Pyramid Coder with Nonlinear Prediction Panu Chaichanavong Burt/Adelson pyramid coder A nonlinear prediction Aliasing effect A switching method Conclusion

Burt/Adelson Pyramid Coder Introduced by Burt and Adelson (1983) Gaussian Laplacian Quantized and transmitted Original image Reconstructed image

A Nonlinear Prediction By Florencio and Schafer (1994) Filter Just subsample! Interpolator Replication Weighted median of 6 neighbor pixels Median of 4 neighbor pixels 1 1 1 1 2 1 2 3 2 Lower resolution image Predicted image

A Nonlinear Prediction (2) Burt/Adelson coder with nonlinear prediction

Aliasing Effect Test image

Aliasing Effect (2) Gaussian filter Only subsampling

Linear low-pass with weight shown above A Switching Method Let’s look at the following 4x4 filters .032 .058 .058 .032 .058 .102 .102 .058 0 0 0 0 0 0 1 0 0 0 0 0 0 1 2 0 0 3 4 0 Filter3 Linear low-pass with weight shown above Filter2 Median of average Filter1 Pick one !

A Switching Method (2) Input1 Input2 Input1: may be an edge, use filter1 Input2: high frequency, use filter3 How can we distinguish these inputs?

A Switching Method (3) Let D = sum of difference of adjacent pixel values sd = standard deviation of 16 pixel values p = D/sd Decision criterion: p < 18, use filter1 18 < p < 22, use filter2 p > 22, use filter3

A Switching Method (4) Filtered subsampled image Filter used Filter1

A Switching Method (5) Reconstructed image Method PSNR (dB) Bit-rate (bit/pixel) B/A 32.77 0.8278 Nonlinear 34.00 0.6544 Switch 33.58 0.6501 Reconstructed image

A Switching Method (6) Images in the Gaussian pyramid Filter used

Conclusion Low-pass filter reduces aliasing effect but gives blurred image Some nonlinear prediction preserves edges and details but may introduces annoying aliasing A decision criterion is presented to switch among various filters to select an appropriate one for a particular input