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Wavelet-based Image Compression

Using Human Visual System Models

Andrew P. Beegan

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

(Virginia Tech)

in partial fulfillment of the requirements for the degree of

Master of Science

in

Electrical Engineering

Dr. Amy E. Bell, Chair

Dr. A. Lynn Abbott

Dr. Brian D. Woerner

May 2001

Blacksburg, Virginia

Keywords: image compression, wavelets, multiwavelets

HVS, subjective testing

Copyright 2001, Andrew P. Beegan

Wavelet-based Image Compression

Using Human Visual System Models

Andrew P. Beegan

(ABSTRACT)

Recent research in transform-based image compression has focused on the wavelet transform

due to its superior performance over other transforms. Performance is often measured solely

in terms of peak signal-to-noise ratio (PSNR) and compression algorithms are optimized

for this quantitative metric. The performance in terms of subjective quality is typically

not evaluated. Moreover, the sensitivities of the human visual system (HVS) are often not

incorporated into compression schemes.

This thesis develops new wavelet models of the HVS and illustrates their performance for

various scalar wavelet and multiwavelet transforms. The performance is measured quantita-

tively (PSNR) and qualitatively using our new perceptual testing procedure.

Our new HVS model is comprised of two components: CSF masking and asymmetric com-

pression. CSF masking weights the wavelet coefficients according to the contrast sensitivity

function (CSF)–a model of humans’ sensitivity to spatial frequency. This mask gives the

most perceptible information the highest priority in the quantizer. The second component

of our HVS model is called asymmetric compression. It is well known that humans are more

sensitive to luminance stimuli than they are to chrominance stimuli; asymmetric compression

quantizes the chrominance spaces more severely than the luminance component.

The results of extensive trials indicate that our HVS model improves both quantitative

and qualitative performance. These trials included 14 observers, 4 grayscale images and 10

color images (both natural and synthetic). For grayscale images, although our HVS scheme

lowers PSNR, it improves subjective quality. For color images, our HVS model improves

both PSNR and subjective quality. A benchmark for our HVS method is the latest version

of the international image compression standard–JPEG2000. In terms of subjective quality,

our scheme is superior to JPEG2000 for all images; it also outperforms JPEG2000 by 1 to 3

dB in PSNR.

We would like to thank the National Science Foundation for their support; this research was

made possible through their sponsorship.

iii

Acknowledgments

This work would not have been possible without the guidance and support I received from

Dr. Amy Bell. When my research led me to a wall, she always guided me to the next

open door. Her constructive criticism–always offered with a smile–fueled our research and

polished this thesis into its final form.

I offer my gratitude to Dr. BrianWoerner and Dr. Lynn Abbott for serving on my committee.

My DSPCL cohorts, Lakshmi Iyer and Manish Manglani, were my source of truth. The task

was never complete without their judgment.

I would also like to thank my parents Dr. Paul and Christine Beegan. Their love and

dedication to their six children are extraordinary. Through them I have learned that my

education is not an obstacle, but an opportunity.

iv

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Significance of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Outline of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Image Compression Using Wavelets 5

2.1 Transform-based Image Compression . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Grayscale and Color Image Compression . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Grayscale Image Compression . . . . . . . . . . . . . . . . . . . . . . 6

2.2.2 Color Image Compression . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 The Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Scalar Wavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.2 Multiwavelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 SPIHT Quantization and Shuffling . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 JPEG2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Human Visual System in Image Compression 15

v

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 CSF Masking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 DWT CSF Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.2 Band-average CSF Masks . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 Asymmetric Color Compression . . . . . . . . . . . . . . . . . . . . . . . . . 26

4 Performance Measures 27

4.1 PSNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Subjective Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.1 Experimental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2.2 Goals of Subjective Experiments . . . . . . . . . . . . . . . . . . . . . 30

4.2.3 Expert vs. Non-Expert Analysis . . . . . . . . . . . . . . . . . . . . . 31

4.3 Correlation of Quantitative and Qualitative Measures . . . . . . . . . . . . . 31

4.4 Results of Previous Related Research . . . . . . . . . . . . . . . . . . . . . . 33

5 Experimental Results 36

5.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.1.1 Grayscale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.2 Color . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.3 Shuffling for the Multiwavelet Transform . . . . . . . . . . . . . . . . 38

5.2 Results for Natural Grayscale Images . . . . . . . . . . . . . . . . . . . . . . 38

5.2.1 Results for Lena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2.2 Results for Lighthouse . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2.3 Results for Barbara . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.4 Results for Ruler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

vi

5.3 Results for Natural Color Images . . . . . . . . . . . . . . . . . . . . . . . . 50

5.3.1 Results for Lena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.3.2 Results for Mandrill . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.3.3 Results for Lighthouse . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.3.4 Results for Helen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.3.5 Results for Owl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4 Results for Synthetic Color Images . . . . . . . . . . . . . . . . . . . . . . . 66

5.4.1 Results for DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4.2 Results for Satellite . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4.3 Results for Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.4.4 Results for Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.4.5 Results for Color16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.5 Correlation Results for Image Groups . . . . . . . . . . . . . . . . . . . . . . 81

5.6 Comparison with JPEG2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6 Conclusion 86

6.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.1.1 Grayscale Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.1.2 Natural Color Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.1.3 Synthetic Color Images . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.1.4 HVS on vs. JPEG2000 . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.1.5 Correlations for Image Groups . . . . . . . . . . . . . . . . . . . . . . 88

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

A Test Images 91

vii

List of Figures

2.1 Transform image compression system design . . . . . . . . . . . . . . . . . . 6

2.2 (a) Lena image represented in the YCbCr color space. (b) Luminance com-

ponent. (c) Chrominance-red component. (d) Chrominance-blue component. 8

2.3 Block diagram of the color image compression algorithm. . . . . . . . . . . . 9

2.4 The analysis and synthesis stages of a 2-D, 1-level scalar wavelet decomposition. 9

2.5 One level scalar wavelet (Bi 9/7) decomposition of the lighthouse image. . . 10

2.6 Comparison of one-level (a) scalar wavelet and (b) multiwavelet decompositions. 11

2.7 The analysis stage of a 2-D, 1-level multiwavelet decomposition with r = 2. . 12

2.8 Illustration of coefficient shuffling method. Selected pixels are numbered to

indicate correspondence. (a) Before shuffling. (b) After shuffling. . . . . . . . 13

2.9 Subbands in 2-level multiwavelet decomposition after coefficient shuffling.

Solid lines denote new subband boundaries. Dashed lines denote subband

boundaries that are removed by coefficient shuffling. . . . . . . . . . . . . . . 14

3.1 Luminance Constrast Sensitivity Function . . . . . . . . . . . . . . . . . . . 16

3.2 Block diagram of CSF masking method. . . . . . . . . . . . . . . . . . . . . 17

3.3 5-level Bi9/7 wavelet decomposition of CSF for 6-weight mask. . . . . . . . . 18

3.4 The V subspaces for the 5-level Bi9/7 wavelet decomposition of the CSF. . . 20

3.5 DWT CSF mask with 11 unique weights. . . . . . . . . . . . . . . . . . . . . 21

viii

3.6 Band-average CSF mask with 6 unique weights. . . . . . . . . . . . . . . . . 23

3.7 CSF curve shown with the 6-weight band-average CSF mask. . . . . . . . . . 24

3.8 (a) Close-up of original lighthouse. (b) Reconstructed with 11-weight DWT

CSF mask at 0.250 bpp, PSNR=31.85 dB. (c) Reconstructed with 6-weight

band-average CSF mask at 0.250 bpp, PSNR=31.74 dB. . . . . . . . . . . . 25

4.1 Instructions page for subjective quality testing procedure. . . . . . . . . . . . 29

4.2 Sample image comparison as presented in the subjective quality testing pro-

cedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.1 (a) Original Lena. (b) Reconstruction compressed with Bi22/14 scalar wavelet

without CSF masking at 0.250 bpp, PSNR=33.80 dB. (c) Reconstruction

compressed with Bi22/14 scalar wavelet with CSF masking at 0.250 bpp,

PSNR=33.47 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.2 (a) Original Lighthouse. (b) Reconstruction compressed with Bi22/14 scalar

wavelet without CSF masking at 0.250 bpp, PSNR=26.91 dB. (c) Reconstruc-

tion compressed with Bi22/14 scalar wavelet with CSF masking at 0.250 bpp,

PSNR=25.80 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 (a) Original Ruler. (b) Reconstruction compressed with BSA9/7 multiwavelet

(without shuffling) without CSF masking at 1.000 bpp, PSNR=26.62 dB.

(c) Reconstruction compressed with BSA9/7 multiwavelet (without shuffling)

with CSF masking at 1.000 bpp, PSNR=25.16 dB. . . . . . . . . . . . . . . 49

5.4 (a) Original Lena. (b) Reconstruction compressed with Bi22/14 scalar wavelet

without HVS at 0.167 bpp, PSNR=30.92 dB. (c) Reconstruction compressed

with Bi22/14 scalar wavelet with HVS at 0.167 bpp, PSNR=31.97 dB. . . . 52

5.5 (a) Original Mandrill. (b) Reconstruction compressed with Bi9/7 scalar wavelet


with Bi9/7 scalar wavelet with HVS at 0.417 bpp, PSNR=24.85 dB. . . . . . 56

ix

5.6 (a) Original Lighthouse. (b) Reconstruction compressed with Bi22/14 scalar

wavelet CSF off/Asymmetric off at 0.167 bpp, PSNR=26.18 dB. (c) Recon-

struction compressed with Bi22/14 scalar wavelet CSF on/Asymmetric off at

0.167 bpp, PSNR=25.66 dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.7 (a) Original Helen. (b) Reconstruction compressed with BSA7/5 multiwavelet


with BSA7/5 multiwavelet with HVS at 0.250 bpp, PSNR=34.68 dB. . . . . 62

5.8 (a) Original Owl. (b) Reconstruction compressed with SA4 multiwavelet with-

out HVS at 0.417 bpp, PSNR=25.87 dB. (c) Reconstruction compressed with

SA4 multiwavelet with HVS at 0.417 bpp, PSNR=29.68 dB. . . . . . . . . . 65

5.9 (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet


with Bi22/14 scalar wavelet with HVS at 2.75 bpp, PSNR=38.48 dB. . . . . 68

5.10 (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet


with Bi22/14 scalar wavelet with HVS at 0.167 bpp, PSNR=34.40 dB. . . . 69

5.11 (a) Original Satellite. (b) Reconstruction compressed with BSA7/5 multi-

wavelet without HVS at 0.250 bpp, PSNR=23.29 dB. (c) Reconstruction com-

pressed with BSA7/5 multiwavelet without HVS at 0.250 bpp, PSNR=24.11

dB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.12 (a) Original Map. (b) Reconstruction compressed with BSA7/5 multiwavelet


with BSA7/5 multiwavelet without HVS at 0.417 bpp, PSNR=27.65 dB. . . 76

5.13 (a) Original Lena. (b) Reconstruction compressed with JPEG2000 (Bi9/7)

at 0.417 bpp, PSNR=32.24 dB. (c) Reconstruction compressed with Bi22/14

scalar wavelet with HVS at 0.417 bpp, PSNR=34.66 dB. . . . . . . . . . . . 83

5.14 (a) Original Metal. (b) Reconstruction compressed with JPEG2000 (Bi9/7)

at 0.250 bpp, PSNR=30.90 dB. (c) Reconstruction compressed with Bi22/14

scalar wavelet with HVS at 0.250 bpp, PSNR=35.52 dB. . . . . . . . . . . . 84

x

A.1 Lena (grayscale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.2 Barbara (grayscale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.3 Lighthouse (grayscale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.4 Ruler (grayscale). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.5 Lena. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.6 Helen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

