1 A Unified Rate-Distortion Analysis Framework for Transform Coding Student : Ho-Chang Wu Student : Ho-Chang Wu Advisor : Prof. David W. Lin Advisor : Prof. David W. Lin Group Meeting on 2005/06/08

2 Outline ► Introduction of rate control ► Motivation ► R-D analysis  ρ-domain  Linear rate regulation  Unified R-D curve estimation algorithm  Experimental results ► Reference

3 Rate Control (1/2) ► Optimize the perceived picture quality and achieve a given constant average bit rate by controlling the allocation of the bits DCT/ wavelet Quantization Quantization parameter Data Representation Coding Input picture Bandwidth Picture quality

4 Rate Control (2/2) ► Use adaptive quantizer to control the bit rate or distortion ► R(q), D(q) => R-D curve

5 Motivation ► Find a unified R-D estimation and control algorithm for all typical transform coding systems ► Accuracy and robustness ► Current algorithms are not good enough

6 Outline ► Introduction of rate control ► Motivation ► R-D analysis  ρ-domain  Linear rate regulation  Unified R-D curve estimation algorithm  Experimental results ► Reference

7 ρ-domain ► ρ: the percentage of zeros among the quantized coefficients, i.e. the percentage of the coefficients in the dead zone ► ρ monotonically increases with q  One-to-one mapping between ρ and q ► ► ρ D(x) : disribution of transformed coefficients M : image size

8 ρ-domain ► R(q), D(q) => R(ρ), D(ρ) ► Decomposition for analysis: Basis functions Coefficients

9 A(ρ), B(ρ), and C(ρ) ► Different coding algorithms correspond to different decomposition coefficients ► For JPEG coding algorithm

10 Q nz (ρ) and Q z (ρ) ► They can characterize the transform coefficients to be quantized and coded ► Pseudo coding bit rate ► Q z : average of the sizes of all run length numbers. ► Q nz : average of the sizes of all nonzero coefficients.

11 ► Define Q nz (ρ) and Q z (ρ) as follows  Conversion to 1-D array: raster or zig-zag scan  Binary representation ► Size for a nonzero number x (sign-magnitude representation) ► Total bits ► Average Q nz (ρ) and Q z (ρ) M: total number of coefficients inside the picture

12 Why use ρ-domain ? ► Statistical properties ► Use 24 sample images to analysis the correlation among Q(ρ) and ρ or among Q(q) and q

13 ► Condition: Wavelet transform and uniform threshold quantization Y-axis: pseudo coding bit rate X-axis: ρ Y-axis: pseudo coding bit rate X-axis: q Q nz : solid Q z : dotted

14 Fast estimation of Q nz (ρ) and Q z (ρ) ► Q nz is modeled as a straight line passing through the point [1,0]  ► So we need another point [Q nz (q o ), ρ(q o ) ] to find the slope κ  ► There is very strong correlation between κ and Q z (ρ) ► => Very low complexity

15 Outline ► Introduction of rate control ► Motivation ► R-D analysis  ρ-domain  Linear rate regulation  Unified R-D curve estimation algorithm  Experimental results ► Reference

16 Linear rate regulation ► A method to optimize the estimation of R(ρ) ► An approximate way is to find six points of R(ρ) and do linear interpolation to get R(ρ) ► Utilize the result of earlier work  R(ρ)=θ(1-ρ) ► Then the optimum estimation of slope θ is given by ► Optimum R(ρ) is

17 Outline ► Introduction of rate control ► Motivation ► R-D analysis  ρ-domain  Linear rate regulation  Unified R-D curve estimation algorithm  Experimental results ► Reference

18 Unified R-D curve estimation algorithm ► Step 1 – Generate the distribution  Histogram of transform coefficients ► Step 2 – Estimate Q nz (ρ) and Q z (ρ) ► Step 3 – Estimate Rate curve  Estimate R(ρ) and obtain R(q) by mapping ► Step 4 – Compute distortion curve  D(q) can be directly computed from the distribution information

19 Experimental results ► Different transformcoding

20 Experimental results ► JPEG

21 Experimental results ► MPEG-4

22 Conclusion ► The proposed algorithm has the following advantages  Accuracy  Lower computational complexity  Unified R-D curve estimation algorithm

23 Reference ► Zhihai He, and Sanjit K. Mitra, “ A Unified Rate-Distortion Analysis Framework for Transform Coding, ” IEEE Trans. Circuit Syst. Video Technol., vol. 11, pp – 1236, DEC ► Yun Q. Shi, and Huifang Sun, “ IMAGE and VIDEO COMPRESSION for MULTIMEDIA ENGINEERING ”