william k. pratt - digital image processing 2007

DIGITAL IMAGE
PROCESSING
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DIGITAL IMAGE
PROCESSING
PIKS Scientific Inside
Fourth Edition
WILLIAM K. PRATT
PixelSoft, Inc.
Los Altos, California
WILEY-INTERSCIENCE
A John Wiley & Sons, Inc., Publication
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About the cover:
The first image on the left is the
peppers_gamma original color image.
The second image is the edge map of the luma component of the first image produced by a derivative of
Gaussian edge detector.
The third image is the
cat original color image.
The fourth image is the spatial gain image of the luma component of the
cat image produced by a Wallis
statistical differencing operator.
The fifth image is the result of Wallis processing on the luma component and amplitude stretching of the
chrominance components of the
cat image.
The lower right image is a sharpened version of the original image obtained by subtracting an amplitude
weighted version of the blurred image from a weighted version of the original image. The processing
technique is called unsharp masking.

Copyright © 2007 by John Wiley & Sons, Inc., All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
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Library of Congress Cataloging-in-Publication Data:
Pratt, William K.
Digital image processing : PIKS Scientific inside / William K. Pratt.—, 4th ed.
p. cm.
“A Wiley-Interscience publication.”
Includes bibliographical references and index.

ISBN: 978-0-471-76777-0
1. Image processing—Digital techniques. I. Title.
TA1632.P7 2007
621.36'7—dc22 2006046397
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1
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To my wife, Shelly,
whose image needs no enhancement
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vii
CONTENTS
Preface xiii
Acknowledgments xvii
PART 1 CONTINUOUS IMAGE CHARACTERIZATION 1
1 Continuous Image Mathematical Characterization 3
1.1 Image Representation, 3
1.2 Two-Dimensional Systems, 5
1.3 Two-Dimensional Fourier Transform, 10
1.4 Image Stochastic Characterization, 14
2 Psychophysical Vision Properties 23
2.1 Light Perception, 23
2.2 Eye Physiology, 26
2.3 Visual Phenomena, 29
2.4 Monochrome Vision Model, 33
2.5 Color Vision Model, 39
3 Photometry and Colorimetry 45
3.1 Photometry, 45
3.2 Color Matching, 49

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viii CONTENTS
3.3 Colorimetry Concepts, 54
3.4 Tristimulus Value Transformation, 61
3.5 Color Spaces, 63
PART 2 DIGITAL IMAGE CHARACTERIZATION 89
4 Image Sampling and Reconstruction 91
4.1 Image Sampling and Reconstruction Concepts, 91
4.2 Monochrome Image Sampling Systems, 99
4.3 Monochrome Image Reconstruction Systems, 110
4.4 Color Image Sampling Systems, 119
5 Image Quantization 127
5.1 Scalar Quantization, 127
5.2 Processing Quantized Variables, 133
5.3 Monochrome and Color Image Quantization, 136
PART 3 DISCRETE TWO-DIMENSIONAL PROCESSING 145
6 Discrete Image Mathematical Characterization 147
6.1 Vector-Space Image Representation, 147
6.2 Generalized Two-Dimensional Linear Operator, 149
6.3 Image Statistical Characterization, 153
6.4 Image Probability Density Models, 158
6.5 Linear Operator Statistical Representation, 162
7 Superposition and Convolution 165
7.1 Finite-Area Superposition and Convolution, 165
7.2 Sampled Image Superposition and Convolution, 174
7.3 Circulant Superposition and Convolution, 181
7.4 Superposition and Convolution Operator Relationships, 184
8 Unitary Transforms 189
8.1 General Unitary Transforms, 189
8.2 Fourier Transform, 193

8.3 Cosine, Sine and Hartley Transforms, 199
8.4 Hadamard, Haar and Daubechies Transforms, 204
8.5 Karhunen–Loeve Transform, 211
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CONTENTS ix
9 Linear Processing Techniques 217
9.1 Transform Domain Processing, 217
9.2 Transform Domain Superposition, 220
9.3 Fast Fourier Transform Convolution, 225
9.4 Fourier Transform Filtering, 233
9.5 Small Generating Kernel Convolution, 241
PART 4 IMAGE IMPROVEMENT 245
10 Image Enhancement 247
10.1 Contrast Manipulation, 248
10.2 Histogram Modification, 259
10.3 Noise Cleaning, 267
10.4 Edge Crispening, 284
10.5 Color Image Enhancement, 291
10.6 Multispectral Image Enhancement, 298
11 Image Restoration Models 307
11.1 General Image Restoration Models, 307
11.2 Optical Systems Models, 310
11.3 Photographic Process Models, 314
11.4 Discrete Image Restoration Models, 322
12 Image Restoration Techniques 329
12.1 Sensor and Display Point Nonlinearity Correction, 329
12.2 Continuous Image Spatial Filtering Restoration, 335
12.3 Pseudoinverse Spatial Image Restoration, 345
12.4 SVD Pseudoinverse Spatial Image Restoration, 359
12.5 Statistical Estimation Spatial Image Restoration, 364

