vii
TABLE OF CONTENTS
CHAPTER
1
TITLE
PAGE
DECLARATION
ii
DEDICATION
iii
ACKNOWLEDGMENTS
iv
ABSTRACT
v
ABSTRAK
vi
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xi
LIST OF SYMBOLS
xvi
LIST OF ABBREVIATIONS
xviii
LIST OF APPENDICES
xix
INTRODUCTION
1
1.1 Background of Study
1
1.2 Statement of Problems
3
1.3 The Purpose of this Research
3
1.4 Research Objectives
4
1.5 Significance of Study
4
1.6 Scope of Research
5
viii
2
3
4
LITERATURE REVIEW
6
2.1 Edge Image Acquisition
6
2.2 Slanting Edge Method
8
2.3 The concept of Resolution
12
2.4 Modulation Transfer Function (MTF)
13
2.5 The ESF and the LSF
16
RESEACH METHODOLOGY
19
3.1 Introduction
19
3.2 Edge Image Production
19
3.3 Angle of Measurement
26
3.4 ESF and LSF Computation
28
3.5 MTF Computation
32
RESULTS AND DISCUSSION
34
4.1 Determination of MTF
34
4.1.1 Image 1 (0 degree)
35
4.1.2 Image 1 (5 degrees)
36
4.1.3 Combination of MTFs for Edge Image 1
39
4.1.4 Image 2 (0 degree)
40
4.1.5 Image 2 (7 degree)
42
4.1.6 Combination of MTFs for Edge Image 2
43
4.1.7 Image 3 (0 degree)
45
4.1.8 Image 3 (6 degree)
47
4.1.9 Combination of MTFs for Edge Image 3
48
4.1.10 Image 4 (0 degree)
49
4.1.11 Image 4 (5 degree)
51
4.1.12 Combination of MTFs for Edge Image 4
53
4.2 Discussion
55
4.3 Comparison of MTFs
58
ix
5
CONCLUSIONS AND PROPOSED FUTURE WORK
60
5.1 Conclusions
60
5.2 Future Work
61
REFERENCES
Appendices A - C
62
65 - 86
x
LIST OF TABLES
TABLE NO.
4.1
4.2
TITLE
PAGE
Comparison of the MTF values for a straight (0 degree) and
slanted (2 and 5 degrees) of edge images from a 0.05 mm
thick lead in the conventional radiography system
58
Comparison of the MTF values for a straight (0 degree)
and slanted (1, 2 and 5 degrees) of edge images from
a 1.08 mm thick lead in the computed radiography
FCR system
59
xi
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
2.1
The edge test device and its holder (Samei et. al., 1998)
6
2.2
The schematic of the three-step alignment procedure for
the edge device (Samei et. al., 1998)
7
Orientation of edge relative to pixel matrix
(schematically, edge angle exaggerated) (Buhr et. al., 2003)
11
The modulation (M) of image intensity is defined as
(
)⁄(
) (Bourne, 2010)
14
A typical MTF for a film-screen detector (Prince
and Links, 2006)
15
The edge and line spread functions can be used to determine
a direction-specific MTF
17
The Line spread function (LSF), and edge spread function
(ESF) are shown isometrically (top) and in profile (bottom)
(Bushberg et al., 2002)
18
3.1
Flow chart of Edge algorithm steps
20
3.2
The experimental set up for the measurement and the
arrangement of the screen-film (cassette), bar pattern test
object, lead step, and lead mask on the rig (Hassan et al.,
2002)
21
2.3
2.4
2.5
2.6
2.7
xii
3.3
The chest X-ray machine for the measurement and the
arrangement of the imaging plate (IP cassette type CC), an
edge test device which is placed close to the detector (photo
was taken from UTM health centre).
22
The light beam diaphragm of a chest X-ray tube and the
beam cone covers 3 cm away from each side of an edge
test device (photo was taken from UTM health centre).
23
Edge images for a 0.05 mm thick lead taken from the
conventional radiography system
24
Edge images for an 0.48 mm thick aluminum taken from the
computed radiography FCR system
24
Edge images for an 1.2 mm thick aluminum taken from the
computed radiography FCR system
25
Edge images for a 1.08 mm thick lead taken from the
computed radiography FCR system
25
3.9
Edge detections
26
3.10
Angle determination by Radon transforms
27
3.11
Estimated edge angle which is about 2 degrees for one of
the slanted edge image
28
Re-projection and binning of the two-dimensional edge
image data into a one-dimensional trace perpendicular
to the edge (Samei et al., 1998)
29
Mapped and Sorted the Edge Spread Function (ESF)
for a slanted edge image
30
Binned and smoothed the edge spread function (ESF)
for a slanted edge image
32
Smoothed the line spread function (LSF) for a slanted
edge image
33
3.4
3.5
3.6
3.7
3.8
3.12
3.13
3.14
3.15
xiii
4.1
4.2
4.3
The smoothed ESF of a straight edge image of 0.05 mm
thick lead for the radiographic screen-film system.
