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Front Matter
Published: 2012
DOI: 10.1117/
This section contains the series introduction, series list, preface, table of contents, and glossary of symbols.

Library of Congress Cataloging-in-Publication Data

Iftekharuddin, Khan M. (Khan Mohammad), 1966-

Field guide to image processing / Khan M. Iftekharuddin, Abdul A. Awwal.

p. cm. – (Field field guides; FG25)

Includes bibliographical references and index.

ISBN 978-0-8194-9021-6

1. Image processing. 2. Image compression. I. Awwal Abdul A. S. II. Title.

TA1637.I34 2012



Published by


P.O. Box 10

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Phone: +1.360.676.3290

Fax: +1.360.647.1445



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Printed in the United States of America.

First printing


Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at

John E. Greivenkamp,Series Editor

College of Optical Sciences

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:

Adaptive Optics, Robert Tyson & Benjamin Frazier

Atmospheric Optics, Larry Andrews

Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich

Diffractive Optics, Yakov Soskind

Geometrical Optics, John Greivenkamp

Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel

Image Processing, Khan Iftekharuddin & Abdul Awwal

Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels

Interferometric Optical Testing, Eric Goodwin & Jim Wyant

Laser Pulse Generation, Rüdiger Paschotta

Lasers, Rüdiger Paschotta

Microscopy, Tomasz Tkaczyk

Optical Fabrication, Ray Williamson

Optical Fiber Technology, Rüdiger Paschotta

Optical Lithography, Chris Mack

Optical Thin Films, Ronald Willey

Polarization, Edward Collett

Probability, Random Processes, and Random Data Analysis, Larry Andrews & Ronald Phillips

Radiometry, Barbara Grant

Special Functions for Engineers, Larry Andrews

Spectroscopy, David Ball

Visual and Ophthalmic Optics, Jim Schwiegerling

Wave Optics, Dan Smith

Field Guide to Visual and Ophthalmic Optics

Image-processing specialists use concepts and tools to solve practical problems. Some of these tools are linear, while others are nonlinear. The specialist develops a recipe for solving this problem by combining various tools in different sequences. To solve a given problem, one recipe may call for image preprocessing followed by feature extraction and finally object recognition. Another recipe may skip the preprocessing and feature extraction, and instead perform the recognition directly using a matched filter on the raw image data. Once a recipe is selected, it may require a number of parameters, that, depending on the practical constraint, may need to be optimized to obtain the best result given the image quality, dimension, or content.

In this Field Guide, we introduce a set of basic image-processing concepts and tools: image transforms and spatial domain filtering; point processing techniques; the Fourier transform and its properties and applications; image morphology; the wavelet transform; and image compression and data redundancy techniques. From these discussions, readers can gain an understanding of how to apply these various tools to image-processing problems. However, true mastery is only gained when one has an opportunity to work with some of these tools.

We acknowledge our gratitude to our family members and parents for giving us the opportunity to work on this book. In particular, Dr. Iftekharuddin would like thank Tasnim and Labib for their constant support, and parents Muhammad Azharuddin and Khaleda Khanam for their encouragement; Dr. Awwal would like to thank Syeda, Ibrahim, and Maryam for their constant support, and parents Mohammad Awwal and Saleha Khatoon for their encouragement.

Khan Iftekharuddin

Old Dominion University

Abdul Awwal

Lawrence Livermore National Laboratory

Table of Contents

Glossary of Symbols and Notation ix

Image-Processing Basics 1

Image Processing Overview 1

Random Signals 2

General Image-Processing System 3

Simple Image Model 4

Sampling and Quantization 5

Spatial-Domain Filtering 6

Image Transforms 6

Image Scaling and Rotation 7

Point Processing 8

Spatial-Domain Convolution Filters 9

Convolution 10

Linear Filters 11

Gradient Filters 13

Histogram Processing 15

Frequency-Domain Filtering 17

The Fourier Transform 17

Discrete Fourier Transform 18

Properties of the Fourier Transform 19

Convolution and Correlation in the Fourier Domain 20

More Properties of the Fourier Transform 21

Spectral Density 22

Properties of the Discrete Fourier Transform 23

Discrete Correlation and Convolution 26

Circular Convolution and Zero Padding 27

Matched Filtering 28

Filtering with the Fourier Transform 29

Low-Pass and High-Pass Filtering 30

Sampling 31

Spectrum of a Sampled Signal 32

More Sampling 33

Spectrum of a Finite Periodic Signal 34

Image Restoration 36

Image Restoration 36

Linear Space-Invariant Degradation 37

Discrete Formulation 38

Algebraic Restoration 39

Motion Blur 40

Inverse Filtering 42

Weiner Least-Squares Filtering 43

Segmentation and Clustering 44

Image Segmentation and Clustering 44

Hough Transform 46

Clustering 48

Image Morphology 50

Erosion and Dilation 50

Opening and Closing 52

Hit-or-Miss Transform 53

Thinning 54

Skeletonization 55

Gray-Level Morphology 56

Training a Structuring Element 57

Time-Frequency-Domain Processing 58

Wavelet Transform 58

Types of Fourier Transforms 59

Wavelet Basis 60

Continuous Wavelet Transform 61

Wavelet Series Expansion 62

Discrete Wavelet Transform 63

Subband Coding 64

Mirror Filter and Scaling Vector 65

Wavelet Vector and 1D DWT Computation 66

2D Discrete Wavelet Transform 67

Image Compression 69

Data Redundancy 69

Error-Free Compression 70

Spatial Redundancy 71

Differential Encoding Example 72

Block Truncation Coding: Lossy Compression 73

Discrete Cosine Transform 74

JPEG Compression 75

Equation Summary 76

Biography 81

Index 82

Glossary of Symbols and Notation


Admissibility condition

e p, q (t)

Windowed Fourier transform






Fourier transform operator


1D discrete signal


Correlation operation

F n

Fourier series expansion


Discrete Fourier transform of 1D signal

F(u, v)

Fourier-transformed image


Convolution operation

f(x, y)


f^(x, y)

Restored (approximate) image

G(n, m)

Discrete Fourier transform of 2D signal


Degradation model

H −1

Inverse filter

H(u, v)

2D filter in the frequency domain

h(x, y)

2D filter (transfer function) in the spatial domain




Hit-and-miss transform

i(x, y)





Degraded image

n(x, y)

2D noise in spatial domain

p x, y (x, y)

Probability density function (PDF)




rect function

R f f (x, y)


R f g (x, y)


r(x, y)


sinc(a u)

sinc function


Transformation matrix

W f (a, b)

Wavelet transform

δ m, n

2D discrete Kronecker delta


Delta function




Standard deviation


1D scaling vector

Ψ a, b (x)

Wavelet basis function


1D wavelet vector


Image processing

Image compression

Image filtering

Linear filtering

Electronic filtering

Filtering (signal processing)

Optical filters

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