1. Rate-distortion modeling of scalable video coders 指導教授：許子衡 教授 學生：王志嘉

2. 2 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.

3. 3 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

4. 4 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.

5. 5 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

6. 6 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.

7. 7 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

8. 8 Fig.1

9. 9 Motivation (iii) This bound is specifically developed for wavelet-based coding schemes. Mallat extend it to transform-based low bitrate images: constant parameter

10. 10 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

11. 11 R-D Model For Scalable Coders— Preliminaries (ii) 2 Gamma function △ is the quantization step.

12. 12 R-D Model For Scalable Coders— Preliminaries (iii) When r= 2, k = 1. we obtain the popular MSE formula for uniform quantizers: β is 12 if the quantization step is much smaller than the signal variance

13. 13 Distortion Analysis (i) In the transform domain, distortion D consists of two parts: 1) distortion D i from discarding the insignificant coefficients in (- △, △ ) 2) distortion D s from quantizing the significant coefficients Given this notation, we have the following lemma. Lemma 1: Assuming that the total number of transform coefficients U is N and the number of significant coefficients is M,MSE distortion D is:

14. 14 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

15. 15 Fig.2

16. 16 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.

17. 17 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:

18. 18 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.

19. 19 Fig.4

20. 20 Fig.5

21. 21 Experimental Results (ii) Additionally, Fig. 6 shows the same comparison in PFGS-coded Coastguard and Mobile.

22. 22 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.