A.7 Lighthouse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.8 Mandrill. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.9 Owl. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.10 DNA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

A.11 Satellite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.12 Map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.13 Metal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

A.14 Color 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

xi

List of Tables

5.1 Correlation coefficients for grayscale Lena. . . . . . . . . . . . . . . . . . . . 39

5.2 Scalar wavelet PSNR (in dB) results for grayscale Lena. . . . . . . . . . . . . 39

5.3 Multiwavelet PSNR (in dB) results for grayscale Lena with shuffling. . . . . 40

5.4 Correlation coefficients for grayscale Lighthouse. . . . . . . . . . . . . . . . . 42

5.5 Scalar wavelet PSNR results (in dB) for grayscale Lighthouse. . . . . . . . . 42

5.6 Multiwavelet PSNR (in dB) results for grayscale Lighthouse with shuffling. . 43

5.7 Correlation coefficients for grayscale Barbara. . . . . . . . . . . . . . . . . . 45

5.8 Scalar wavelet PSNR results (in dB) for grayscale Barbara. . . . . . . . . . . 45

5.9 Multiwavelet PSNR (in dB) results for grayscale Barbara with shuffling. . . . 46

5.10 Multiwavelet PSNR (in dB) results for grayscale Barbara without shuffling. . 46

5.11 Correlation coefficients for grayscale Ruler. . . . . . . . . . . . . . . . . . . . 47

5.12 Scalar wavelet PSNR results (in dB) for grayscale Ruler. . . . . . . . . . . . 47

5.13 Multiwavelet PSNR (in dB) results for grayscale Ruler with shuffling. . . . . 48

5.14 Multiwavelet PSNR (in dB) results for grayscale Ruler without shuffling. . . 48

5.15 Correlation coefficients for color Lena. . . . . . . . . . . . . . . . . . . . . . 51

5.16 Scalar wavelet PSNR (in dB) results for color Lena. . . . . . . . . . . . . . . 51

5.17 Multiwavelet PSNR (in dB) results for color Lena with shuffling. . . . . . . . 53

xii

5.18 Correlation coefficients for color Mandrill. . . . . . . . . . . . . . . . . . . . 54

5.19 Scalar wavelet PSNR (in dB) results for color Mandrill. . . . . . . . . . . . . 55

5.20 Multiwavelet PSNR (in dB) results for color Mandrill with shuffling. . . . . . 55

5.21 Correlation coefficients for color Lighthouse. . . . . . . . . . . . . . . . . . . 57

5.22 Scalar wavelet PSNR (in dB) results for color Lighthouse. . . . . . . . . . . . 58

5.23 Multiwavelet PSNR (in dB) results for color Lighthouse with shuffling. . . . 58

5.24 Correlation coefficients for color Helen. . . . . . . . . . . . . . . . . . . . . . 60

5.25 Scalar wavelet PSNR (in dB) results for color Helen. . . . . . . . . . . . . . 61

5.26 Multiwavelet PSNR (in dB) results for color Helen with shuffling. . . . . . . 61

5.27 Correlation coefficients for color Owl. . . . . . . . . . . . . . . . . . . . . . . 63

5.28 Scalar wavelet PSNR (in dB) results for color Owl. . . . . . . . . . . . . . . 64

5.29 Multiwavelet PSNR (in dB) results for color Owl with shuffling. . . . . . . . 64

5.30 Correlation coefficients for color DNA. . . . . . . . . . . . . . . . . . . . . . 67

5.31 Scalar wavelet PSNR (in dB) results for color DNA. . . . . . . . . . . . . . . 67

5.32 Multiwavelet PSNR (in dB) results for color DNA with shuffling. . . . . . . . 70

5.33 Correlation coefficients for color Satellite. . . . . . . . . . . . . . . . . . . . . 71

5.34 Scalar wavelet PSNR (in dB) results for color Satellite. . . . . . . . . . . . . 72

5.35 Multiwavelet PSNR (in dB) results for color Satellite with shuffling. . . . . . 72

5.36 Correlation coefficients for color Map. . . . . . . . . . . . . . . . . . . . . . . 74

5.37 Scalar wavelet PSNR (in dB) results for color Map. . . . . . . . . . . . . . . 74

5.38 Multiwavelet PSNR (in dB) results for color Map with shuffling. . . . . . . . 75

5.39 Correlation coefficients for color Metal. . . . . . . . . . . . . . . . . . . . . . 77

5.40 Scalar wavelet PSNR (in dB) results for color Metal. . . . . . . . . . . . . . 77

5.41 Multiwavelet PSNR (in dB) results for color Metal with shuffling. . . . . . . 78

xiii

5.42 Scalar wavelet PSNR (in dB) results for Color16. . . . . . . . . . . . . . . . 79

5.43 Multiwavelet PSNR (in dB) results for Color16 with shuffling. . . . . . . . . 80

5.44 Correlation of subjective quality with: PSNR and HVS on. . . . . . . . . . . 82

5.45 Comparing color image compression: HVS on vs. JPEG2000. . . . . . . . . 85

xiv

Chapter 1

Introduction

1.1 Motivation

In the emerging digital era, family photo albums are stored not only on the bookshelf, but also

on the personal computer. A medical doctor can make a diagnosis using a full 3-dimensional

image on a computer screen–not long ago surgery would have been necessary to capture the

same critical point of view. Satellite images of earth and places beyond are continually being

transmitted over communication channels. The Internet–still in its childhood–continues

to flourish and impact our personal and professional lives. Common to these and many other

applications is the storage of digital imagery.

The proliferation of digital media has motivated innovative methods for compressing digital

images. The popular Joint Photographic Experts Group (JPEG) and Graphical Interchange

Format (GIF) standards have been the prevailing methodologies in image compression in the

past decade [22]. Alternatively, recent research in digital image compression has explored

and improved the utility of the wavelet transform; its success as a compression technique

has prompted its inclusion in the JPEG2000 standard. In addition to the traditional wavelet

transform (referred to here as the scalar wavelet transform), alternative wavelet-based com-

1

2

pression schemes have shown great promise. They are multiwavelets, wavelet packets, and

multiwavelets packets.

The performance of each of these methods depends on the image content; performance

varies for natural and synthetic images and for high and low frequency content. For in-

stance, multiwavelets have been shown to capture high-frequency content better than scalar

wavelets, especially when used with shuffling–a SPIHT-like1 quantization scheme [14, 20].

Scalar wavelets still perform best on natural images with low frequency content such as the

commonly-used Lena image.

However, research to date has been limited to grayscale images and the results published in

the literature often show only one or two images. In addition, the human visual system (HVS)

has not been incorporated into most current wavelet-based compression schemes. Finally,

common quantitative performance metrics, such as peak signal to noise ratio (PSNR), do

not always correlate with qualitative evaluations–especially for color images. This thesis

has two main objectives.

1. Improve scalar wavelet and multiwavelet compression for both grayscale and color

images by incorporating models of particular HVS characteristics.

2. Evaluate the performance of these wavelet-based compression schemes using PSNR

and a qualitative measure.

1.2 Previous Research

Basic wavelet theory and the application of wavelets to image compression has been well-

developed. As scalar wavelet filters developed, variations of the scalar wavelet transform were

introduced–among them is the multiwavelet transform [25, 26, 27, 28]. More recently, alter-

native multiwavelet algorithms have been established, including multiwavelets with shuffling

1SPIHT stands for set partitioning in heirarchical trees

3

[14], balanced multiwavelets [33], and symmetric FIR balanced multiwavelets [21]. In addi-

tion to scalar wavelets and multiwavelets, wavelet packets [4, 5] and multiwavelet packets

[14] have also been introduced. The methods and results in this thesis are concerned with

scalar wavelets, multiwavelets, and multiwavelets with shuffling.

Results that have been reported for the application of an HVS model to wavelet-based image

compression have been inconclusive [17, 18]. The publications in HVS-based compression

rarely present alternatives that are significantly superior to the existing non-HVS method-

ologies. PSNR is the standard quantitative performance metric in the image compression

community. Subjective metrics that have been reported do not present consistent and com-

plete results to validate their use [7, 16, 34].

1.3 Significance of this Thesis

The application of an HVS model to image compression is a recent research area [17, 18]. The

application of wavelet-based compression schemes to color images has also received limited

attention in the research community. Results have recently been reported for color image

compression using scalar wavelets and an HVS model [17]. Although some of these methods

are similar to those described in this thesis, the results are comparatively minimal and

inconclusive. This thesis presents different methods as well as a more thorough evaluation.

The contributions of this thesis are as follows.

1. The development and evaluation of wavelet-based HVS methods for image compression.

These include: a wavelet-based contrast sensitivity function (CSF) weighting mask; an

asymmetric compression of the Y(luminance)/Cb(chrominance-blue)/Cr(chrominance-

red) spaces for color image compression; and, the combination of these two new meth-

ods.

2. A comparison of the best known scalar wavelets and multiwavelets for the compression

4

of color images.

3. Results are examined both qualitatively and quantitatively for a comprehensive set

of different image types and the correlation between the two performance metrics is

found.

4. A subjective image quality testing procedure for expert and non-expert observers. Our

analysis includes more observers than presented in previous research.

1.4 Outline of this Thesis

Chapter 2 provides a brief background on transform-based image compression, graycale and

color image compression, and scalar wavelets and multiwavelets. We continue with a short

explanation of the SPIHT quantizer and the modified SPIHT quantization method called

shuffling for multiwavelet decompositions. Chapter 2 concludes with a summary of the

JPEG2000 standard. Chapter 3 provides some background on the human visual system and

the application of this science to digital image compression. Our innovative techniques em-

ployed in the experiments are explained. Chapter 4 provides a summary of the performance

measures used in this thesis, including a new and complete subjective testing procedure for

image quality. Chapter 5 presents the experimental results which show the superiority of

our HVS scheme over the most recent wavelet-based techniques and JPEG2000. Chapter 6

provides a summary and conclusion to this thesis along with suggestions for future work in

this area.

Chapter 2

Image Compression Using Wavelets

2.1 Transform-based Image Compression

The goal of image compression is to reduce the number of bits needed to represent an

image while maintaining a desirable quality. The methodologies can be divided into two

types–lossless and lossy compression. If the compression algorithm is lossless, the original

image can be reconstructed perfectly from the compressed version. In the case of lossy

compression, the original cannot be reconstructed perfectly from the compressed version.

The best lossless schemes do not achieve competitive compression ratios compared to their

lossy counterparts. For this reason, perfect reconstruction is often sacrificed for the superior

compression performance provided by a lossy compression scheme.

The most successful image compression algorithms are transform-based. Figure 2.1 shows

a block diagram of the transform image compression system [13]. First, the image is trans-

formed into a domain where the image information is represented in a more compact form.

For example, the popular JPEG standard [22] employs the discrete cosine transform (DCT);

it converts the image data to transform coefficients that are a function of spatial frequency.

Large-valued DCT coefficients indicate detail areas with high spatial frequency. Small-valued

5

6

Transform Quantizer EntropyCoder

Image Storage/Transmission

Figure 2.1: Transform image compression system design

DCT coefficients indicate smooth areas with low spatial frequency. This thesis is concerned

with the wavelet transform; this family of transforms is described in Section 2.3.

Next, the transform coefficients are quantized. This lossy stage, in which information is

irretrievably thrown away, results in a compressed image. An effective quantizer assigns

more bits to those coefficients that represent the most information, and fewer bits to those

coefficients that represent less information. In this thesis, we employ the SPIHT quantizer

and a variation of this scheme; they are detailed in Section 2.4 [14, 20].

