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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
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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
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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
without HVS at 0.417 bpp, PSNR=23.29 dB. (c) Reconstruction compressed
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
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. . . . . 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
without HVS at 2.75 bpp, PSNR=51.80 dB. (c) Reconstruction compressed
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
without HVS at 0.167 bpp, PSNR=33.66 dB. (c) Reconstruction compressed
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
without HVS at 0.417 bpp, PSNR=24.99 dB. (c) Reconstruction compressed
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)
Y (8:1), Cb (64:1), Cr (64:1) for an overall compression ratio of 19.20:1 (0.417 bpp)
Y (16:1), Cb (64:1), Cr (64:1) for an overall compression ratio of 32.00:1 (0.250 bpp)
Y (32:1), Cb (64:1), Cr (64:1) for an overall compression ratio of 48.00:1 (0.167 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
BSA 7/5 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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.
Correlation All Observers Non-experts Experts
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.
SA4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 32.92 29.48 26.84 24.33
CSF on 32.05 28.60 25.93 24.20
ORT4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 32.93 29.48 26.85 24.34
CSF on 32.06 28.61 25.94 24.21
BSA 9/7 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 32.47 29.29 26.76 24.39
CSF on 31.72 28.39 25.86 24.29
BSA 7/5 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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.
Correlation All Observers Non-experts Experts
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.
SA4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 34.59 29.50 26.27 23.84
CSF on 33.32 28.65 25.34 23.54
ORT4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 34.65 29.55 26.29 23.83
CSF on 33.38 28.69 25.36 23.54
BSA 9/7 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 34.67 30.01 26.60 24.05
CSF on 33.34 28.99 25.72 23.84
BSA 7/5 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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
BSA 7/5 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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.
Correlation All Observers Non-experts Experts
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.
SA4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 28.13 18.03 13.32 11.10
CSF on 26.47 16.12 12.90 11.30
ORT4 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 28.06 18.02 13.33 11.10
CSF on 26.44 16.13 12.90 11.29
BSA 9/7 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 25.55 16.92 11.97 10.56
CSF on 25.15 16.26 12.73 11.37
BSA 7/5 MW(sh) 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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
BSA 9/7 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
CSF off 26.62 19.39 15.03 11.59
CSF on 25.16 16.40 12.70 11.32
BSA 7/5 MW 1.000 bpp 0.500 bpp 0.250 bpp 0.125 bpp
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.
Correlation All Observers Non-experts Experts
PSNR 1 1 1
HVS on 1 1 1
Table 5.16: Scalar wavelet PSNR (in dB) results for color Lena.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
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
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.64 34.22 32.19 30.92
CSF off, Asymmetric on 36.23 34.81 33.75 32.09
CSF on, Asymmetric off 42.44 33.54 32.05 30.71
CSF on, Asymmetric on 36.28 34.66 33.22 31.97
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.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.45 33.05 31.11 29.38
CSF off, Asymmetric on 35.65 34.18 32.85 30.90
CSF on, Asymmetric off 42.29 32.82 30.90 29.54
CSF on, Asymmetric on 35.56 33.84 32.40 30.65
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.45 33.07 31.14 29.40
CSF off, Asymmetric on 35.65 34.19 32.87 30.92
CSF on, Asymmetric off 42.29 32.84 30.92 29.56
CSF on, Asymmetric on 35.57 33.86 32.43 30.68
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 41.84 33.27 31.47 29.92
CSF off, Asymmetric on 35.72 34.09 32.91 31.25
CSF on, Asymmetric off 41.53 32.85 31.32 30.04
CSF on, Asymmetric on 35.65 33.65 32.41 31.09
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.47 33.13 31.15 29.44
CSF off, Asymmetric on 35.64 34.19 32.88 30.93
CSF on, Asymmetric off 42.25 32.83 30.93 29.54
CSF on, Asymmetric on 35.55 33.83 32.45 30.67
54
Table 5.18: Correlation coefficients for color Mandrill.
