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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
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2 Outline ► Introduction of rate control ► Motivation ► R-D analysis ρ-domain Linear rate regulation Unified R-D curve estimation algorithm Experimental results ► Reference
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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
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4 Rate Control (2/2) ► Use adaptive quantizer to control the bit rate or distortion ► R(q), D(q) => R-D curve
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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
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6 Outline ► Introduction of rate control ► Motivation ► R-D analysis ρ-domain Linear rate regulation Unified R-D curve estimation algorithm Experimental results ► Reference
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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
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8 ρ-domain ► R(q), D(q) => R(ρ), D(ρ) ► Decomposition for analysis: Basis functions Coefficients
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9 A(ρ), B(ρ), and C(ρ) ► Different coding algorithms correspond to different decomposition coefficients ► For JPEG coding algorithm
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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.
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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
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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
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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
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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
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15 Outline ► Introduction of rate control ► Motivation ► R-D analysis ρ-domain Linear rate regulation Unified R-D curve estimation algorithm Experimental results ► Reference
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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
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17 Outline ► Introduction of rate control ► Motivation ► R-D analysis ρ-domain Linear rate regulation Unified R-D curve estimation algorithm Experimental results ► Reference
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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
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19 Experimental results ► Different transformcoding
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20 Experimental results ► JPEG
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21 Experimental results ► MPEG-4
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22 Conclusion ► The proposed algorithm has the following advantages Accuracy Lower computational complexity Unified R-D curve estimation algorithm
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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. 1221 – 1236, DEC. 2001 ► Yun Q. Shi, and Huifang Sun, “ IMAGE and VIDEO COMPRESSION for MULTIMEDIA ENGINEERING ”
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