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# Pyramid coder with nonlinear prediction - PowerPoint PPT Presentation

Pyramid coder with nonlinear prediction. Laurent Meunier Antoine Manens. Framework. No quantization : lossless coding Open-loop = Closed-loop Ideal VLC coder for each level of the pyramid. Criteria. Global compression rate of the pyramid

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Presentation Transcript

Laurent Meunier

Antoine Manens

• No quantization : lossless coding

• Open-loop = Closed-loop

• Ideal VLC coder for each level of the pyramid

• Global compression rate of the pyramid

• SNR and visual quality of the partially reconstructed pictures

• Cost of the decoding process

• Haar

• Gaussian filters(Burt & Adelson, 1983)

• Ideal filters

• Optimal filters for piecewise polynomial fitting (Chin, Choi, Luo, 1992)

• Splines (Unser, Aldroubi, Eden, 1993)

• Efficient, but introduces blurring and aliasing

More complicated to analyse.

Reduce and Expand Filters chosen from intuition/experiments, no guarantee of optimality.

Review of non-linear techniques

• Multi-level median filter (Defee, Neuvo, 1991)

• Anisotropic pyramid (You, Kaveh,1996)

• Hyp: Decimation filter is given

• Problem : find 4 predictors for the even-even, odd-even, even-odd and odd-odd pixels.

• Optimal solution : conditional expected value of the pixel given its neighbourhood for each predictor.

• The implementation requires to reduce the number of possible neighbourhoods

• => Partition the image using features likeaverage intensity, gradient, presence of edges, texture.

• Example: image obtained with 3 features (avg intensity, grad/x, grad/y) 8 levels of quantization 8x8x8 = 512 cells

• Pretty coarse because only one intensity per cell.

• Solution :Use an optimal linear predictor that takes the local best fitting plane instead of the expected value.

• Train the predictor using a set of images.

Hybrid Method edges

• Motivation : some methods do a better job than the others in some kind of neighborhoods

Implementation : the algorithm switches technique depending on the type of neighborhood. Use a training set to learn decision table.

Visual comparison edges

Original

Cubic interpolation

Optimal non-linear

Numerical results edges

Entropies :

• Lena : 7.44

• Burt(0.6) : 5.69

• Spline(3) : 5.61

• Cubic interpolation : 5.43

• Approx. opt. NL : 5.39

• MMF : 5.35

• DPCM : 5.03

Conclusion edges

• Significant improvements over the Burt&Adelson pyramid were achieved both in terms of compression rate and of SNR of the partially reconstructed images

• Rate reduction is lower than with DPCM. The lossless algorithm should therefore be used only where progressive transmission is necessary.

• More thorough study of the feature choice and of the number of bins for the proposed NL technique is necessary.

• Further study should include the issue of quantization (variable bit-allocation and non-optimal VLC)