Correlation All Observers Non-experts Experts
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.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.71 23.29 22.06 21.18
CSF off, Asymmetric on 27.92 25.31 23.42 21.97
CSF on, Asymmetric off 34.85 22.71 21.90 21.01
CSF on, Asymmetric on 27.88 24.85 23.06 21.87
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.71 23.31 22.10 21.21
CSF off, Asymmetric on 27.97 25.38 23.47 22.04
CSF on, Asymmetric off 34.75 22.61 21.85 21.18
CSF on, Asymmetric on 27.91 24.87 23.04 21.82
Table 5.20: Multiwavelet PSNR (in dB) results for color Mandrill with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 27.66 24.69 22.79 21.55
CSF off, Asymmetric on 34.79 22.55 21.65 20.90
CSF on, Asymmetric off 27.72 25.02 23.08 21.68
CSF on, Asymmetric on 35.55 23.04 21.81 20.96
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 27.67 24.71 22.80 21.55
CSF off, Asymmetric on 34.80 22.56 21.66 20.91
CSF on, Asymmetric off 27.72 25.03 23.09 21.69
CSF on, Asymmetric on 35.55 23.05 21.82 20.96
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 27.64 24.49 22.60 21.51
CSF off, Asymmetric on 34.07 22.54 21.60 20.98
CSF on, Asymmetric off 27.70 24.93 23.05 21.60
CSF on, Asymmetric on 34.85 23.01 21.73 20.95
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 27.64 24.64 22.67 21.54
CSF off, Asymmetric on 34.76 22.63 21.65 20.94
CSF on, Asymmetric off 27.72 25.05 23.12 21.70
CSF on, Asymmetric on 35.58 23.10 21.83 20.97
56
(a)
(b) (c)
Figure 5.5: (a) Original Mandrill. (b) Reconstruction compressed with Bi9/7 scalar wavelet
without HVS at 0.417 bpp, PSNR=23.29 dB. (c) Reconstruction compressed with Bi9/7
scalar wavelet with HVS at 0.417 bpp, PSNR=24.85 dB.
57
Table 5.21: Correlation coefficients for color Lighthouse.
Correlation All Observers Non-experts Experts
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
correlation between all observers and HVS on (1).
58
Table 5.22: Scalar wavelet PSNR (in dB) results for color Lighthouse.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 44.02 30.48 27.62 26.07
CSF off, Asymmetric on 43.55 35.46 31.23 27.62
CSF on, Asymmetric off 43.76 28.32 26.31 25.51
CSF on, Asymmetric on 43.59 34.56 30.15 26.30
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 44.04 30.48 27.62 26.18
CSF off, Asymmetric on 43.38 35.52 31.27 27.62
CSF on, Asymmetric off 43.66 28.20 26.29 25.66
CSF on, Asymmetric on 43.37 34.34 29.75 26.30
Table 5.23: Multiwavelet PSNR (in dB) results for color Lighthouse with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.50 34.12 29.71 26.15
CSF off, Asymmetric on 43.48 28.82 26.16 25.27
CSF on, Asymmetric off 42.61 34.85 30.81 27.39
CSF on, Asymmetric on 43.84 30.05 27.40 25.79
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.52 34.13 29.71 26.18
CSF off, Asymmetric on 43.48 28.84 26.19 25.28
CSF on, Asymmetric off 42.62 34.86 30.81 27.40
CSF on, Asymmetric on 43.84 30.06 27.41 25.81
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.64 33.80 29.25 26.24
CSF off, Asymmetric on 42.62 28.57 26.24 25.30
CSF on, Asymmetric off 42.76 34.57 30.67 27.29
CSF on, Asymmetric on 43.22 29.91 27.30 25.73
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 42.53 34.02 29.28 26.24
CSF off, Asymmetric on 43.38 28.68 26.25 25.24
CSF on, Asymmetric off 42.70 34.84 30.80 27.37
CSF on, Asymmetric on 43.85 30.03 27.38 25.80
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.
Correlation All Observers Non-experts Experts
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.
Table 5.24 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).
61
Table 5.25: Scalar wavelet PSNR (in dB) results for color Helen.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 46.17 35.67 33.69 32.50
CSF off, Asymmetric on 43.53 38.68 35.88 33.57
CSF on, Asymmetric off 45.74 35.13 33.44 32.42
CSF on, Asymmetric on 43.18 38.08 35.12 33.27
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 46.18 35.84 33.86 32.70
CSF off, Asymmetric on 43.58 38.77 36.03 33.72
CSF on, Asymmetric off 45.69 35.24 33.58 32.45
CSF on, Asymmetric on 43.56 38.12 35.31 33.44
Table 5.26: Multiwavelet PSNR (in dB) results for color Helen with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 45.72 35.04 32.93 31.78
CSF off, Asymmetric on 41.94 37.75 35.08 32.68
CSF on, Asymmetric off 45.59 34.61 32.88 31.57
CSF on, Asymmetric on 42.00 37.01 34.58 32.63
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 45.75 35.06 32.95 31.79
CSF off, Asymmetric on 41.96 37.77 35.09 32.69
CSF on, Asymmetric off 45.61 34.64 32.89 31.58
CSF on, Asymmetric on 42.02 37.04 34.60 32.64
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 44.97 34.97 33.04 31.97
CSF off, Asymmetric on 42.46 37.71 35.11 32.84
CSF on, Asymmetric off 44.86 34.59 33.03 31.79
CSF on, Asymmetric on 42.60 36.87 34.67 32.84
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 45.79 35.06 32.99 31.76
CSF off, Asymmetric on 42.12 37.87 35.19 32.74
CSF on, Asymmetric off 45.59 34.66 32.94 31.54
CSF on, Asymmetric on 42.02 37.02 34.68 32.68
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.
