1. Optimal Quantization Scheme for Biorthogonal Wavelets for Coding and Data hiding 台北科技大學資工所 指導教授：楊士萱 研究生：廖武傑 2003/2/27

2. Outline Motivation Filter implementation Experimental results Future work

3. Motivation The difference of between 9/7 and other filters for JPEG-2000 is small, but it is significant for SPIHT. Can we modify the coding algorithm to make other filters (such as 5/3) to achieve better performance?

4. Difference between JPEG2000 and SPIHT No inter-scale correlation is employed in JPEG- 2000. SPIHTJPEG-2000 Better entropy coding and more wavelet- independent quantization are employed in JPEG- 2000.

5. Key point to SPIHT Coding efficiency Orthogonality -NOM (near-orthogonality measure ) Zero-tree -energy compaction

6. Outline Motivation Filter implementation Experimental results Future work

7. Filter-bank implementation Lifting-Based Filtering: Convolution-Based Filtering: Dot products between the two filter masks and the signal.

8. Filter-bank implementation M. D. Adams and F. Kossentini, “Reversible integer to integer wavelet transforms for Image compression: performance evaluation and analysis” IEEE Trans. Image processing, Jun. 2000 we’ve implemented lifting-based filters:5/3, 9/7-F, 9/7-M, 5/11-A, 5/11-C, 13/7-T, 13/7-C, 2/6, 2/10, 6/14 and convolution-based filter:9/7, 10/18, haar, D4, D6.

9. Outline Motivation Filter implementation Experimental results Future work

10. SPIHT coding efficiency(”Lena”) bpp5/39/7-F9/7-M5/11-A5/11-C13/7-C13/7-T 0.062526.9027.6627.0826.9226.8226.9627.21 0.12529.7130.2529.7829.8429.7929.9429.90 0.2532.6033.2432.8732.8132.8833.0433.07 0.535.7536.1735.9335.9235.8936.1436.13 1.038.8738.8438.8038.8938.8039.0339.00 bpp2/62/106/14 0.062527.0927.1527.32 0.12529.7029.9530.06 0.2532.6232.9533.07 0.535.6135.9036.04 1.038.6838.6638.95 Lifting scheme:

11. SPIHT coding efficiency(cont.) Bpp10/189/75/3D_6D_4Haar 0.062527.9227.5927.3826.8326.4225.42 0.12530.6830.5330.0329.3828.9727.53 0.2533.7533.5832.9432.3531.8530.21 0.536.8636.7436.0735.7535.2433.50 1.039.9639.9239.2939.2638.9237.47 convolution scheme:

12. Energy distribution(5/3,”Lena”) Lifting scheme, 5 level decomposition, level5-level3

13. Energy distribution(9/7-F,”Lena”) Lifting scheme, 5 level decomposition, level5-level3

14. Coding performance at various scaling 5/3,”Lena” scaling0.031250.06250.1250.250.51.02.0 1.05.6422.7326.4927.9232.4636.4839.90 1.122.823.8727.5831.5235.1237.1441.43 1.223.4126.4629.0431.9535.3738.7142.65 1.323.9326.5829.5832.6035.8339.0042.91 1.41424.3126.9029.7132.6035.7538.8742.46 1.524.9527.1229.6932.3535.3238.7942.95 1.624.4726.9529.6432.3535.1538.5242.62 1.724.9526.9929.2632.0735.0938.2642.45 1.824.4126.7329.2731.9634.3338.2442.48 1.924.4326.9028.8931.7734.3237.6842.23 2.024.4526.6228.9831.5734.1037.3941.79

15. Coding performance at various scaling 9/7-F,”Lena” scaling0.031250.06250.1250.250.51.02.0 1.05.6627.2129.2732.5435.6638.2640.75 1.124.8827.4730.3833.3636.2838.5041.31 1.225.0727.5430.2733.2336.2638.9841.83 1.325.1227.5930.3233.1536.1038.9141.90 1.41425.0727.3829.9632.8235.9238.7641.66 1.524.7927.2029.9532.7435.5138.5641.94 1.624.7027.2729.4532.5535.4238.3641.71 1.724.7926.9229.1832.3434.8338.1541.20 1.824.5826.6329.1032.0934.6537.9638.98 1.924.6326.8428.9231.8134.8137.5439.43 2.024.6826.2428.8532.0634.2337.3637.46

16. Outline Motivation Filter implementation Experimental results Future work

17. Modify the scaling constant for biorthogonal wavelets to achieve better performance. Experiment for data hiding. (such as DWT domain watermarking).