Optimal Quantization Scheme for Biorthogonal Wavelets for Coding an

d 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

Outline

• Motivation

• Filter implementation

• Experimental results

• Future work

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?

Difference between JPEG2000 and SPIHT

• No inter-scale correlation is employed in JPEG-2000.

SPIHT JPEG-2000

• Better entropy coding and more wavelet-independent quantization are employed in JPEG-2000.

Key point to SPIHT Coding efficiency

• Orthogonality

-NOM (near-orthogonality measure )

• Zero-tree

-energy compaction

Outline

• Motivation

• Filter implementation

• Experimental results

• Future work

Filter-bank implementation

• Lifting-Based Filtering:

• Convolution-Based Filtering:

Dot products between the two filter masks and the signal.

2

)22()2()12()12(

nxnxnxny

4

2)12()12()2()2(

nynynxny

Filter-bank implementation

• M. D. Adams and F. Kossentini, “Reversible integer to integer wavelet transforms for Image compression: performance evaluation and analysis” IEEE Trans. Im

age 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.

Outline

• Motivation

• Filter implementation

• Experimental results

• Future work

SPIHT coding efficiency(”Lena”)

bpp 5/3 9/7-F 9/7-M 5/11-A 5/11-C 13/7-C 13/7-T

0.0625 26.90 27.66 27.08 26.92 26.82 26.96 27.21

0.125 29.71 30.25 29.78 29.84 29.79 29.94 29.90

0.25 32.60 33.24 32.87 32.81 32.88 33.04 33.07

0.5 35.75 36.17 35.93 35.92 35.89 36.14 36.13

1.0 38.87 38.84 38.80 38.89 38.80 39.03 39.00

bpp 2/6 2/10 6/14

0.0625 27.09 27.15 27.32

0.125 29.70 29.95 30.06

0.25 32.62 32.95 33.07

0.5 35.61 35.90 36.04

1.0 38.68 38.66 38.95

Lifting scheme:

SPIHT coding efficiency(cont.)

Bpp 10/18 9/7 5/3 D_6 D_4 Haar

0.0625 27.92 27.59 27.38 26.83 26.42 25.42

0.125 30.68 30.53 30.03 29.38 28.97 27.53

0.25 33.75 33.58 32.94 32.35 31.85 30.21

0.5 36.86 36.74 36.07 35.75 35.24 33.50

1.0 39.96 39.92 39.29 39.26 38.92 37.47

convolution scheme:

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

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

Coding performance at various scaling5/3,”Lena”

scaling 0.03125 0.0625 0.125 0.25 0.5 1.0 2.0

1.0 5.64 22.73 26.49 27.92 32.46 36.48 39.90

1.1 22.8 23.87 27.58 31.52 35.12 37.14 41.43

1.2 23.41 26.46 29.04 31.95 35.37 38.71 42.65

1.3 23.93 26.58 29.58 32.60 35.83 39.00 42.91

1.414 24.31 26.90 29.71 32.60 35.75 38.87 42.46

1.5 24.95 27.12 29.69 32.35 35.32 38.79 42.95

1.6 24.47 26.95 29.64 32.35 35.15 38.52 42.62

1.7 24.95 26.99 29.26 32.07 35.09 38.26 42.45

1.8 24.41 26.73 29.27 31.96 34.33 38.24 42.48

1.9 24.43 26.90 28.89 31.77 34.32 37.68 42.23

2.0 24.45 26.62 28.98 31.57 34.10 37.39 41.79

Coding performance at various scaling9/7-F,”Lena”

scaling 0.03125 0.0625 0.125 0.25 0.5 1.0 2.0

1.0 5.66 27.21 29.27 32.54 35.66 38.26 40.75

1.1 24.88 27.47 30.38 33.36 36.28 38.50 41.31

1.2 25.07 27.54 30.27 33.23 36.26 38.98 41.83

1.3 25.12 27.59 30.32 33.15 36.10 38.91 41.90

1.414 25.07 27.38 29.96 32.82 35.92 38.76 41.66

1.5 24.79 27.20 29.95 32.74 35.51 38.56 41.94

1.6 24.70 27.27 29.45 32.55 35.42 38.36 41.71

1.7 24.79 26.92 29.18 32.34 34.83 38.15 41.20

1.8 24.58 26.63 29.10 32.09 34.65 37.96 38.98

1.9 24.63 26.84 28.92 31.81 34.81 37.54 39.43

2.0 24.68 26.24 28.85 32.06 34.23 37.36 37.46

Outline

• Motivation

• Filter implementation

• Experimental results

• Future work

Future work

• Modify the scaling constant for biorthogonal wavelets to achieve better performance.

• Experiment for data hiding. (such as DWT domain watermarking).