Correlation All Observers Non-experts Experts
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.
Table 5.27 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).
64
Table 5.28: Scalar wavelet PSNR (in dB) results for color Owl.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 41.47 26.98 25.09 23.79
CSF off, Asymmetric on 41.46 31.41 27.79 25.06
CSF on, Asymmetric off 40.55 26.84 25.16 23.71
CSF on, Asymmetric on 41.70 30.09 27.54 25.14
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 41.81 27.12 25.30 23.94
CSF off, Asymmetric on 41.72 31.62 27.93 25.27
CSF on, Asymmetric off 40.76 26.97 25.21 23.87
CSF on, Asymmetric on 41.86 30.19 27.68 25.19
Table 5.29: Multiwavelet PSNR (in dB) results for color Owl with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 40.31 25.87 24.12 22.74
CSF off, Asymmetric on 39.91 30.14 26.56 24.08
CSF on, Asymmetric off 39.36 25.92 23.97 22.81
CSF on, Asymmetric on 39.96 29.68 26.47 23.94
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 40.36 25.89 24.14 22.76
CSF off, Asymmetric on 39.93 30.19 26.58 24.10
CSF on, Asymmetric off 39.43 25.94 23.99 22.83
CSF on, Asymmetric on 39.99 29.73 26.50 23.95
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 39.99 26.31 24.65 23.25
CSF off, Asymmetric on 40.84 30.33 26.92 24.61
CSF on, Asymmetric off 38.92 26.44 24.58 23.41
CSF on, Asymmetric on 40.96 29.81 26.97 24.54
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 40.59 25.97 24.17 22.76
CSF off, Asymmetric on 40.00 30.38 26.72 24.13
CSF on, Asymmetric off 39.56 26.13 24.00 22.94
CSF on, Asymmetric on 39.97 29.87 26.64 23.97
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.
Correlation All Observers Non-experts Experts
PSNR 1 1 1
HVS on 1 1 1
Table 5.31: Scalar wavelet PSNR (in dB) results for color DNA.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.86 39.73 36.21 33.69
CSF off, Asymmetric on 39.37 39.11 38.02 35.46
CSF on, Asymmetric off 52.07 38.87 35.50 33.28
CSF on, Asymmetric on 38.59 38.28 36.74 34.62
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.80 39.72 36.06 33.66
CSF off, Asymmetric on 39.29 39.02 37.89 35.27
CSF on, Asymmetric off 51.98 38.91 35.30 33.32
CSF on, Asymmetric on 38.48 38.13 36.54 34.40
68
(a)
(b) (c)
Figure 5.9: (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet
without HVS at 2.75 bpp, PSNR=51.80 dB. (c) Reconstruction compressed with Bi22/14
scalar wavelet with HVS at 2.75 bpp, PSNR=38.48 dB.
69
(a)
(b) (c)
Figure 5.10: (a) Original DNA. (b) Reconstruction compressed with Bi22/14 scalar wavelet
without HVS at 0.167 bpp, PSNR=33.66 dB. (c) Reconstruction compressed with Bi22/14
scalar wavelet with HVS at 0.167 bpp, PSNR=34.40 dB.
70
Table 5.32: Multiwavelet PSNR (in dB) results for color DNA with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.86 39.36 35.44 33.24
CSF off, Asymmetric on 37.69 37.49 36.36 34.05
CSF on, Asymmetric off 51.92 38.79 34.83 31.96
CSF on, Asymmetric on 37.02 36.81 35.65 33.34
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.85 39.35 35.45 33.25
CSF off, Asymmetric on 37.70 37.49 36.37 34.06
CSF on, Asymmetric off 51.91 38.79 34.84 31.97
CSF on, Asymmetric on 37.03 36.82 35.66 33.35
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.54 38.06 34.80 32.90
CSF off, Asymmetric on 37.60 37.03 35.85 33.70
CSF on, Asymmetric off 50.78 37.42 34.30 32.04
CSF on, Asymmetric on 37.16 36.54 35.29 33.20
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 51.89 39.04 35.21 33.08
CSF off, Asymmetric on 37.45 37.23 36.08 33.84
CSF on, Asymmetric off 51.95 38.50 34.67 31.83
CSF on, Asymmetric on 36.98 36.75 35.51 33.27
71
Table 5.33: Correlation coefficients for color Satellite.