The final step is coding. Typically an entropy coder is used to remove redundancy in the

bit stream. The arithmetic, Huffman, and run-length coding schemes are the most popular

entropy coders [22]. In this thesis we do not perform entropy coding; instead we focus on

the transform and quantization steps.

2.2 Grayscale and Color Image Compression

2.2.1 Grayscale Image Compression

A digital grayscale image is typically represented by 8 bits per pixel (bpp) in its uncompressed

form. Each pixel has a value ranging from 0 (black) to 255 (white). Transform methods are

applied directly to a two dimensional image by first operating on the rows, and then on the

columns. Transforms that can be implemented in this way are called separable.

7

2.2.2 Color Image Compression

A digital color image is stored as a three-dimensional array and uses 24 bits to represent each

pixel in its uncompressed form. Each pixel contains a value representing a red (R), green

(G), and blue (B) component scaled between 0 and 255–this format is known as the RGB

format. Image compression schemes first convert the color image from the RGB format to

another color space representation that separates the image information better than RGB.

In this thesis the color images are converted to the luminance (Y), chrominance-blue (Cb),

and chrominance-red (Cr) color space.

The luminance component represents the intensity of the image and looks like a grayscale

version of the image. The chrominance-blue and chrominance-red components represent the

color information in the image. The Y, Cb, and Cr components are derived from the RGB

space by the following relations [1].

Y = 16 + 65.481 ·R+ 128.553 ·G+ 24.966 · B (2.1)

Cb = 128− 37.797 ·R− 74.203 ·G+ 112 ·B (2.2)

Cr = 128 + 112 ·R− 93.786 ·G− 18.214 · B (2.3)

Figure 2.2 shows the Lena image in the YCbCr color space and in each of the three compo-

nents. This illustrates the advantage of using the YCbCr color space–most of the informa-

tion is contained in the luminance space (Figure 2.2(b)).

Figure 2.3 shows a block diagram of the color space conversion. Each of the three components

(Y, Cb, and Cr) is input to the coder. The PSNR is measured for each compressed component

(Yout, Cbout, and Crout) just as we do for grayscale images. The three output components

are reassembled to form a reconstructed 24-bit color image (Imageout). This is also evaluated

8

(a) (b)

(c) (d)

Figure 2.2: (a) Lena image represented in the YCbCr color space. (b) Luminance component.

(c) Chrominance-red component. (d) Chrominance-blue component.

using PSNR for a 24-bit color image–see equations 4.4 and 4.3 [19] in Section 4.1.

2.3 The Wavelet Transform

Recent research in the image compression community has explored and developed the utility

of the wavelet transform. The wavelet transform performs an octave subband decomposition

of an image.

Introductions to wavelet theory may be found in books by Strang and Nguyen [24] and

Vetterli and Kovacevic [30]. Detailed mathematical mathematical treatments of wavelet

9

Image Image

Y Y

Cb

Cr

Cb

Cr

Coder

Coder

Coder

out

out

out

out

Figure 2.3: Block diagram of the color image compression algorithm.

Image

Analysis Synthesis

ReconstructedImage

h

h

h

g

g

g

LL

HL

LH

HH

h

h

h

g

g

g

2

2

2

2

2

22

2

2

2

2

2

Figure 2.4: The analysis and synthesis stages of a 2-D, 1-level scalar wavelet decomposition.

theory be found in books by Ingrid Daubechies [6] and Stephane Mallat [12]. The next two

sections quickly summarize the wavelet techniques employed in this thesis.

2.3.1 Scalar Wavelets

Figure 2.4 shows the analysis and synthesis stages of a 2-dimensional, 1-level scalar wavelet

decomposition. The output of the first analysis stage is the low-low (LL) subband (an

approximation of the original image); the high-low (HL) subband (the horizontal detail);

the low-high (LH) subband (the vertical details); and, the high-high (HH) subband (the

diagonal details). The synthesis stage recontructs the image. In a multiple-level scalar

wavelet decomposition, only the LL subband is iterated.

10

Figure 2.5: One level scalar wavelet (Bi 9/7) decomposition of the lighthouse image.

Figure 2.5 illustrates a one-level scalar wavelet decomposition of the lighthouse image using

the biorthogonal 9/7 filter (compare with Figure 2.6(a)).

Two scalar wavelet filters have demonstrated great success in numerous prior image com-

pression tests; the first is the biorthogonal “Bi9/7” filter [2] and the second is the recently

introduced biorthogonal “Bi22/14” filter [32]. The Bi22/14 filter has been shown to perform

at least as well, or better than, the Bi9/7 and other scalar filters in many image compression

tests [32]. We employ both of these scalar wavelet filters in our experiments.

2.3.2 Multiwavelets

Multiwavelets are similar to wavelets, but with some important differences. The image is

split into a two-element vector and preprocessed before the multiwavelet decomposition.

11

In particular, whereas wavelets have an associated scaling function φ(t) and wavelet func-

tion ψ(t), multiwavelets have two or more scaling and wavelet functions. For notational

convenience, the set of scaling functions can be written using the vector notation Φ(t) ≡[φ1(t) φ2(t) · · · φr(t)]

T , where Φ(t) is called the multiscaling function. Likewise, the mul-

tiwavelet function is defined as Ψ(t)≡ [ψ1(t) ψ2(t) · · · ψr(t)]T . The multiwavelet two-scale

equations resemble those for scalar wavelets:

Φ(t) =√2

∞Xk=−∞

Hk Φ(2t−k), (2.4)

Ψ(t) =√2

∞Xk=−∞

Gk Φ(2t−k). (2.5)

Note, however, that {Hk} and {Gk} are matrix filters, i.e. Hk and Gk are r×r matrices foreach integer k.

Figure 2.7 shows the analysis stage of a 2-dimensional, 1-level multiwavelet decomposition

for r = 2. Here, there are 16 subbands (compared to the 4 subbands in Figure 2.4). Figure

2.6 compares the one-level scalar wavelet and multiwavelet decompositions. Similar to scalar

wavelets, in a typical multiple-level multiwavelet decomposition only the LiLj (i, j = 1, 2)

subband is iterated.

In this work, both orthogonal and biorthogonal multiwavelets are tested and all are from

Figure 2.6: Comparison of one-level (a) scalar wavelet and (b) multiwavelet decompositions.

12

2

2

2

2

2

2

H

H

H

H

H

G

G

G

G

G

2

2

2

2

Image

L L1 1

L L2 1

H L1 1

H L2 1

L L1 2

L L2 2

H L1 2

H L2 2

L H1 1

L H2 1

H H1 1

H H12

L H1 2

L H2 2

H H1 2

H H2 2

Figure 2.7: The analysis stage of a 2-D, 1-level multiwavelet decomposition with r = 2.

the class of symmetric-antisymmetric multifilters with r = 2. The orthogonal symmetric-

antisymmetric multifilters used are “SA4” and “ORT4” (unbalanced versions) [29, 35]. The

biorthogonal symmetric-antisymmetric multifilters are “BSA7/5” and “BSA9/7” [8]. All

multiwavelet tests use the preprocessing and signal extension method of Xia and Jiang [35]

and the decomposition iteration technique of Martin and Bell in which only the L1L1 subband

is iterated [14].

2.4 SPIHT Quantization and Shuffling

The SPIHT1 quantizer is an embedded coder that achieves good performance by exploiting

the spatial dependencies in the subbands of the scalar wavelet decomposition [20]. The

assumptions that the SPIHT quantizer makes about spatial relations between subbands

holds for scalar wavelets, but not for multiwavelets.

1SPIHT stands for set partitioning in heirarchical trees

13

Figure 2.8: Illustration of coefficient shuffling method. Selected pixels are numbered to

indicate correspondence. (a) Before shuffling. (b) After shuffling.

Breaking the image into a two-element vector creates a decomposition as seen in Figure

2.6(b). In the scalar wavelet transform, the three highpass subbands are now 2×2 blocksof smaller subbands in the multiwavelet transform. The multiwavelet transform destroys

the spatial relationship that SPIHT presumes. To work around this limitation, we utilize a

new quantization method called shuffling that allows multiwavelet decompositions to receive

most of the benefits of using a quantizer like SPIHT [14]. The basic idea behind shuffling is

to rearrange each 2×2 block so that coefficients corresponding to the same spatial locationsare placed together. In this way the spatial relationships that SPIHT requires are recreated.

An example of shuffling for one 2×2 block is illustrated in Figure 2.8. Figure 2.9 shows howthe decomposition boundaries change with shuffling in a 2-level, 2-D, multiwavelet transform

where only the L1L1 block is iterated. The dashed lines show the structure that is removed

by shuffling. Notice that with shuffling, a 2-level multiwavelet decomposition has the same

structure as a 4-level scalar wavelet decomposition. Previous results indicate that shuffling

significantly improves the performance of multiwavelet image compression.

14

Figure 2.9: Subbands in 2-level multiwavelet decomposition after coefficient shuffling. Solid

lines denote new subband boundaries. Dashed lines denote subband boundaries that are

removed by coefficient shuffling.

2.5 JPEG2000

The JPEG2000 standard implements the discrete wavelet (scalar) transform using the LeGall

(5,3) [10] filter for lossless compression and the biorthogonal (9,7) filter [2] for lossy com-

pression. Each subband of the decomposition is entropy coded using bit-plane arithmetic

coding [3]. The JPEG2000 algorithm allows for a variety of several options including: region

of interest (ROI) coding; scalability; error resilience; and, watermarking [23]. JPEG2000

also has options to incorporate HVS sensitivities: visual frequency masking and asymmetric

compression of the chrominance spaces [3]. This thesis presents results that indicate our

wavelet-based compression techniques’ superior qualitative and quantitative performance

over JPEG2000.

Chapter 3

Human Visual System in Image

Compression

3.1 Background

Human visual system (HVS) research offers mathematical models of how humans see the

world around them. For example, models have been developed to characterize humans’

sensitivity to brightness and color [31].

The contrast sensitivity function (CSF) describes humans’ sensitivity to spatial frequencies

[31]. A model of the CSF for luminance (or grayscale) images, originally proposed by Mannos

and Sakrison [9, 15], is given by:

H(f) = 2.6(0.192 + 0.114f)e[−(0.114f)1.1] (3.1)

where spatial frequency is f = (f 2x + f

2y )

0.5 with units of cycles/degree. Note: fx and fy are

the spatial frequencies in the horizontal and vertical directions respectively. We normalize

the spatial frequency with the following relation:

15

16

f(cycles/degree) = fn(cycles/pixel) · fs(pixels/degree) (3.2)

where fn is the normalized spatial frequency with units of cycles/pixel. Since our observers

are sitting at an approximate viewing distance of 2 feet, fs is set to 64 pixels/degree. This

value for fs is equivalent to a viewing distance of four times the image height (the image

height is approximately 6 inches). In equation (3.2), since f has a range between 0 and fs/2,

fn has a range between 0 and 0.5.

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

Normalized spatial frequency

Rela

tive

sensitiv

ity

Figure 3.1: Luminance Constrast Sensitivity Function

Figure 3.1 depicts the CSF curve; it characterizes luminance sensitivity of the HVS as a

function of normalized spatial frequency. The CSF is a bandpass filter: the HVS is most

sensitive to spatial frequencies between 0.03 and 0.23, and less sensitive to very low and very

high frequencies.

CSF curves exist for chrominance stimuli as well. However, unlike luminance stimuli, hu-

mans’ sensitivity to chrominance stimuli is relatively uniform across spatial frequency [31].

