DIGITAL IMAGE PROCESSING
Mathematical and Computational Methods
"You British asses, who expect to hear ever some new thing...
ABOUT THE AUTHOR
Jonathan Blackledge graduated in physics from Imperial College and music
from the Royal College of Music,...
DIGITAL IMAGE PROCESSING
Mathematical and Computational Methods
JONATHAN M. BLACKLEDGEt
Professor of Digital Signal Proces...
HORWOOD PUBLISHING LIMITED
CoIl House, Westergate, Chichester, West Sussex, P020 3QL, England.
First published in 2005.
@J...
v
Foreword
Newspapers and the popular scientific press today publish many examples of
highly impressive images. These imag...
vi
• investigation of fractal images, fractal dimension segmentation, image
texture, the coding and storing of large quant...
vii
Preface
Digital Image Processing complements Digital Signal Processing (Horwood
Publishing 2003) which was based on te...
viii
acoustic radiation with the aim of exploring tlu theory, methods and some of
the applications of incoherent and coher...
ix
build. References to other important texts and/or key scientific papers are
included at the end of each chapter or with...
x
Acknowledgements
The material presented has been used by numerous postgraduate students
studying for their MSc and PhD d...
Notation
Alphabetical
A(k)
A
b
B
C
Cn m
CL
CR
D
D
ID
2D
3D
e
E
f(r)
I f(r) I
Ilf(r)11
fij
IlfijII
F(k)
FT
r:
Fij
g(r Iro, ...
xii
n
Ni j
O(x, y)
0
p(r)
p(r, t)
Pij
P(k)
Pi j
P(X)
P(a Ib)
P(Z,O)
P(k)
r,
Ps
P
Pr[x(t)]
q
Re[J]
r
d2r
d3r
s(r)
s(r, t)
S...
Greek
0: Chirping parameter, or first Lame parameter
f3 Second Lame parameter, or angle, or spectral exponent
"f General s...
xiv
Operators
V, /
EEl, 8
0, •
[> <l, <l [>
(-)
(~ )72
iJ
B
det
FI
F- I
I
F2
fr.-I2
iI
i.
R
R-I
®
88
(~ ~ )
Homogeneous li...
Glossary
Mathematical and Statistical
xv
AC
ACF
AM
BHPF
BLPF
BL
CDP
COTF
DC
DCT
DFT
FT
FFT
FM
FIR
HPF
IDFT
IFS
IRF
IOTF
IP...
xvi
Computer Science
B-Scan
CASE
CD
CPU
DSP
DIP
GUI
I/O
IT
PCNG
PRNG
RAM
Brightness-mode Scan
Computer Aided Software Engi...
Contents
Foreword .
Preface .
Acknowledgements
Notation .
Glossary of Terms
Introduction
v
vii
x
xi
xv
1
I Mathematical an...
xviii CONTENTS
2.12 Discussion. . . . . . . . . . . . 47
2.13 Summary of Important Results 47
2.14 Further Reading 49
3 Th...
CONTENTS
4.6.4 Inhomogeneous EM Wave Equations
4.7 Elastic Field Equations .
4.8 Inhomogeneous Elastic Wave Equation .
4.9...
xx
6.2 Solution to the Helmholtz Equation .
6.2.1 The Born Approximation .
6.2.2 Validity of the Born Approximation
6.2.3 ...
CONTENTS xxi
8.3.2 Operator Analysis . 258
8.3.3 Geometric Analysis. 259
8.4 Back-Projection PSF . . . . 261
8.5 The Centr...
xxii CONTENTS
10.3.2 Green Function for Airborne SAR .. . . . 325
10.3.3 Wave Equations for SAR 326
10.3.4 Determination o...
CONTENTS
III Digital Image Processing Methods
12 Image Restoration and Reconstruction
12.1 Introduction ....
12.2 Image Re...
xxiv
15 Image Enhancement
15.1 Basic Transforms .
15.1.1 Logarithmic Transform
15.1.2 Exponential Transform.
15.2 Histogra...
CONTENTS
16.10 Further Reading
17 Statistical Modelling and Analysis
17.1 Random Scattering Theory . . . . . . . . . . . ....
xxvi CONTENTS
18.13.1 Green Function Solution to the Fraci ional Diffusion
Equation 591
18.13.2 Fractional De-Diffusion .....
CONTENTS
Solutions to Problems: Part III
Solutions to Problems: Part IV
B Supplementary Problems
C Fourier Transform of a ...
Introduction
Of the five senses that human beings and most other animals have, the visual
system, is arguably the most imp...
2 INTRODUCTION
law gives a spectrum with a well defined maximum corresponding to a specific
wavelength. This law, expresse...
INTRODUCTION 3
at which we hear, was shifted by 50% above or below middle C, would the
instruments of the orchestra exist ...
4 INTRODUCTION
imaging); Seismic prospecting (seismic reflection imaging, seismic tomography,
vibro-seismic imaging); Indu...
INTRODUCTION 5
where the image is separable and can be processed digitally by operating on
each column and each row separa...
6 INTRODUCTION
If a wavefield is denoted by u(x, y, z, t) which is taken to have both amplitude
A(x, y, z, t) and phase B(...
INTRODUCTION 7
is used extensively for this purpose. This equation is given by
data = (instrument function) convolved (inf...
8 INTRODUCTION
alone in which multiple scattering is (assumed to be) negligible. This basis for
the imaging equation is ex...
INTRODUCTION 9
by the accuracy of the point spread function. Image fuzziness is related to the
physical model used to desc...
10 INTRODUCTION
Suppose the object plane is denoted by the function f(x, y), then from (i)
above we can say that the scatt...
INTRODUCTION 11
Figure 1: An incoherent optical image (above) and a coherent (Synthetic Aper-
ture Radar) image of the sam...
12 INTRODUCTION
represented by a function of two variables, f(x, y) say, which gives a number
z = f(x, y) corresponding to...
INTRODUCTION 13
can be reconstructed exactly from its digital form as long as the sampling
frequency (i.e. samples per lin...
14 INTRODUCTION
Figure 2: A digital image sampled using (from left to right) 128x128, 64x64,
32x32 and 16x16 pixels.
Figur...
INTRODUCTION 15
floating point arithmetic. A floating point field can of course be quantized for
display purposes and anal...
16 INTRODUCTION
The restoration/reconstruction problem is concerned with the recovery of in-
formation encoded in an image...
INTRODUCTION
About this Book
17
This book establishes the underlying physical principles linking different imag-
ing metho...
18 INTRODUCTION
as solutions to programming questions given at the end of each of the four
main parts of the book. The sof...
INTRODUCTION
Image restoration and reconstruction
19
Concerned with processes that aim to recover the information containe...
20 INTRODUCTION
by the phase information of the object function being 'mixed' with the point
spread function (via the conv...
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Jonahtan m. blackledge_-_digital_image_processing._mathematical_and_computational_methods
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