1Statistical Analysis and Distortion Modeling of MPEG-4 FGSMin DaiMin DaiElectrical EngineeringTexas A&M University, TX 77843Dmitri LoguinovDmitri LoguinovComputer ScienceTexas A&M University, TX 77843Hayder RadhaHayder RadhaElectrical and Computer EngineeringMichigan State University, MI 488242• Rate-distortion (R-D) theory– The fundamental tradeoff in the design of any lossycompression systemBackground A typical R-D curveR D • R-D function:– A bound on achievable (or theoretically possible) distortion for a given coding rate– A powerful tool in Internet streaming3Background (cont.)• Scalable coding is widely applied in Internet streaming– Provides the capability of recovering video information by partially decoding the compressed bitstream– Fine Granular Scalability (FGS) has been chosen in the MPEG-4 standard• Fine granular scalability (FGS):– One low-bitrate base layer (BL) to provide a low, but guaranteed quality– One high-bitrate enhancement layer (EL) to provide fine quality improvement– EL can be truncated at any codeword4Motivation • Current status:– No current closed-form R-D model can capture all the complexities of a real encoder– No specific work has been done on R-D modeling of scalable video coding for Internet streaming• Goals in this paper: – Understand the statistical properties of FGS input and propose a more accurate statistical model for it– Study the bitplane coding process in FGS and derive a closed-form distortion model5Related work on Statistical Models• Input to FGS EL: – DCT residue between the original image and the reconstructed image from BL• The two most popular models of DCT residue:– Zero-mean Gaussian distribution: ||2)(xexfλ−λ=22221)(σ−σπ=xexf– Laplacian distribution (double exponential):6Related work on Statistical Models0.00.10.20.30.4-15 -10 -5 0 5 10 15DCT residueProbabilityreal PMFGaussianLaplacian1.E-061.E-041.E-021.E+000 10203040DCT residueProbabilityreal PMFGaussianLaplacian• The PMF of DCT residue with Gaussian and Laplacian estimations in frame 0 of the Foreman CIF sequence (left). Logarithmic scale of PMFs for the positive residue (right).7Proposed Statistical Model• Mixture Laplacian model:||1||0102)1(2)(xxepepxfλ−λ−λ−+λ=• We use the Expectation-Maximization (EM) algorithm to obtain Maximum-likelihood (ML) estimation for parameters { p, λ0, λ1}where λ0denotes the small variance Laplacian distribution and λ1denotes the large variance Laplacian distribution8Results of Proposed Model0.00.10.20.30.4-20 -10 0 10 20DCT residueProbabilityreal PMFmixture1.E-061.E-041.E-021.E+000 10203040DCT residueProbabilityreal PMFmixture• The real PMF and mixture Laplacian (left) and the logarithmic scale of the positive part (right)9More Results00.020.040.060.080.10.120 90 180 270frame numbererrorGaussianLaplacianmixture 00.010.020.030.040.050.060 90 180 270frame numbererrorGaussianLaplacianmixture • The weighted absolute error of estimation in Foreman CIF (left) and Coastguard CIF (right)All test sequences are coded at 10fps and 128 kb/s in the base layer10• Classical model:• A variation of the classical model (proposed by Chiang et al. in 1997):RXD2222−σε=21 −−+= bDaDRwhere ε2is a signal-dependent constant, σX2denotes the signal variance and R is the bitratewhere parameters a, b are obtained empiricallyCurrent Distortion Models• Distortion model for Uniform Quantizer (UQ):2()D∆=∆ βwhere ∆ is quantization step and βequals 1211Performance of Current Models30405060700.E+00 2.E+05 4.E+05 6.E+05FGS EL bitsPSNR (dB)Chiang et al.real PSNRUQclassical2030405060700.E+00 2.E+05 4.E+05 6.E+05 8.E+05FGS EL bitsPSNR (dB)Chiang et al.real PSNRUQclassical• Performances of current models in frame 0 (left) and frame 252 of Foreman CIF (right)12A more Accurate Distortion Model• For each component in the mixture-Laplacian model, the distortion is: where ∆ is the quantization step of each bitplane in the FGS EL and p is the probability of Laplacian component 02(1)221112() 1 , 0,1(1 )iiiiiiDe ie−λ ∆−−λ ∆−∆= ∆−+ + − =λλλ−)()1()()(10∆⋅−+∆⋅=∆DpDpD• Final version:13Experimental Results02468090180270frame numberavg abs error (dB)classicalUQ modelour model024680 90 180 270frame numberaveg abs error(dB)classicalUQ modelour model• The average absolute errors in Foreman CIF (left) and Coastguard CIF (right)14Conclusion• This paper proposed an accurate statistical model for DCT residue• Based on this statistical model, we derived a closed-form distortion function for FGS EL• In summary, this paper provides a good starting point for further research on FGS