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

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 like average 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)