The next two sections describe the methods that we developed to take advantage of the

non-uniform behavior of the luminance CSF in wavelet-based image compression.

17

3.2 CSF Masking

WaveletDecomposition

QuantizationX XImage

CSFMask

InverseCSFMask

ReconstructedImage

Figure 3.2: Block diagram of CSF masking method.

CSF masking is the name we use to refer to the method of weighting the wavelet coefficients

relative to their perceptual importance. Figure 3.2 shows how the CSF mask is applied and

subsequently inverted in the compression system. The design problem is how to transform

the CSF curve in Figure 3.1 into a mask of weights that will multiply the wavelet coefficients.

We designed and evaluated two CSF masking methods: the DWT CSF mask and the band-

average CSF mask.

3.2.1 DWT CSF Masks

The first step in creating a DWT CSF mask is to perform a wavelet decomposition of the

CSF curve. Next we determine the mask weights from this decomposition. These weights

were determined using two different methods and led to two DWT CSF masks: the 6-weight

DWT CSF mask and the 11-weight DWT CSF mask.

The 6-weight DWT CSF mask is formed in the following manner.

1. Take the DWT of the CSF curve in Figure 3.1. Figure 3.3 shows a 5-level Bi9/7 wavelet

decomposition of the CSF curve with the subspaces (W5, . . .W1, V1) explicitly labeled.

2. Label the peak of the W5 subspace as p5, the peak of the W4 subspace as p4, and so

on. The peak of the V1 subspace is denoted q1.

18

3. In this first level of the decomposition, the weights for the LH, HL, and HH subbands

are given by p5.

4. In the second level of the decomposition, the weights for the LHLL, HLLL, and HHLL

subbands are given by p4. In each subsequent level of the decomposition, continue to

weight the bandpass subbands in this manner.

5. At the final level, the weight for the lowest frequency subband (LL LL LL LL LL) is

given by q1. This method yields 6 unique weights in the mask.

6. Finally, all of the peaks are normalized so that the lowest peak is equal to one.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

1

2

3

4

5

6

7

8

W ,p5 5

W ,p4 4

W ,p3 3

W ,p2 2

W ,p1 1V ,q1 1

Normalized Frequency

Ma

gn

itu

de

Figure 3.3: 5-level Bi9/7 wavelet decomposition of CSF for 6-weight mask.

The 11-weight DWT CSF mask is formed in the following manner.

19

1. Take the DWT of the CSF curve in Figure 3.1. Figure 3.4 shows the wavelet decom-

position of the CSF curve with all of the V subspaces; the W subspaces remain the

same as shown in Figure 3.3.

2. Label the peak of the W5 subspace as p5, the peak of the W4 subspace as p4, and so

on. Label the peak of the V5 subspace as q5, the peak of the V4 subspace as q4, and so

on.

3. In the first level of the decomposition, the weight for the HH subband is given by p5.

The weights for the LH and HL subbands are given by√q5 · p5.

4. In the second level of the decomposition, the weight for HHLL subband is given by

p4. The weights for the LHLL and HLLL subbands are given by√q4 · p4. In each

subsequent level of the decomposition, continue to weight the bandpass subbands in

this manner.

5. At the final level, the weight for the lowest frequency subband (LL LL LL LL LL) is

given by q1. This method yields 11 unique weights in the mask.

6. Finally, all of the peaks are normalized so that the lowest peak is equal to one.

Figure 3.5 shows the final 11-weight DWT CSF mask with the weights shown for each

subband.

20

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

1

2

3

4

5

6

7

V ,q5 5

V4,q4

V3,q3

V2,q2

V1,q1

Normalized Frequency

Ma

gn

itu

de

Figure 3.4: The V subspaces for the 5-level Bi9/7 wavelet decomposition of the CSF.

21

4.74

7.20

3.75

5.30

3.48

3.48

3.78

3.55

3.21

2.33

1.00

Figure 3.5: DWT CSF mask with 11 unique weights.

22

3.2.2 Band-average CSF Masks

A band-average CSF mask gets its weights directly from the CSF curve in the normalized

spatial frequency domain–not in the wavelet domain like the DWT CSF masks. For a five-

level wavelet decomposition of the image, the band-average CSF mask is a 6-weight mask.

Each CSF weight is computed as the average of the CSF curve in its corresponding frequency

band. Again, all of the weights are normalized such that smallest is one. Figure 3.6 shows

the 6-weight, band-average CSF mask. Figure 3.7 shows the CSF curve with the 6 weights

superimposed.

23

1.79

2.35

2.87

3.16

2.56

1.00

Figure 3.6: Band-average CSF mask with 6 unique weights.

24

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0.5

1

1.5

2

2.5

3

Normalized spatial frequency

Rela

tive

sensitiv

ity

1.00

2.56

3.16

2.87

2.35

1.79

Figure 3.7: CSF curve shown with the 6-weight band-average CSF mask.

25

Numerous trials showed that the 6-weight band-average CSF mask subjectively outperformed

the two DWT CSF masks for all image types–despite the band-average mask’s slightly lower

PSNRs. Figure 3.8 shows that the subjective quality of the band-average mask is better than

the 11-weight DWT mask (the best of the two DWT masks). Although the band-average

mask yields a lower PSNR, it subjectively outperforms the 11-weight DWT mask (notice

the reduced ringing effects around the lighthouse edges). Only the results for the 6-weight

band-average mask will appear in Chapter 5.

(a)

(b) (c)

Figure 3.8: (a) Close-up of original lighthouse. (b) Reconstructed with 11-weight DWT CSF

mask at 0.250 bpp, PSNR=31.85 dB. (c) Reconstructed with 6-weight band-average CSF

mask at 0.250 bpp, PSNR=31.74 dB.

26

3.3 Asymmetric Color Compression

The HVS is more sensitive to the luminance (Y) space than it is to the two chrominance

spaces (blue Cb and red Cr). We compressed the chrominance spaces more than the lumi-

nance space for optimum subjective quality at a fixed bit rate in the compressed image. We

refer to this new scheme as asymmetric compression. In our asymmetric compression exper-

iments, the chrominance spaces are always compressed at a 64:1 ratio (0.125 bpp), while the

luminance space is compressed at ratios: 1:1 (8 bpp), 8:1 (1 bpp), 16:1 (0.5 bpp), and 32:1

(0.25 bpp).

Chapter 4

Performance Measures

4.1 PSNR

Peak signal-to-noise ratio (PSNR) is the standard method for quantitatively comparing a

compressed image with the original. For an 8-bit grayscale image, the peak signal value

is 255. Hence the PSNR of an M×N 8-bit grayscale image x and its reconstruction x is

calculated as [22]:

PSNR = 10 log10

Ã2552

MSE

!, (4.1)

where the mean square error (MSE) is defined as

MSE =1

MN

M−1Xm=0

N−1Xn=0

|x(m,n)− x(m,n)|2 . (4.2)

PSNR is measure in decibels (dB).

For color images, the reconstruction of all three color spaces must be considered in the PSNR

calculation. The MSE is calculated for the reconstruction of each color space. The average

of these three MSEs is used to generate the PSNR of the reconstructed RGB image (as

compared to the original 24-bit RGB image). The color PSNR equations are as follows [19]:

27

28

PSNR = 10 log2552

MSERGB

, (4.3)

MSERGB =MSEred +MSEblue +MSEgreen

3, (4.4)

where MSEred (or green or blue) is similar to equation (4.2) for each color space.

4.2 Subjective Quality

Image compression research literature typically reports performance based solely on the

quantitative PSNR metric. However, a small improvement in PSNR (less than 1 dB) does

not always correspond to an improvement in subjective quality. For this reason, we developed

a subjective quality testing procedure to qualitatively evaluate our reconstructed images.

We present our results in terms of both this qualitative measure and the quantitative PSNR

measure.

Previous research that reports the use of a subjective quality testing procedure is often

incomplete with respect to: the number of expert and non-expert observers; the number

of test images; the subjective criteria; and, the significance of the results [7, 16, 34]. We

developed a simple, comprehensive subjective quality testing procedure; it is described in

the remainder of this section.

4.2.1 Experimental Conditions

First the observer is presented with the test instructions (see Figure 4.1). The observer

is asked to “choose the image which more closely resembles the original image”. Then the

observer views a computer screen on which an original image and two reconstructed images

(A and B) are displayed (see Figure 4.2). If the observer is not able to distinguish between

29

the two images, he or she is instructed to choose “Not Distinguishable”. Then the next set

of three images is displayed.

Figure 4.1: Instructions page for subjective quality testing procedure.

The observer is presented with 22 comparisons in all. He or she sits at a viewing distance of

approximately 2 feet from the screen.

The specifications of the monitor that was used in these tests are as follows:

• Model: Dell M990;

• Screen dimensions: 19” (48.3 cm) flat and square (18.0” viewable image size);

• Phosphor Dot pitch: 0.26 mm;

• Deflection angle: 100 degrees;

30

Figure 4.2: Sample image comparison as presented in the subjective quality testing proce-

dure.

• Faceplate coating: Anti-glare, anti-static;

• Resolution: 1024×768; and,

• Refresh rate: 75 Hz.

Each observer experienced the same lighting and viewing conditions.

4.2.2 Goals of Subjective Experiments

The goals of these subjective image comparisons is to determine the effect of the following

on compression performance: compression with CSF masking for grayscale and color images;

asymmetric compression for color images; and, asymmetric compression with CSF masking

31

for color images. It is not feasible to present a comparison for every reconstructed image;

thus, each comparison presented to the observer characterizes the behavior of one particular

compression feature for a particular image type. For example, to capture subjective data

for how CSF masking affects the compression of natural, low frequency, color images, the

Lena image–compressed with and without CSF masking–is used as the comparison. The

subjective test images (22 in all) are a comprehensive set of natural, synthetic, low frequency,

high frequency, grayscale, and color images. The original test images are shown in Appendix

A.

4.2.3 Expert vs. Non-Expert Analysis

The 4 expert observers are members of the Digital Signal Processing and Communications

Laboratory at Virginia Tech. We know to look for edge detail, ringing artifacts, block

artifacts, consistency in smooth regions, and general aesthetic quality.

The 10 non-expert observers are unbiased. In most cases they have never seen the original

test images. They are given no prior information or instruction aside from those shown in

Figure 4.1.

4.3 Correlation of Quantitative and Qualitative Mea-

sures

We developed a new correlation method for determining the relationship between the quan-

titative and qualitative data. The correlation of the quantitative (PSNR) and qualitative

metrics is calculated in the following manner. For each of the 22 comparisons, three “answer

sheets” are generated.

• The first answer sheet is for PSNR. If the “A” compressed image has a higher PSNR

32

than the “B” compressed image, then “A” receives a “1” and “B” receives a “-1”. If

the two PSNRs differ by less than 0.1 dB, both images are given a “0”.

• The second answer sheet is for expert subjective quality. The compressed image thatis judged subjectively superior by the expert creator is given a mark of “1”; the other

image receives a “-1”. If the expert creator judges that the two images are not subjec-

tively distinguishable, both images are given a mark of “0”. Note: the expert creator

always corresponds to HVS on except at the highest bit rate (2.75 bpp).

• The third answer sheet is for subjective quality as judged by the observer. The com-pressed image that is judged subjectively superior by the observer is given a mark of

“1”; the other image receives a “-1”. If the observer judges that the two images are

not subjectively distinguishable, both images are given a mark of “0”.

