.

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R-D Modeling (ii)

Fig. 3 demonstrates two typical examples of the actual bitrate Rand its linear estiniation in FGS and PFGS video frames.

Using the ρ-domain model, we have our main result as following.

Theorem 1 ： The distortion of scalable video coders is given by:

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Experimental Results (i)

We apply the proposed model (14) to various scalable video frames to evaluate its accuracy. Fig. 4 shows two examples of R-D curves for I (left) and P (right) frames of FGS-coded CIF Foreman.

All results shown in this paper utilize videos in the CIF format with the base layer coded at 128 kb/s and 10 frames/s. We contrast the performance of the proposed model with that of the other two models in FGS-coded Foreman and Carphone in Fig. 5.

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Fig.4

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Fig.5

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Experimental Results (ii)

Additionally, Fig. 6 shows the same comparison in PFGS-coded Coastguard and Mobile.

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Conclusion

This paper analyzed the distortion of scalable coders and proposed a novel R-D model from the perspective of approximation theory.

Given the lack of R-D modeling of scalable coders, we believe this work will benefit both Internet streaming applications and theoretical discussion in this area.