Correlation All Observers Non-experts Experts
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).
Table 5.33 shows the correlation coefficients for same trial. The table depicts the following:
a strong positive correlation between all observers and PSNR (0.79); and, a strong positive
correlation between all observers and HVS on (0.79).
72
Table 5.34: Scalar wavelet PSNR (in dB) results for color Satellite.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.23 24.35 23.39 22.71
CSF off, Asymmetric on 29.16 25.74 24.33 23.35
CSF on, Asymmetric off 34.39 24.35 23.48 22.70
CSF on, Asymmetric on 29.20 25.67 24.35 23.43
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.17 24.43 23.45 22.72
CSF off, Asymmetric on 29.25 25.81 24.42 23.44
CSF on, Asymmetric off 34.23 24.42 23.40 22.73
CSF on, Asymmetric on 29.19 25.67 24.36 23.37
Table 5.35: Multiwavelet PSNR (in dB) results for color Satellite with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.03 24.25 23.27 22.44
CSF off, Asymmetric on 28.95 25.55 24.11 23.13
CSF on, Asymmetric off 34.16 24.27 23.21 22.47
CSF on, Asymmetric on 28.95 25.47 24.09 23.06
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 35.04 24.26 23.28 22.45
CSF off, Asymmetric on 28.96 25.56 24.12 23.13
CSF on, Asymmetric off 34.17 24.28 23.22 22.48
CSF on, Asymmetric on 28.96 25.47 24.10 23.07
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 34.18 24.14 23.26 22.44
CSF off, Asymmetric on 28.99 25.34 23.96 23.12
CSF on, Asymmetric off 33.21 24.27 23.23 22.57
CSF on, Asymmetric on 28.95 25.19 24.01 23.06
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 34.93 24.30 23.29 22.45
CSF off, Asymmetric on 28.98 25.58 24.14 23.15
CSF on, Asymmetric off 33.99 24.36 23.23 22.51
CSF on, Asymmetric on 28.92 25.44 24.11 23.05
73
(a)
(b) (c)
Figure 5.11: (a) Original Satellite. (b) Reconstruction compressed with BSA7/5 multiwavelet
without HVS at 0.250 bpp, PSNR=23.29 dB. (c) Reconstruction compressed with BSA7/5
multiwavelet without HVS at 0.250 bpp, PSNR=24.11 dB.
74
Table 5.36: Correlation coefficients for color Map.
Correlation All Observers Non-experts Experts
PSNR 1 1 1
HVS on 1 1 1
Table 5.37: Scalar wavelet PSNR (in dB) results for color Map.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 39.97 25.26 24.01 23.33
CSF off, Asymmetric on 40.02 28.91 25.79 23.98
CSF on, Asymmetric off 38.76 24.96 24.01 23.26
CSF on, Asymmetric on 39.95 27.82 25.23 23.98
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 40.13 25.33 24.14 23.42
CSF off, Asymmetric on 40.84 29.03 25.90 24.10
CSF on, Asymmetric off 38.75 24.98 24.08 23.33
CSF on, Asymmetric on 40.71 27.88 25.32 24.03
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).
75
Table 5.38: Multiwavelet PSNR (in dB) results for color Map with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 39.55 24.99 23.82 23.03
CSF off, Asymmetric on 37.60 28.38 25.39 23.72
CSF on, Asymmetric off 38.36 24.78 23.78 23.00
CSF on, Asymmetric on 37.61 27.70 25.09 23.68
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 39.58 24.99 23.83 23.03
CSF off, Asymmetric on 37.62 28.40 25.39 23.73
CSF on, Asymmetric off 38.39 24.79 23.79 23.01
CSF on, Asymmetric on 37.64 27.71 25.10 23.69
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 38.92 24.87 23.85 22.96
CSF off, Asymmetric on 39.15 28.24 25.29 23.79
CSF on, Asymmetric off 37.53 24.60 23.80 23.08
CSF on, Asymmetric on 38.98 27.44 25.00 23.73
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 39.59 24.99 23.89 23.00
CSF off, Asymmetric on 37.56 28.37 25.42 23.78
CSF on, Asymmetric off 38.25 24.77 23.83 23.02
CSF on, Asymmetric on 37.74 27.65 25.13 23.73
76
(a)
(b) (c)
Figure 5.12: (a) Original Map. (b) Reconstruction compressed with BSA7/5 multiwavelet
without HVS at 0.417 bpp, PSNR=24.99 dB. (c) Reconstruction compressed with BSA7/5
multiwavelet without HVS at 0.417 bpp, PSNR=27.65 dB.