Once the answer sheets have been tabulated, the following correlations are calculated for

each trial: correlation of all observers and PSNR; correlation of expert observers and PSNR;

and, correlation of non-expert observers and PSNR. The correlation of observers and PSNR

tells us about the relationship between subjective quality and PSNR.

Also calculated for each trial: correlation of all observers and expert creator; correlation

of expert observers and expert creator; and, correlation of non-expert observers and expert

creator. The correlation of observers and expert creator tells us about the relationship

between subjective quality and HVS on.

In addition we calculate the same correlations for all grayscale images, for all color images,

all trials together, and other subsets as explained in Section 5.5. In this way we can show

whether and how strongly the quantitative and qualitative results compare.

We measure correlation using the correlation coefficient statistic; it ranges from -1.0 to +1.0.

The closer the correlation coefficient is to +1 (-1), the more closely the data is related by a

linear relationship with a positive (negative) slope. A correlation coefficient close to 0 implies

no significant linear relationship between the quantitative and qualitative results. If the

33

correlation coefficient is close to +1, then PSNR increases as subjective quality improves. If

the correlation coefficient is close to -1, then PSNR decreases as subjective quality improves..

It is important to note that a correlation coefficient measures similarity; it does not indicate

a cause and effect relationship between the quantitative and qualitative results.

Before the subjective data was examined, we categorized the correlation coefficients (ρ) in

the following manner:

• −0.25 < ρ < 0.25 ≡ “no correlation”;

• 0.25 < ρ < 0.5 ≡ “mild positive correlation”;

• 0.5 < ρ < 1 ≡ “strong positive correlation”;

• −0.5 < ρ < −0.25 ≡ “mild negative correlation”; and,

• −1 < ρ < −0.5 ≡ “strong negative correlation”.

A recent survey of quality measurements indicates that the widely-used PSNR measure often

does not reflect spurious artifacts and does not always correlate with visual error perception

[7]. Our results show that this is true in some instances. However in most cases with our

new HVS method “on”, we observe a strong positive correlation between the qualitative and

quantitative results.

4.4 Results of Previous Related Research

Several other methods to incorporate the sensitivities of the HVS into a wavelet-based com-

pression scheme have been reported in previous research. Nadenau et al. introduced an HVS

scheme that used the entire W subspaces of the CSF DWT decomposition as filters [16]. In

this way, local frequency variation was captured within a subband. Similar to our research,

this work presented a wavelet-based (Bi9/7 scalar wavelet) scheme for the compression of

34

color images. However, this work differs from our research in several ways. First, instead

of using the YCbCr color model, an opponent color space model was used. Second, the

subjective testing procedure used a different comparison. This subjective testing procedure

asked the observer to compare a set of images compressed at several different bit rates to the

same image compressed with JPEG. Third, only 3 test images and 7 observers were used.

Furthermore, there was no distinction between expert and non-expert observers. It is also

important to note that the subjective evaluations were made using printed images (and not

on a computer screen). The results of this work indicated compression ratio improvements

from 13 to 49 percent over SPIHT (depending on image type).

The same researchers reintroduced this CSF filtering scheme along with a CSF masking

scheme [17]. However, only results for the CSF filtering scheme were reported in this paper.

Here, the CSF filtering scheme was added to JPEG2000 and the results were compared

to plain JPEG2000. Similar to our research, this work presented a wavelet-based (Bi9/7

scalar wavelet) scheme for the compression of color images. However, only 3 test images

and 6 observers were used in their subjective testing procedure. Images that were not

distinguishable from the original were classified as “perfect” and images that “would be

judged as lossless if no original were given” were classified as “good”. Again there was no

distinction between expert and non-expert observers and the evaluations were made using

printed images. The results indicated compression ratio improvements from 28 to 29 percent

over plain JPEG2000. Futhermore, CSF masking was reported to be computationally simpler

and more efficient than CSF filtering.

Results have also been published for a CSF masking scheme that is based on image content

[18]. Similar to our research, this scheme was wavelet-based (Bi9/7 scalar wavelet) and

categorized test images by type (predominantly smooth, containing mostly edge information,

and predominantly detailed). In this work, the grayscale images were segmented into smooth,

edge, and detail regions; trial and error determined mask weights for each of the these three

region types. However, this method for determining the mask weights was not a direct

incorporation of the CSF. The results indicated a decrease in PSNR when their CSF mask

35

was applied and their examples showed perceptual improvement only at very low bit rates.

They did not conduct a subjective testing procedure.

Chapter 5

Experimental Results

5.1 Implementation

The experiments presented in this thesis compare wavelet-based image compression methods

with and without our new HVS model. The quantitative comparison is made using PSNR

and the qualitative comparison is made using the judgements of expert and non-expert ob-

servers. We present a comprehensive correlation analysis of the quantitative and qualitative

results. In addition, we compare the quantitative and qualitative results to JPEG2000–the

latest version of the international compression standard [11]. Although we are given no ex-

plicit explanation, we suspect that the version of JPEG2000 used for our results employs

asymmetric compression at a ratio of 1:2:2 (Y:Cb:Cr) with no visual frequency masking.

To simplify the explanations of the results, if CSF masking and asymmetric compression are

both on, then the trial will be described as “HVS on”. If CSF masking and asymmetric com-

pression are both off, then the example will be described as “HVS off”. Otherwise, the exam-

ple will be described explicitly as either “CSF off/Asymmetric on” or “CSF on/Asymmetric

off”.

The following summarizes the varying factors in the experiments.

36

37

5.1.1 Grayscale

• We compress the 8-bit grayscale images with and without CSF masking.

• We compress the grayscale images at the following compression ratios: 8:1 (1.000 bpp);16:1 (0.500 bpp); 32:1 (0.250 bpp); and, 64:1 (0.125 bpp) (all of the color images are

24-bit).

5.1.2 Color

• We compress the 8-bit luminance and 8-bit chrominance spaces at the same bit ratewithout CSF masking. This is described as HVS off.

• We compress the luminance and chrominace spaces asymmetrically without CSF mask-ing in the following manner:

Y (1:1), Cb (64:1), Cr (64:1) for an overall compression ratio of 2.91:1 (2.750 bpp)




This will be described as CSF off/Asymmetric on.

• We compress without asymmetric compression and with CSF masking. This is de-scribed as CSF on/Asymmetric off.

• We compress with asymmetric compression and with CSF masking. This is describedas HVS on.

The compression of the grayscale and color images is performed with the scalar wavelets and

multiwavelets listed in Chapter 2.

38

5.1.3 Shuffling for the Multiwavelet Transform

Previous image compression research has shown that shuffling almost always improves PSNR

performance for grayscale images [13]. Our results for grayscale and color images are consis-

tent with these results; in our trials, shuffling introduces an improvement of 0.2 to 0.6 dB.

The only exceptions are the Barbara and Ruler images. For these two images, compression

without shuffling performs slightly better in terms of PSNR. Non-shuffling results are shown

for Barbara and Ruler; for all other images only the shuffling results are shown.

5.2 Results for Natural Grayscale Images

5.2.1 Results for Lena

Lena, one of the most common test images in compression research, consists primarily of

low frequency content. Compression with CSF masking (i.e. HVS on) always yields a lower

PSNR than compression without CSF masking (i.e. HVS off ) for all scalar wavelets and

multiwavelets at all bit rates. HVS on lowers PSNR by approximately 0.2 to 0.3 dB for scalar

wavelets and approximately 0.8 dB for multiwavelets. Tables 5.2 and 5.3 list the complete

PSNR results for Lena. The Bi22/14 scalar wavelet depicts the best PSNR performance at

all bit rates.

Although judgment varied for the non-expert observers, all expert observers judged HVS

on to be a subjective improvement to the Lena image compressed with the Bi22/14 scalar

wavelet at 0.250 bpp. Figure 5.1 shows this example. HVS on removed the ringing artifacts

around the edges in (c) that are present in (b). This is counter to the PSNR result for this

example. HVS off yields a PSNR improvement over HVS on by 0.33 dB.

Table 5.1 shows the correlation coefficients for the same trial. The table depicts the fol-

lowing: a mild negative correlation between all observers and PSNR (-0.36); no negative

39

Table 5.1: Correlation coefficients for grayscale Lena.

Correlation All Observers Non-experts Experts

PSNR -0.36 -0.10 -1

HVS on 0.36 0.10 1

Table 5.2: Scalar wavelet PSNR (in dB) results for grayscale Lena.

Bi9/7 SW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 39.83 36.71 33.59 30.54

CSF on 38.77 35.60 33.19 30.58

Bi22/14 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 39.95 36.88 33.80 30.81

CSF on 38.73 35.73 33.47 30.68

correlation between non-expert observers and PSNR (-0.10); a strong negative correlation

between expert observers and PSNR (-1); no correlation between all observers and HVS

on (0.36); no correlation between non-expert observers and HVS on; and, a strong positive

correlation between the expert observers and HVS on (1).

40

Table 5.3: Multiwavelet PSNR (in dB) results for grayscale Lena with shuffling.

SA4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 39.06 35.39 31.97 29.08

CSF on 38.12 34.81 31.69 28.74

ORT4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 39.09 35.43 32.01 29.10

CSF on 38.15 34.85 31.73 28.75

BSA 9/7 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 38.49 35.55 32.62 29.81

CSF on 37.40 34.73 32.31 29.59


CSF off 39.08 35.43 31.96 28.95

CSF on 38.14 34.92 31.77 28.79

41

(a)

(b) (c)

Figure 5.1: (a) Original Lena. (b) Reconstruction compressed with Bi22/14 scalar wavelet

without CSF masking at 0.250 bpp, PSNR=33.80 dB. (c) Reconstruction compressed with

Bi22/14 scalar wavelet with CSF masking at 0.250 bpp, PSNR=33.47 dB.

42

Table 5.4: Correlation coefficients for grayscale Lighthouse.


PSNR -0.43 -0.20 -1

HVS on 0.43 0.20 1

Table 5.5: Scalar wavelet PSNR results (in dB) for grayscale Lighthouse.

Bi9/7 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 33.42 29.80 26.87 24.58

CSF on 32.16 28.32 25.63 24.46

Bi22/14 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 33.52 29.84 26.91 24.63

CSF on 31.98 28.12 25.80 24.58

5.2.2 Results for Lighthouse

In terms of PSNR, the Bi22/14 scalar wavelet performs best for the lighthouse image, which

has a mix of low and high frequency content. However, this best scalar wavelet outperforms

the best multiwavelet (ORT4) by less than 0.5 dB. Tables 5.5 and 5.6 depict the complete

PSNR results for the lighthouse image.

Although non-expert observers did not consistently agree, expert observers judged that HVS

on improves subjective quality in the lighthouse image at 0.250 bpp. Figure 5.2 shows this

example. Although blurring and ringing artifacts are reduced in the ground and along the

edges of the lighthouse, in post-test interviews non-expert observers who chose image (b)

over image (c) focused on the fence region in the image where HVS on introduces smoothing.

Table 5.4 shows the correlation coefficients for the same trial. The table depicts the following:

a mild negative correlation between all observers and PSNR (-0.43); and, a mild positive

correlation between all observers and HVS on (0.43).

43

Table 5.6: Multiwavelet PSNR (in dB) results for grayscale Lighthouse with shuffling.


CSF off 32.92 29.48 26.84 24.33

CSF on 32.05 28.60 25.93 24.20


CSF off 32.93 29.48 26.85 24.34

CSF on 32.06 28.61 25.94 24.21


CSF off 32.47 29.29 26.76 24.39

CSF on 31.72 28.39 25.86 24.29


CSF off 32.88 29.48 26.84 24.37

CSF on 31.99 28.56 25.92 24.30

44

(a)

(b) (c)

Figure 5.2: (a) Original Lighthouse. (b) Reconstruction compressed with Bi22/14 scalar

wavelet without CSF masking at 0.250 bpp, PSNR=26.91 dB. (c) Reconstruction compressed

with Bi22/14 scalar wavelet with CSF masking at 0.250 bpp, PSNR=25.80 dB.

