11

A Unified Rate-Distortion A Unified Rate-Distortion Analysis Framework for Analysis Framework for

Transform CodingTransform Coding

Student : Ho-Chang WuStudent : Ho-Chang Wu

Advisor : Prof. David W. Advisor : Prof. David W. LinLin

Group Meeting on 2005/06/08Group Meeting on 2005/06/08

2

OutlineOutline

► Introduction of rate controlIntroduction of rate control►MotivationMotivation►R-D analysisR-D analysis

ρ-domainρ-domain Linear rate regulationLinear rate regulation Unified R-D curve estimation algorithmUnified R-D curve estimation algorithm Experimental resultsExperimental results

►ReferenceReference

3

Rate Control (1/2)Rate Control (1/2)►Optimize the perceived picture quality Optimize the perceived picture quality

and achieve a given constant average and achieve a given constant average bit rate by controlling the allocation of bit rate by controlling the allocation of the bitsthe bits

DCT/ wavelet

Quantization

Quantization parameter

Data

RepresentationCoding

Input

picture

Bandwidth

Picture quality

4

Rate Control (2/2)Rate Control (2/2)

►Use adaptive quantizer to control the Use adaptive quantizer to control the bit rate or distortionbit rate or distortion

►R(q), D(q) => R-D curveR(q), D(q) => R-D curve

5

MotivationMotivation

►Find a unified R-D estimation and Find a unified R-D estimation and control algorithm for all typical control algorithm for all typical transform coding systemstransform coding systems

►Accuracy and robustnessAccuracy and robustness►Current algorithms are not good Current algorithms are not good

enoughenough

6

OutlineOutline

► Introduction of rate controlIntroduction of rate control►MotivationMotivation►R-D analysisR-D analysis

ρ-domainρ-domain Linear rate regulationLinear rate regulation Unified R-D curve estimation algorithmUnified R-D curve estimation algorithm Experimental resultsExperimental results

►ReferenceReference

7

ρ-domainρ-domain

► ρ: the percentage of zeros among the ρ: the percentage of zeros among the quantized coefficients, i.e. the percentage of quantized coefficients, i.e. the percentage of

the coefficients in the dead zonethe coefficients in the dead zone► ρ monotonically increases with qρ monotonically increases with q

One-to-one mapping between ρ and qOne-to-one mapping between ρ and q

► ρD(x) : disribution of transformed

coefficients

M : image size

1= ( )M

D x dx

8

ρ-domainρ-domain

►R(q), D(q) => R(ρ), D(ρ) R(q), D(q) => R(ρ), D(ρ) ►Decomposition for analysis:Decomposition for analysis:

Basis functions

Coefficients

9

A(ρ), B(ρ), and C(ρ)A(ρ), B(ρ), and C(ρ)

►Different coding algorithms correspond Different coding algorithms correspond to different decomposition coefficientsto different decomposition coefficients

►For JPEG coding algorithmFor JPEG coding algorithm

10

QQnznz(ρ) and Q(ρ) and Qzz(ρ)(ρ)

►They can characterize the transform They can characterize the transform coefficients to be quantized and codedcoefficients to be quantized and coded

►Pseudo coding bit ratePseudo coding bit rate►QQz z : average of the sizes of all run : average of the sizes of all run

length length numbers.numbers.►QQnznz : average of the sizes of all nonzero : average of the sizes of all nonzero

coefficients.coefficients.

11

►Define QDefine Qnznz(ρ) and Q(ρ) and Qzz(ρ) as follows(ρ) as follows Conversion to 1-D array: raster or zig-zag Conversion to 1-D array: raster or zig-zag

scan scan Binary representationBinary representation

►Size for a nonzero number x (sign-magnitude Size for a nonzero number x (sign-magnitude representation)representation)

►Total bitsTotal bits

►AverageAverage

QQnznz(ρ) and Q(ρ) and Qzz (ρ) (ρ)

M: total number of coefficients inside the picture

12

Why use ρ-domain ?Why use ρ-domain ?

