Pyramid coder with nonlinear prediction
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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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Pyramid coder with nonlinear prediction

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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

  • SNR and visual quality of the partially reconstructed pictures

  • Cost of the decoding process


Review of linear techniques

  • 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


Improvement can be obtained on specific visual patterns like edges

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)


Optimal NL interpolation

  • 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.


Implementation of the optimal NL filter

  • 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

  • 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.


Method mapping


Visual comparison

Original

Burt&Adelson with a = 0.6

Cubic interpolation

Optimal non-linear


Numerical results

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

  • 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)


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