45

Table 5.7: Correlation coefficients for grayscale Barbara.


PSNR -0.64 -0.50 -1

HVS on 0.64 0.50 1

Table 5.8: Scalar wavelet PSNR results (in dB) for grayscale Barbara.

Bi9/7 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 35.75 30.82 27.04 24.37

CSF on 34.46 28.98 25.40 24.01

Bi22/14 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 36.22 31.24 27.35 24.40

CSF on 34.89 29.20 25.46 24.14

5.2.3 Results for Barbara

Barbara is a popular natural test image because of the high frequency pattern in her pants

alongside the smooth regions in the face and background. Barbara is the only grayscale

image in which shuffling does not introduce an improvement in terms of PSNR. Tables 5.8,

5.9, 5.10 list the complete PSNR results for Barbara.

Subjectively, all expert observers and 7 out of 10 non-expert observers confirmed the fact that

HVS on introduces perceptual improvement for this high frequency natural image. Table

5.7 shows the correlation coefficients for the Barbara image (Bi22/14 at 0.250 bpp). The

table depicts the following: a strong negative correlation between all observers and PSNR

(-0.64); and, a strong positive correlation between all observers and HVS on (0.64).

46

Table 5.9: Multiwavelet PSNR (in dB) results for grayscale Barbara with shuffling.


CSF off 34.59 29.50 26.27 23.84

CSF on 33.32 28.65 25.34 23.54


CSF off 34.65 29.55 26.29 23.83

CSF on 33.38 28.69 25.36 23.54


CSF off 34.67 30.01 26.60 24.05

CSF on 33.34 28.99 25.72 23.84


CSF off 34.91 29.74 26.42 23.74

CSF on 33.55 28.89 25.49 23.60

Table 5.10: Multiwavelet PSNR (in dB) results for grayscale Barbara without shuffling.

SA4 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 34.60 29.58 26.30 23.82

CSF on 33.32 28.58 25.24 23.46

ORT4 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 34.66 29.64 26.33 23.86

CSF on 33.36 28.62 25.26 23.46

BSA 9/7 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 34.71 30.25 26.80 24.31

CSF on 33.30 28.92 25.67 23.78


CSF off 34.92 29.85 26.48 23.85

CSF on 33.53 28.67 25.40 23.48

47

Table 5.11: Correlation coefficients for grayscale Ruler.


PSNR -0.43 -0.60 0

HVS on 0.43 0.60 0

Table 5.12: Scalar wavelet PSNR results (in dB) for grayscale Ruler.

Bi9/7 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 23.79 16.31 12.99 11.78

CSF on 21.77 15.07 13.72 12.10

Bi22/14 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 24.26 17.72 12.89 11.06

CSF on 23.28 13.74 12.99 11.51

5.2.4 Results for Ruler

Ruler is the synthetic image for the grayscale test set (see Figure 5.3(a)). Ruler is different

from the other grayscale images because multiwavelets perform better than scalar wavelets

at 2.75, 0.417, and 0.250 bpp. The Bi9/7 performs best in terms of PSNR at 0.250 and 0.167

bpp. The difference between scalar wavelets and multiwavelets at the three higher bit rates

is significant–the disparity ranges from 1.3 to 3.9 dB. Tables 5.12, 5.13, and 5.14 list the

complete PSNR results for ruler.

Figure 5.3 shows an example of HVS on for the ruler image. Expert observers split on

the subjective improvement introduced by HVS on. Some saw that the blurring in (b) was

removed by HVS on in (c). Table 5.11 shows the correlation coefficients for the same trial.

The table depicts the following: a mild negative correlation between all observers and PSNR

(-0.43); and, a mild positive correlation between all observers and HVS on (0.43).

48

Table 5.13: Multiwavelet PSNR (in dB) results for grayscale Ruler with shuffling.


CSF off 28.13 18.03 13.32 11.10

CSF on 26.47 16.12 12.90 11.30


CSF off 28.06 18.02 13.33 11.10

CSF on 26.44 16.13 12.90 11.29


CSF off 25.55 16.92 11.97 10.56

CSF on 25.15 16.26 12.73 11.37


CSF off 26.70 18.64 13.20 11.10

CSF on 26.01 17.08 13.05 11.33

Table 5.14: Multiwavelet PSNR (in dB) results for grayscale Ruler without shuffling.

SA4 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 26.64 18.02 13.45 10.89

CSF on 26.01 16.13 12.89 11.21

ORT4 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp

CSF off 26.60 18.02 13.46 10.89

CSF on 25.98 16.13 12.90 11.20


CSF off 26.62 19.39 15.03 11.59

CSF on 25.16 16.40 12.70 11.32


CSF off 26.31 18.29 13.26 11.00

CSF on 25.57 17.07 13.04 11.33

49

(a)

(b) (c)

Figure 5.3: (a) Original Ruler. (b) Reconstruction compressed with BSA9/7 multiwavelet

(without shuffling) without CSF masking at 1.000 bpp, PSNR=26.62 dB. (c) Reconstruction

compressed with BSA9/7 multiwavelet (without shuffling) with CSF masking at 1.000 bpp,

PSNR=25.16 dB.

50

5.3 Results for Natural Color Images

5.3.1 Results for Lena

In terms of PSNR, the Bi22/14 scalar wavelet is consistently superior to the Bi9/7 and all

multiwavelets across all four bit rates. However, the Bi22/14 scalar wavelet quantitatively

outperforms the best multiwavelet only slightly; the difference ranges from 0.01 to 0.5 dB.

Notice in Table 5.16, at 2.75 bpp, CSF on/Asymmetric off (PSNR=42.44) outperforms CSF

off/Asymmetric on (PSNR=36.23) by 6.21 dB for the Bi22/14 scalar wavelet. However, at

the three lower bit rates, CSF off/Asymmetric on outperforms CSF on/Asymmetric off by

more than 1 dB. This trend is also seen when comparing HVS off to HVS on. At 2.75 bpp,

HVS off exceeds HVS on by 6.32 dB. At the three lower bits rates, HVS on surpasses HVS

off by 0.44 dB (0.417 bpp), 1.03 dB (0.250 bpp), and 1.05 dB (0.167 bpp). We see this flip

in PSNR performance for all images. The effect of asymmetric compression dominates at

0.417, 0.250, and 0.167 bpp. Tables 5.16 and 5.17 give the complete PSNR results for Lena.

Qualitatively, observers confirmed that HVS on improves image quality for Lena. Figure

5.4(b) is compressed with HVS off and (c) is compressed with HVS on. The ringing artifacts

are absent in (c) resulting in smoother regions in the face and cleaner edges throughout. All

14 observers, both expert and non-expert, judged that the Lena image compressed with HVS

on is subjectively superior to the Lena image compressed with HVS off.

Table 5.15 shows the correlation coefficients for the same trial. The table depicts the follow-

ing: a strong positive correlation between all observers and PSNR (1); and, a strong positive

correlation between all observers and HVS on (1).

51

Table 5.15: Correlation coefficients for color Lena.


PSNR 1 1 1

HVS on 1 1 1

Table 5.16: Scalar wavelet PSNR (in dB) results for color Lena.


CSF off, Asymmetric off 42.58 34.10 32.06 30.81

CSF off, Asymmetric on 36.10 34.70 33.61 31.92

CSF on, Asymmetric off 42.48 33.48 31.85 30.59

CSF on, Asymmetric on 36.20 34.60 33.13 31.76






52

(a)

(b) (c)

Figure 5.4: (a) Original Lena. (b) Reconstruction compressed with Bi22/14 scalar wavelet

without HVS at 0.167 bpp, PSNR=30.92 dB. (c) Reconstruction compressed with Bi22/14

scalar wavelet with HVS at 0.167 bpp, PSNR=31.97 dB.

53

Table 5.17: Multiwavelet PSNR (in dB) results for color Lena with shuffling.





















54

Table 5.18: Correlation coefficients for color Mandrill.


PSNR 0.50 0.30 1

HVS on 0.50 0.30 1

5.3.2 Results for Mandrill

Mandrill is a natural image with significant high frequency content. As with most test

images, the Bi22/14 scalar wavelet gives the best PSNR performance at all bit rates. The

Bi22/14 outperforms the best multiwavelets by 0.1 to 0.3 dB. Again we see CSF masking

dominate at the highest bit rate and asymmetric compression dominate at the three lower

bit rates. At 2.75 bpp, HVS off outperforms HVS on by 6 to 8 dB (depending on the wavelet

or multiwavelet filter). At the other three bit rates, HVS on outperforms HVS off by 0.01

to 1.5 dB. Tables 5.19 and 5.20 give the complete PSNR results for mandrill.

The subjective quality results show that HVS on improves performance. Figure 5.5 (b) and

(c) shows the Mandrill image compressed with HVS off and HVS on at a compression ratio

of 19.2:1 (0.417 bpp). The blurring that occurs in the nose region of (b) is not present in (c).

The expert observers all agreed that HVS on shows an improvement. In post-test interviews,

non-experts reported that they did not focus on the nose and therefore found it difficult to

sense a change in the high frequency patterns that persist in the rest of the image.

Table 5.18 shows the correlation coefficients for the same trial. The table depicts the fol-

lowing: a strong positive correlation between all observers and PSNR (0.5); and, a strong

positive correlation between all observers and HVS on (0.5).

55

Table 5.19: Scalar wavelet PSNR (in dB) results for color Mandrill.











Table 5.20: Multiwavelet PSNR (in dB) results for color Mandrill with shuffling.





















56

(a)

(b) (c)

Figure 5.5: (a) Original Mandrill. (b) Reconstruction compressed with Bi9/7 scalar wavelet



57

Table 5.21: Correlation coefficients for color Lighthouse.


PSNR 1 1 1

HVS on 1 1 1

5.3.3 Results for Lighthouse

Lighthouse represents a mix of low and high frequency content. Although the Bi22/14 scalar

wavelet continues to outperform all other methods in terms of PSNR, the disparity between

HVS on and HVS off is smaller at 2.75 bpp. With Lena and Mandrill, we observed HVS

off outperforming HVS on by several dB at this highest bit rate. With lighthouse, the

difference between the two is only 0.67 dB for the Bi22/14 scalar wavelet. At 0.417 and

0.250 bpp, HVS on outperforms HVS off by 3.86 dB and 2.13 dB respectively for the same

filter. At 0.167, the difference is only 0.12 dB. At the two middle bit rates (0.417 and

0.250), we see asymmetric compression dominating more than usual. This is interesting

because qualitatively, the effect of CSF on/Asymmetric off in the lighthouse image is more

distinguishable than we see in the other test images. Tables 5.22 and 5.23 give the complete

PSNR results for lighthouse.

As stated above, the effect of CSF on/Asymmetric off is more apparent in the lighthouse

image than in any other test image. Figure 5.6 shows an example of CSF masking at 0.167

bpp. Image (c) (CSF on/Asymmetric off ) shows less blurring in the ground area and along

the edges of the lighthouse. All expert observers and 8 out of 10 non-expert observers agreed,

choosing (c) over (b) in the subjective quality testing procedure.

Table 5.21 shows the correlation coefficients for same trial. The table depicts the following:

a strong positive correlation between all observers and PSNR (1); and, a strong positive


58

Table 5.22: Scalar wavelet PSNR (in dB) results for color Lighthouse.











