Pyramid coder with nonlinear prediction

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Pyramid coder with nonlinear prediction
Laurent Meunier Antoine Manens
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Framework

• No quantization lossless coding
• Open-loop Closed-loop
• Ideal VLC coder for each level of the pyramid

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Criteria

• Global compression rate of the pyramid
• SNR and visual quality of the partially
  reconstructed pictures
• Cost of the decoding process

4
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

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Review of non-linear techniques

• Multi-level median filter (Defee, Neuvo, 1991)
  
• Anisotropic pyramid (You, Kaveh,1996)

• 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.

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

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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.

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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.
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Method mapping
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Visual comparison
Original
BurtAdelson with a 0.6
Cubic interpolation
Optimal non-linear
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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

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Conclusion

• Significant improvements over the BurtAdelson
  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)