Pyramid coder with nonlinear prediction

Laurent MeunierAntoine 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

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.

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

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

Entropies :

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)