Download Pyramid coder with nonlinear prediction

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 bitallocation and non-optimal VLC)