Table 5.23: Multiwavelet PSNR (in dB) results for color Lighthouse with shuffling.





















59

(a)

(b) (c)

Figure 5.6: (a) Original Lighthouse. (b) Reconstruction compressed with Bi22/14 scalar

wavelet CSF off/Asymmetric off at 0.167 bpp, PSNR=26.18 dB. (c) Reconstruction com-

pressed with Bi22/14 scalar wavelet CSF on/Asymmetric off at 0.167 bpp, PSNR=25.66

dB.

60

Table 5.24: Correlation coefficients for color Helen.


PSNR 1 1 1

HVS on 1 1 1

5.3.4 Results for Helen

The Helen image is similar to Lena in that it has mostly low frequency content in the face with

some high frequency content in the hat. In the Helen image, we see the characteristic PSNR

results seen in the other natural test images. CSF masking dominates at the highest bit

rate (2.75 bpp). At this bit rate CSF on/Asymmetric off outperforms CSF off/Asymmetric

on by 2 to 4 dB depending on wavelet method. We see this behavior switch at the three

lower bit rates again; HVS on is superior to HVS off by 2.28 dB (0.417 bpp), 1.45 dB(0.250

bpp), and 0.7 dB (0.167 bpp) for the Bi22/14. Tables 5.25 and 5.26 give the complete PSNR

results for Helen.

Figure 5.7 shows how the application of HVS on subjectively improves multiwavelet com-

pression on the Helen image. In (b) (HVS off ), the blocking artifacts characteristic of the

multiwavelet transform are present. HVS on (c) shows that the blocking artifacts are miti-

gated and the subjective quality improves. All 14 expert and non-expert observers saw the

same results and chose (c) over (b) in the subjective quality testing procedure.




61

Table 5.25: Scalar wavelet PSNR (in dB) results for color Helen.











Table 5.26: Multiwavelet PSNR (in dB) results for color Helen with shuffling.





















62

(a)

(b) (c)

Figure 5.7: (a) Original Helen. (b) Reconstruction compressed with BSA7/5 multiwavelet

without HVS at 0.250 bpp, PSNR=32.99 dB. (c) Reconstruction compressed with BSA7/5

multiwavelet with HVS at 0.250 bpp, PSNR=34.68 dB.

63

Table 5.27: Correlation coefficients for color Owl.


PSNR 1 1 1

HVS on 1 1 1

5.3.5 Results for Owl

Owl is a natural image that–like mandrill–is comprised of primarily high frequency content.

Owl is like lighthouse in that there is little quantitative disparity between HVS on and HVS

off at 2.75 bpp. In fact, HVS on outperforms HVS off for both scalar wavelets and the BSA

multifilters by a nominal amount. The BSA9/7 filter is the best among the multiwavelets at

2.75, 0.25, and 0.167 bpp. At 0.417 bpp, a rare exception occurs; the BSA7/5 multiwavelet

without shuffling performs best in terms of PSNR among all multiwavelets. The Bi22/14

scalar wavelet still outperforms all methods at all bit rates. Tables 5.28 and 5.29 give the

complete PSNR results for Owl.

Figure 5.8 illustrates the qualitative effect of HVS on on the owl image compressed with the

SA4 multiwavelet to 0.417 bpp. The blocking artifacts in (b) are removed in (c). All expert

and non-expert observers confirmed this judgement in the subjective quality test.




64

Table 5.28: Scalar wavelet PSNR (in dB) results for color Owl.











Table 5.29: Multiwavelet PSNR (in dB) results for color Owl with shuffling.





















65

(a)

(b) (c)

Figure 5.8: (a) Original Owl. (b) Reconstruction compressed with SA4 multiwavelet without

HVS at 0.417 bpp, PSNR=25.87 dB. (c) Reconstruction compressed with SA4 multiwavelet

with HVS at 0.417 bpp, PSNR=29.68 dB.

66

5.4 Results for Synthetic Color Images

5.4.1 Results for DNA

DNA is a synthetic image with large areas of uniformity separated by sharp edges; it yields

some interesting results. At 2.75 bpp, HVS off outperforms HVS on by 13.32 dB for the

Bi22/14 scalar wavelet. With the natural test images–in all cases–at 0.417 bpp (and lower

rates) the results shifted and HVS on outperformed HVS off. With DNA, at 0.417 bpp HVS

off continues to outperform HVS on by 1.59 dB (Bi22/14). At 0.250 bpp the shift occurs

with HVS on outperforming HVS off by 0.48 dB, and by 0.74 dB at 0.167 bpp.

The quantitative results for the multiwavelets are varied. At all bit rates shuffling introduces

improvement in terms of PSNR. At 2.75 bpp, the BSA7/5 is superior. At 0.417 bpp, the

SA4 is the best multiwavelet. At 0.250 and 0.167 bpp, the ORT4 outperforms the other

multiwavelet filters. Tables 5.31 and 5.32 give the complete PSNR results for DNA.

As stated above, at 2.75 bpp, HVS off outperforms HVS on by 13.32 dB. However, this

significant difference in PSNR is subjectively not distinguishable at these high PSNRs; Figure

5.9 shows this comparison. HVS on does introduce subjective improvement at the lower bit

rates. Figure 5.10 shows the DNA image compressed with HVS on and HVS off at 0.167

bpp. In (c), HVS on removes the blurring and ringing artifacts that persist in (b). This

judgement is backed by the opinion of all expert and non-expert observers.

Table 5.30 shows the correlation coefficients for same trial shown in Figure 5.10. The table

depicts the following: a strong positive correlation between all observers and PSNR (1); and,

a strong positive correlation between all observers and HVS on (1).

67

Table 5.30: Correlation coefficients for color DNA.


PSNR 1 1 1

HVS on 1 1 1

Table 5.31: Scalar wavelet PSNR (in dB) results for color DNA.











68

(a)

(b) (c)

Figure 5.9: (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet



69

(a)

(b) (c)

Figure 5.10: (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet



70

Table 5.32: Multiwavelet PSNR (in dB) results for color DNA with shuffling.





















71

Table 5.33: Correlation coefficients for color Satellite.


PSNR 0.79 0.70 1

HVS on 0.79 0.70 1

5.4.2 Results for Satellite

Satellite is a synthetic image that is comprised of consistent high frequency content through-

out the image. With the satellite image, the PSNR results resemble the results for a typical

natural image. The Bi22/14 is the best method among scalar wavelets and multiwavelets.

However, the Bi22/14 surpasses the best multiwavelet (BSA7/5) by less than 0.5 dB. CSF

masking dominates asymmetric compression at 2.75 bpp; this flips at 0.417 bpp (and lower

bit rates) for all wavelet methods. Tables 5.34 and 5.35 give the complete PSNR results for

the satellite image.

Figure 5.11 shows the qualitative effect of HVS on on the satellite image. As with many of

the test images, severe ringing and blocking artifacts appear in image (b). In (c) (HVS on)

these artifacts are removed. All expert observers reported the same conclusion. Seven out

of ten non-expert observers reported the same conclusion, while three non-experts were not

able to distinguish between (b) and (c).


a strong positive correlation between all observers and PSNR (0.79); and, a strong positive

correlation between all observers and HVS on (0.79).

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Table 5.34: Scalar wavelet PSNR (in dB) results for color Satellite.











Table 5.35: Multiwavelet PSNR (in dB) results for color Satellite with shuffling.





















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(a)

(b) (c)

Figure 5.11: (a) Original Satellite. (b) Reconstruction compressed with BSA7/5 multiwavelet


multiwavelet without HVS at 0.250 bpp, PSNR=24.11 dB.

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Table 5.36: Correlation coefficients for color Map.


PSNR 1 1 1

HVS on 1 1 1

Table 5.37: Scalar wavelet PSNR (in dB) results for color Map.











5.4.3 Results for Map

Map is a synthetic image with large areas of uniform color as well as high frequency content

in the edges and textured regions. With the Bi22/14 scalar wavelet, HVS on is superior at

all bit rates. This is a departure from the results we have seen for most images where HVS

off dominated HVS on at 2.75 bpp. Like the owl image, at 2.75 bpp HVS on surpasses HVS

off for several wavelets including the Bi22/12 scalar wavelet and the BSA9/7 multiwavelet.

Tables 5.37 and 5.38 give the complete PSNR results for the map image.

The map image is compressed with HVS on and HVS off in Figure 5.12. Like the previous

examples, HVS on delivers superior subjective quality. Table 5.36 shows the correlation

coefficients for same trial. The table depicts the following: a strong positive correlation

between all observers and PSNR (1); and, a strong positive correlation between all observers

and HVS on (1).

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Table 5.38: Multiwavelet PSNR (in dB) results for color Map with shuffling.





















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(a)

(b) (c)

Figure 5.12: (a) Original Map. (b) Reconstruction compressed with BSA7/5 multiwavelet


multiwavelet without HVS at 0.417 bpp, PSNR=27.65 dB.

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Table 5.39: Correlation coefficients for color Metal.


PSNR 0.93 0.90 1

HVS on 0.93 0.90 1

Table 5.40: Scalar wavelet PSNR (in dB) results for color Metal.











5.4.4 Results for Metal

The metal image is computer-generated with high frequency content that characterizes a

smooth, metallic texture in the objects (see Appendix A). The quantitative results are similar

to what we have observed for the typical examples. Tables 5.40 and 5.41 give the complete

PSNR results for the metal image.

Subjectively, we also see typical behavior. Table 5.39 shows the correlation coefficients for

the metal image compressed with the ORT4 multiwavelet at 0.167 bpp. Observers compared

HVS on to HVS off. The table depicts the following: a strong positive correlation between

all observers and PSNR (0.93); and, a strong positive correlation between all observers and

HVS on (0.93).

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Table 5.41: Multiwavelet PSNR (in dB) results for color Metal with shuffling.





















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Table 5.42: Scalar wavelet PSNR (in dB) results for Color16.











5.4.5 Results for Color16

We created the color16 test image to observe the behavior of our new methods on an atypical

synthetic image. However, at every bit rate used in this thesis, no subjective change can be

observed in the reconstructed image–all of the PSNRs are high (> 40 dB). The quantitative

results are also a departure from what we have observed for the other test images. Since the

image contains areas of such large uniformity, it is easily compressed and–for this reason–

the PSNRs are unusually high. In a few cases, the PSNR does not change with a lower bit

rate. Tables 5.42 and 5.43 give the complete PSNR results for the color16 image. Color16

was not used in the subjective quality testing procedure, therefore there is no correlation

data.

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Table 5.43: Multiwavelet PSNR (in dB) results for Color16 with shuffling.





















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5.5 Correlation Results for Image Groups

Table 5.44 lists the correlation of PSNR with all observers, non-expert observers, and expert

observers for different image groups. For grayscale images, our results show that although

CSF masking introduces a qualitative improvement as judged by expert and non-expert

observers, CSF masking lowers PSNR in the reconstructed image. The answer sheets of the

expert observers correlate with PSNR with a strong negative correlation coefficient of -0.75.

The non-expert observers agree. Their answer sheets also negatively correlate with PSNR,

yielding a mild negative correlation coefficient of -0.34. The answer sheets of all observers

yield a mild negative correlation of -0.47 for grayscale images.

For color images, the results conclude that HVS on delivers superior image quality compared

to HVS off. HVS on also introduces a significant improvement in terms of PSNR at the

three lower bit rates. The judgments of expert and non-expert observers both yield a strong

positive correlation with the PSNR (0.77 and 0.73 respectively). At the highest bit rate

(2.75 bpp), the effect of HVS on is not distinguishable.