35
The smoothed LSF of a straight edge image of 0.05 mm
thick lead for the radiographic screen-film system
35
The MTF of a straight edge image of 0.05 mm thick lead
for the radiographic screen-film system
36
4.4
The Smoothed ESF of a slanted edge image (5 degrees)
of 0.05 mm thick lead for the radiographic screen-film system 36
4.5
The Smoothed LSF of a slanted edge image (5 degrees)
of 0.05 mm thick lead for the radiographic screen-film system 37
4.6
The MTF of a slanted edge image (5 degrees)
of 0.05 mm thick lead for the radiographic screen-film system 37
4.7
The MTF of a slanted edge image (2 degrees) of 0.05 mm
thick lead for the radiographic screen-film system
38
MTF results of edge images (0 degree, 2 degrees
and 5 degrees) of a 0.05 mm thick lead for the radiographic
screen-film system
39
The Smoothed ESF of a straight edge image of 0.48 mm
thick aluminium for the computed radiography FCR system
40
The Smoothed LSF of a straight edge image of 0.48 mm
thick aluminium for the computed radiography FCR system
41
The MTF of a straight edge image of 0.48 mm thick
aluminium for the computed radiography FCR system
41
The Smoothed ESF of a slanted edge image (7 degrees)
of 0.48 mm thick aluminium for the computed
radiography FCR system
42
The Smoothed LSF of a slanted edge image (7 degrees)
of 0.48 mm thick aluminium for the computed
radiography FCR system
42
4.8
4.9
4.10
4.11
4.12
4.13
xiv
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
The MTF of a slanted edge image (7 degrees) of 0.48 mm
thick aluminium for the computed radiography FCR system
43
MTF results of edge images (0 degree and 7 degrees) of an
0.48 mm thick aluminium for the computed radiography
FCR system
43
The fourth-order polynomial MTF results of edge images
(0 degree and 7 degrees) of an 0.48 mm thick aluminium
for the computed radiography FCR system
44
The Smoothed ESF of a straight edge image of 1.2 mm
thick aluminium for the computed radiography FCR system
45
The Smoothed LSF of a straight edge image of 1.2 mm
thick aluminium for the computed radiography FCR system
46
The MTF of a straight edge image of 1.2 mm thick
aluminium for the computed radiography FCR system
46
The Smoothed ESF of a slanted edge image (6 degrees)
of 1.2 mm thick aluminium for the computed
radiography FCR system
47
The Smoothed LSF of a slanted edge image (6 degrees)
of 1.2 mm thick aluminium for the computed
radiography FCR system
47
The MTF of a slanted edge image (6 degrees) of 1.2 mm
thick aluminium for the computed radiography FCR system
48
MTF results of both edge images (0 degree and 6 degrees)
of an 1.2 mm thick aluminium for the computed radiography
FCR system
48
The Smoothed ESF of a straight edge image of 1.08 mm
thick lead for the computed radiography FCR system
49
The Smoothed LSF of a straight edge image of 1.08 mm
thick lead for the computed radiography FCR system
50
xv
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
The MTF of a straight edge image of 1.08 mm thick lead
for the computed radiography FCR system
50
The Smoothed ESF of a slanted edge image (5 degrees) of
1.08 mm thick lead for the computed radiography
FCR system
51
The Smoothed LSF of a slanted edge image (5 degrees) of
1.08 mm thick lead for the computed radiography
FCR system
51
The MTF of a slanted edge image (5 degrees) of 1.08 mm
thick lead for the computed radiography FCR system
52
The MTF of a slanted edge image (2 degrees) of 1.08 mm
thick lead for the computed radiography FCR system
52
The MTF of a slanted edge image (1 degrees) of 1.08 mm
thick lead for the computed radiography FCR system
53
MTF results of edge images (0 degree, 1 degree, 2 degrees
and 5 degrees) of a 1.08 mm thick lead for the computed
radiography FCR system
53
MTF results of edge images (0 degree, 1 degree, 2 degrees
and 5 degrees) of a 1.08 mm thick lead for the computed
radiography FCR system for spatial frequencies from
0 to 3 cycles/mm with the MTF ranges between 0.6 and 1.05
55
xvi
LIST OF SYMBOLS
( )
( )
M
( )
( )
-
Tilt angle
-
Sub-pixel bin width
-
Slight shift of the sampling positions between the lines
-
Edge Spread Function
-
Spatial frequency
-
Nyquist frequency
-
Sinusoidal amplitude intensity
-
Background intensity
-
Maximum signal intensity
-
Minimum signal intensity
-
Row number
-
Column number
-
Line Spread Function
-
Modulation
-
Input signal modulation
-
Output signal modulation
xvii
-
Average line numbers resulted in a one pixel
p
-
Pixel dimension
pp
-
Pixel pitch
-
Distance from the edge
-
Re-projection angle
(
)
xviii
LIST OF ABBREVIATIONS
DQE
-
Detective Quantum Efficiency
ESF
-
Edge Spread Function
FCR
-
Fuji Computed Radiography
FFD
-
Focus-to-film distance
FFT
-
Fast Fourier transform
IP
-
Imaging plate
LSF
-
Line Spread Function
MTF
-
Modulation Transfer Function
ROI
-
Region-of-interest
xix
LIST OF APPENDICES
APPENDIX
TITLE
PAGE
A
Numerical comparison of MTF values
65
B
MATLAB M-codes for angle determinations
72
C
MATLAB M-codes for computing the ESF,
LSF and the MTF
76