►Statistical propertiesStatistical properties►Use 24 sample images to analysis the Use 24 sample images to analysis the

correlation among Q(ρ) and ρ or among Q(q) correlation among Q(ρ) and ρ or among Q(q) and qand q

13

►Condition: Wavelet transform and Condition: Wavelet transform and uniform threshold quantizationuniform threshold quantization

Y-axis: pseudo coding bit Y-axis: pseudo coding bit raterate

X-axis: ρX-axis: ρ

Y-axis: pseudo coding bit Y-axis: pseudo coding bit raterate

X-axis: qX-axis: q

QQnz nz : solid: solid

QQz z : dotted: dotted

14

Fast estimation of QFast estimation of Qnznz(ρ) and (ρ) and QQzz(ρ)(ρ)

►QQnznz is modeled as a straight line passing is modeled as a straight line passing through the point [1,0]through the point [1,0]

►So we need another point [QSo we need another point [Qnznz(q(qoo), ρ(q), ρ(qoo) ) ] to find the slope κ] to find the slope κ

►There is very strong correlation There is very strong correlation between κ and Qbetween κ and Qzz(ρ)(ρ)

►=> Very low complexity=> Very low complexity

15

OutlineOutline

► Introduction of rate controlIntroduction of rate control►MotivationMotivation►R-D analysisR-D analysis

ρ-domainρ-domain Linear rate regulationLinear rate regulation Unified R-D curve estimation algorithmUnified R-D curve estimation algorithm Experimental resultsExperimental results

►ReferenceReference

16

Linear rate regulationLinear rate regulation

►A method to optimize the estimation of A method to optimize the estimation of R(ρ)R(ρ)

►An approximate way is to find six points of An approximate way is to find six points of R(ρ) and do linear interpolation to get R(ρ)R(ρ) and do linear interpolation to get R(ρ)

►Utilize the result of earlier workUtilize the result of earlier work R(ρ)=θ(1-ρ)R(ρ)=θ(1-ρ)

►Then the optimum estimation of slope θ is Then the optimum estimation of slope θ is given bygiven by

► Optimum R(ρ) is Optimum R(ρ) is

17

OutlineOutline

► Introduction of rate controlIntroduction of rate control►MotivationMotivation►R-D analysisR-D analysis

ρ-domainρ-domain Linear rate regulationLinear rate regulation Unified R-D curve estimation algorithmUnified R-D curve estimation algorithm Experimental resultsExperimental results

►ReferenceReference

18

Unified R-D curve estimation Unified R-D curve estimation algorithmalgorithm

►Step 1 – Step 1 – Generate the distributionGenerate the distribution Histogram of transform coefficientsHistogram of transform coefficients

►Step 2 – Step 2 – Estimate QEstimate Qnznz(ρ) and Q(ρ) and Qzz(ρ)(ρ)

►Step 3 – Step 3 – Estimate Rate curveEstimate Rate curve Estimate R(ρ) and obtain R(q) by mappingEstimate R(ρ) and obtain R(q) by mapping

►Step 4 – Step 4 – Compute distortion curveCompute distortion curve D(q) can be directly computed from the D(q) can be directly computed from the

distribution informationdistribution information

19

Experimental resultsExperimental results

►DifferentDifferent

transformtransform

codingcoding

20

Experimental resultsExperimental results

► JPEGJPEG

21

Experimental resultsExperimental results

►MPEG-4MPEG-4

22

ConclusionConclusion

►The proposed algorithm has the The proposed algorithm has the following advantagesfollowing advantages AccuracyAccuracy Lower computational complexityLower computational complexity Unified R-D curve estimation algorithmUnified R-D curve estimation algorithm

23

ReferenceReference

►Zhihai He, and Sanjit K. Mitra, “A Zhihai He, and Sanjit K. Mitra, “A Unified Rate-Distortion Analysis Unified Rate-Distortion Analysis Framework for Transform Coding,” Framework for Transform Coding,” IEEE Trans. Circuit Syst. Video IEEE Trans. Circuit Syst. Video Technol., vol. 11, pp. 1221 – 1236, Technol., vol. 11, pp. 1221 – 1236, DEC. 2001DEC. 2001

►Yun Q. Shi, and Huifang Sun, “IMAGE Yun Q. Shi, and Huifang Sun, “IMAGE and VIDEO COMPRESSION for and VIDEO COMPRESSION for MULTIMEDIA ENGINEERING”MULTIMEDIA ENGINEERING”