77
Table 5.39: Correlation coefficients for color Metal.
Correlation All Observers Non-experts Experts
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.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 47.77 36.33 33.19 31.12
CSF off, Asymmetric on 40.96 39.11 36.32 33.01
CSF on, Asymmetric off 48.31 35.27 32.49 30.68
CSF on, Asymmetric on 40.98 38.65 35.39 32.33
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 47.86 36.50 33.39 31.28
CSF off, Asymmetric on 41.17 39.39 36.57 33.21
CSF on, Asymmetric off 48.30 35.36 32.79 31.06
CSF on, Asymmetric on 41.27 38.92 35.52 32.65
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).
78
Table 5.41: Multiwavelet PSNR (in dB) results for color Metal with shuffling.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 47.73 34.41 31.79 29.55
CSF off, Asymmetric on 38.67 36.97 34.48 31.46
CSF on, Asymmetric off 47.90 33.87 31.29 29.48
CSF on, Asymmetric on 38.73 36.50 33.86 30.98
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 47.75 34.44 31.83 29.58
CSF off, Asymmetric on 38.69 37.00 34.53 31.50
CSF on, Asymmetric off 47.96 33.94 31.34 29.51
CSF on, Asymmetric on 38.76 36.54 33.91 31.03
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 46.95 34.63 32.16 30.11
CSF off, Asymmetric on 39.88 37.46 34.92 31.90
CSF on, Asymmetric off 46.41 34.19 31.78 30.11
CSF on, Asymmetric on 40.08 36.95 34.22 31.56
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 47.87 34.49 31.79 29.63
CSF off, Asymmetric on 38.75 37.11 34.56 31.47
CSF on, Asymmetric off 48.06 33.73 31.32 29.61
CSF on, Asymmetric on 38.77 36.60 33.95 31.02
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Table 5.42: Scalar wavelet PSNR (in dB) results for Color16.
Bi9/7 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.88 55.88 53.16 47.55
CSF off, Asymmetric on 48.15 48.15 48.15 47.88
CSF on, Asymmetric off 55.89 55.89 53.04 46.70
CSF on, Asymmetric on 46.44 46.44 46.44 46.29
Bi22/14 SW 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.88 55.70 52.69 47.47
CSF off, Asymmetric on 45.50 45.50 45.50 45.19
CSF on, Asymmetric off 55.89 55.20 51.11 46.42
CSF on, Asymmetric on 43.48 43.48 43.47 43.09
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.
SA4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.90 55.90 55.25 52.41
CSF off, Asymmetric on 52.23 52.23 52.23 52.00
CSF on, Asymmetric off 55.90 55.90 55.19 52.90
CSF on, Asymmetric on 51.33 51.33 51.33 51.21
ORT4 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.90 55.90 55.26 52.61
CSF off, Asymmetric on 52.35 52.35 52.35 52.23
CSF on, Asymmetric off 55.90 55.90 55.05 52.78
CSF on, Asymmetric on 51.16 51.16 51.16 51.01
BSA 9/7 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.86 45.81 44.98 43.36
CSF off, Asymmetric on 42.84 42.57 42.83 42.64
CSF on, Asymmetric off 55.87 45.62 44.47 43.02
CSF on, Asymmetric on 42.57 42.26 42.53 41.95
BSA 7/5 MW(sh) 2.750 bpp 0.417 bpp 0.250 bpp 0.167 bpp
CSF off, Asymmetric off 55.91 55.91 55.91 55.05
CSF off, Asymmetric on 55.05 55.05 55.05 55.05
CSF on, Asymmetric off 55.91 55.91 55.81 55.36
CSF on, Asymmetric on 54.64 54.64 54.64 54.54
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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
with HVS at 0.417 bpp, PSNR=34.66 dB.
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(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
with HVS at 0.250 bpp, PSNR=35.52 dB.
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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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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
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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.
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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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Figure A.3: Lighthouse (grayscale). Figure A.4: Ruler (grayscale).
Figure A.5: Lena. Figure A.6: Helen.
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Figure A.7: Lighthouse. Figure A.8: Mandrill.
Figure A.9: Owl. Figure A.10: DNA.
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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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