Grouping all images in the test, non-expert observers correlated with PSNR with a strong

positive correlation of 0.61. Expert observers–although slightly less–also yielded a strong

correlation of 0.51.

5.6 Comparison with JPEG2000

A benchmark for our new compression techniques is the latest version of the international

image compression standard–JPEG2000. Quantitative and qualitative results show that

HVS on–used with the Bi22/14 scalar wavelet–clearly outperforms JPEG2000 for almost

all color images. It is important to note that we do not employ any entropy coding while

JPEG2000 utilizes arithmetic coding. Despite JPEG2000’s advantage, HVS on is the clear

winner in terms of PSNR and subjective quality.

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Table 5.44: Correlation of subjective quality with: PSNR and HVS on.

Correlation of subjective quality with: PSNR HVS on

All Observers judging all images 0.56 0.83

Non-experts judging all images 0.61 0.79

Experts judging all images 0.51 0.94

All observers judging grayscale images -0.47 0.47

Non-experts judging grayscale images -0.34 0.34

Experts judging grayscale images -0.75 0.75

All observers judging low bit rate color images 0.76 0.89

Non-experts judging low bit rate color images 0.77 0.85

Experts judging low bit rate color images 0.73 0.99

For some images, JPEG2000 surpasses our HVS on scheme in terms of PSNR. This oc-

curs when the test image (e.g. Color16 and DNA) has large areas of uniformity that are

compressed more efficiently due to JPEG2000’s arithmetic coding. Table 5.45 gives the com-

plete PSNR results comparing our HVS on scheme using the Bi22/14 to JPEG2000 (with

the Bi9/7 option). The Bi22/14 is used in the comparison because it performed best in

terms of PSNR in our experiments. Subjectively, the difference between compression with

the Bi22/14 and Bi9/7 is not distinguishable using our coder.

Subjectively, HVS on typically captures more detail where JPEG2000 smooths and intro-

duces blurring. Figure 5.13 illustrates the subjective superiority of HVS compression over

JPEG2000 for the Lena image at a compression ratio of 19.2:1. All expert observers and

seven out of ten non-expert observers judged (c) superior to (b).

Figure 5.14 shows the same effect with the metal image. Again all expert observers reported

the HVS-compressed image as superior over the JPEG2000-compressed image. Nine out of

ten non-expert observers agreed with that judgement.

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(a)

(b) (c)

Figure 5.13: (a) Original Lena. (b) Reconstruction compressed with JPEG2000 (Bi9/7) at

0.417 bpp, PSNR=32.24 dB. (c) Reconstruction compressed with Bi22/14 scalar wavelet


84

(a)

(b) (c)

Figure 5.14: (a) Original Metal. (b) Reconstruction compressed with JPEG2000 (Bi9/7)

at 0.250 bpp, PSNR=30.90 dB. (c) Reconstruction compressed with Bi22/14 scalar wavelet


85

Table 5.45: Comparing color image compression: HVS on vs. JPEG2000.

Lena 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 36.28 34.66 33.22 31.97

JPEG2000 38.02 32.24 30.59 29.24

Mandrill 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 27.91 24.87 23.04 21.82

JPEG2000 28.74 22.48 21.48 20.78

Lighthouse 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 43.37 34.34 29.75 26.30

JPEG2000 42.37 30.52 28.19 26.53

Helen 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 43.56 38.12 35.31 33.44

JPEG2000 43.00 34.40 32.53 31.26

Owl 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 41.86 30.19 27.68 25.19

JPEG2000 39.52 26.62 24.72 23.41

DNA 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 38.48 38.13 36.54 34.40

JPEG2000 47.73 35.07 32.12 30.23

Satellite 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 29.19 25.67 24.36 23.37

JPEG2000 29.31 23.66 22.77 22.19

Map 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 40.71 27.88 25.32 24.03

JPEG2000 37.37 24.73 23.41 22.64

Metal 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 41.27 38.92 35.52 32.65

JPEG2000 44.24 33.64 30.90 28.90

Color16 2.75 bpp .417 bpp .250 bpp 0.167 bpp

Bi22/14 SW 43.48 43.48 43.47 43.09

JPEG2000 50.35 50.35 49.99 47.61

Chapter 6

Conclusion

This thesis provides a comprehensive evaluation of an HVS model for wavelet-based grayscale

and color image compression. We first summarize the many results in Chapter 5 and then

discuss some related future work.

6.1 Summary of Results

6.1.1 Grayscale Images

For grayscale images, CSF masking (i.e. HVS on) corresponds to a significant improvement

in the subjective quality of both natural and synthetic images. However, the effect of CSF

masking is only distinguishable at the three lower bit rates. This improvement is interesting

because it corresponds to a consistently lower PSNR (0.5 to 1.0 dB).

For the natural grayscale images, the scalar wavelets (typically the Bi22/14) perform best.

For the synthetic grayscale images, multiwavelets perform better–especially at the higher

bit rates. The Bi9/7 scalar wavelet typically performs better at the lower bit rates for

synthetic images.

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87

6.1.2 Natural Color Images

For natural color images, HVS on corresponds to a significant improvement in the subjective

quality. However, the effect of HVS on is only distinguishable at the three lower bit rates.

The PSNR of HVS on is consistently higher than HVS off for all images at the three lower

bit rates. However, CSF off/Asymmetric on outperforms HVS on in terms of PSNR. At

the highest bit rate (2.75 bpp), the PSNR of HVS off is the largest (except for the owl

image–HVS on is superior by 0.6 dB using the Bi22/14).

The Bi22/14 scalar wavelet quantitatively outperforms the Bi9/7 scalar wavelet and all

multiwavelets at all bit rates.

6.1.3 Synthetic Color Images

For synthetic color images, HVS on corresponds to a significant improvement in the subjec-

tive quality. At the three lower bit rates, the PSNR of HVS on is superior to HVS off for

all synthetic color images (with the exception of DNA at 0.417 bpp). Similar to the natural

color images, CSF off/Asymmetric on outperforms HVS on in terms of PSNR. Unlike the

natural color case–at 2.75 bpp HVS off is not always the superior method. The results at

the high bit rate are mixed.

The quantitative results show that the Bi22/14 is almost always the best wavelet at all

bit rates. Occasionally, the Bi9/7 outperforms the Bi22/14 at 2.75 and 0.417 bpp, but the

difference is minimal in these cases.

6.1.4 HVS on vs. JPEG2000

In terms of subjective quality, HVS on is superior to JPEG2000 for all images. JPEG2000

has a tendency to smooth the image, thereby loosing texture and depth information. Our

HVS compression scheme retains these details, thus delivering subjectively better image

88

reconstruction.

In terms of PSNR, HVS on usually outperforms JPEG2000 by 1 to 3 dB. JPEG2000 only

exceeds HVS on at the highest bit rate on images with large areas of uniformity. For these

images, JPEG2000 has the benefit of arithmetic coding. HVS compression would presumably

surpass JPEG2000 in all cases with the addition of an entropy coder.

6.1.5 Correlations for Image Groups

For all images and all observers, subjective quality has a strong positive correlation with

PSNR. Similarly, subjective quality has a strong positive correlation with HVS on. However,

these results for all images do not reveal an important distinction between the grayscale and

color images.

For all grayscale images and all observers, subjective quality has a mild negative correlation

with PSNR. Conversely, subjective quality has a mild positive correlation with HVS on.

For all color images and all observers, subjective quality has a strong positive correlation

with PSNR. Similarly, subjective quality has a strong positive correlation with HVS on.

These results are a departure from previous claims that subjective quality and PSNR do not

correlate well [7].

For color images, the experts and non-experts agreed on the relationship between subjective

quality and PSNR and on subjective quality and HVS on. For grayscale images, the experts

and non-experts also agreed on the relationship between subjective quality and PSNR and

on subjective quality and HVS on, but to different degrees. Expert observers consistently

perceived the inverse relationship between subjective quality and PSNR, while non-experts

perceived this trend less consistently. Similarly, expert observers consistently perceived the

direct relationship between subjective quality and HVS on, while non-experts perceived this

trend less consistently.

89

6.2 Future Work

This thesis provides the most comprehensive results to date for wavelet-based image com-

pression with a consideration for the HVS. Although our results indicate better quantitative

and qualitative performance than previous research, avenues for improvement remain.

1. The CSF masking operation presented in this thesis applies to scalar wavelets and

multiwavelets. We believe that the same idea can be extended to wavelet packets and

multiwavelet packets. However, constructing a CSF mask for wavelet packets and mul-

tiwavelet packets is not trivial. We anticipate that constructing and applying a CSF

mask to a wavelet packet or multiwavelet packet decomposition will provide quantita-

tive and qualitative improvement similar to what we have seen for scalar wavelets and

multiwavelets.

2. Our color compression scheme transforms the RGB input image into the YCbCr color

space. This is a standard method–it is used in JPEG. However, other color space

models exist and may offer a more suitable breakdown for wavelet-based compression.

Among the other options for color compression is the opponent color space model that

has been used in recent compression research [16].

3. The same HVS compression ideas used here for still images may provide similar im-

provement for digital video compression. CSF masking is a simple operation that can

be applied on a frame by frame basis while adding minimal computational overhead.

4. Both quantitatively and qualitatively, the best multiwavelet rarely outperforms the

best scalar wavelet. New multifilters are continuing to be developed. The family

of balanced multiwavelets [33] and symmetric FIR balanced multiwavelets [21] may

provide performance superior to the multiwavelets used in this thesis.

5. CSF masking was not performed in the two chrominance spaces because humans’

sensitivity to chrominance stimuli is relatively uniform across frequency. However,

90

potential gain may be found in changing the wavelet method in each color space. For

instance, multiwavelets may potentially compress chrominance information better than

scalar wavelets. If trends can be found, we can choose to compress each color space

with a particular wavelet method. Such a scheme may provide additional quantitative

and/or qualitative gain.

Appendix A

Test Images

The test images used in Chapter 5 are displayed here for reference.

Figure A.1: Lena (grayscale). Figure A.2: Barbara (grayscale).

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92

Figure A.3: Lighthouse (grayscale). Figure A.4: Ruler (grayscale).

Figure A.5: Lena. Figure A.6: Helen.

93

Figure A.7: Lighthouse. Figure A.8: Mandrill.

Figure A.9: Owl. Figure A.10: DNA.

94

Figure A.11: Satellite. Figure A.12: Map.

Figure A.13: Metal. Figure A.14: Color 16.

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Vita

Andrew P. Beegan is a native of Westlake, OH on the west side of Cleveland. His academic

and spiritual formation at St. Ignatius High School prepared him well for his undergradu-

ate work at the University of Notre Dame. As a member of the Notre Dame community,

Andy was active in service organizations and piloted fund-raising efforts with his creation

of the GameDay Photo. He earned his bachelor of science degree in electrical engineering

in 1999. Eager to continue his education, Andy went on to complete his masters degree in

electrical engineering at the Virginia Polytechnic Institute and State University in Blacks-

burg, VA. As a graduate student at Virginia Tech, he gained experience in both teaching

and research. During his first semester he taught an industrial electronics laboratory. His

last three semesters were spent working as a graduate research assistant in the Digital Sig-

nal Processing and Communications Laboratory (DSPCL). Andy has also gained experience

as an intern at Netfarm Inc., WorldCom Advanced Networks, and Automated Tech Tools

Inc. His full-time professional career will commence at PanAmSat working as a Satellite

Applications Engineer. Andy comes from a family of six children. In his free time he enjoys

basketball, skiing, drawing, and painting.

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