12.6 Constrained Image Restoration, 369
12.7 Blind Image Restoration, 373
12.8 Multi-Plane Image Restoration, 379
13 Geometrical Image Modification 387
13.1 Basic Geometrical Methods, 387
13.2 Spatial Warping, 400
13.3 Perspective Transformation, 404
13.4 Camera Imaging Model, 407
13.5 Geometrical Image Resampling, 410
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x CONTENTS
PART 5 IMAGE ANALYSIS 419
14 Morphological Image Processing 421
14.1 Binary Image Connectivity, 421
14.2 Binary Image Hit or Miss Transformations, 424
14.3 Binary Image Shrinking, Thinning, Skeletonizing and Thickening, 431
14.4 Binary Image Generalized Dilation and Erosion, 442
14.5 Binary Image Close and Open Operations, 453
14.6 Gray Scale Image Morphological Operations, 455
15 Edge Detection 465
15.1 Edge, Line and Spot Models, 465
15.2 First-Order Derivative Edge Detection, 471
15.3 Second-Order Derivative Edge Detection, 492
15.4 Edge-Fitting Edge Detection, 506
15.5 Luminance Edge Detector Performance, 508
15.6 Color Edge Detection, 522
15.7 Line and Spot Detection, 529
16 Image Feature Extraction 535
16.1 Image Feature Evaluation, 535
16.2 Amplitude Features, 537

16.3 Transform Coefficient Features, 542
16.4 Texture Definition, 545
16.5 Visual Texture Discrimination, 547
16.6 Texture Features, 555
17 Image Segmentation 579
17.1 Amplitude Segmentation, 580
17.2 Clustering Segmentation, 587
17.3 Region Segmentation, 590
17.4 Boundary Segmentation, 595
17.5 Texture Segmentation, 611
17.6 Segment Labeling, 613
18 Shape Analysis 623
18.1 Topological Attributes, 623
18.2 Distance, Perimeter and Area Measurements, 625
18.3 Spatial Moments, 631
18.4 Shape Orientation Descriptors, 643
18.5 Fourier Descriptors, 645
18.6 Thinning and Skeletonizing, 647
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CONTENTS xi
19 Image Detection and Registration 651
19.1 Template Matching, 651
19.2 Matched Filtering of Continuous Images, 655
19.3 Matched Filtering of Discrete Images, 662
19.4 Image Registration, 664
PART 6 IMAGE PROCESSING SOFTWARE 679
20 PIKS Image Processing Software 681
20.1 PIKS Functional Overview, 681
20.2 PIKS Scientific Overview, 704
21 PIKS Image Processing Programming Exercises 715

21.1 Program Generation Exercises, 716
21.2 Image Manipulation Exercises, 717
21.3 Color Space Exercises, 718
21.4 Region-of-Interest Exercises, 720
21.5 Image Measurement Exercises, 721
21.6 Quantization Exercises, 722
21.7 Convolution Exercises, 723
21.8 Unitary Transform Exercises, 724
21.9 Linear Processing Exercises, 725
21.10 Image Enhancement Exercises, 726
21.11 Image Restoration Models Exercises, 728
21.12 Image Restoration Exercises, 729
21.13 Geometrical Image Modification Exercises, 729
21.14 Morphological Image Processing Exercises, 730
21.15 Edge Detection Exercises, 732
21.16 Image Feature Extraction Exercises, 733
21.17 Image Segmentation Exercises, 734
21.18 Shape Analysis Exercises, 735
21.19 Image Detection and Registration Exercises, 735
Appendix 1 Vector-Space Algebra Concepts 737
Appendix 2 Color Coordinate Conversion 753
Appendix 3 Image Error Measures 759
Appendix 4 PIKS Compact Disk 761
Bibliography 763
Index 769
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xii CONTENTS
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xiii
PREFACE

In January 1978, I began the preface to the first edition of Digital Image Processing
with the following statement:
“The field of image processing has grown considerably during the past
decade with the increased utilization of imagery in myriad applications
coupled with improvements in the size, speed and cost effectiveness of dig-
ital computers and related signal processing technologies. Image processing
has found a significant role in scientific, industrial, space and government
applications.”
In January 1991, in the preface to the second edition, I stated:
“Thirteen years later as I write this preface to the second edition, I find
the quoted statement still to be valid. The 1980s have been a decade of sig-
nificant growth and maturity in this field. At the beginning of that decade,
many image processing techniques were of academic interest only; their
execution was too slow and too costly. Today, thanks to algorithmic and
implementation advances, image processing has become a vital cost-effec-
tive technology in a host of applications.”
In August 2000, in the preface to the third edition, I wrote:
“Now, in this beginning of the twenty-first century, image processing
has become a mature engineering discipline. But advances in the theoreti-
cal basis of image processing continue. Some of the reasons for this third
edition of the book are to correct defects in the second edition, delete con-
tent of marginal interest, and add discussion of new, important topics.
Another motivating factor is the inclusion of interactive, computer display
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xiv PREFACE
imaging examples to illustrate image processing concepts. Finally, this
third edition includes computer programming exercises to bolster its theo-
retical content. These exercises can be implemented using the Program-
mer’s Imaging Kernel System (PIKS) application program interface (API).
PIKS is an International Standards Organization (ISO) standard library of

image processing operators and associated utilities.”
Again, for a fourth time, a new edition of Digital Image Processing is offered to
the image processing community. Why? One reason is because advances in the the-
oretical aspects of image processing technology continue at a rapid rate. For exam-
ple, in the year 2005, the IEEE Transactions on Image Processing published 2191
pages of research papers. The IEEE Transactions on Pattern Analysis and Machine
Intelligence was in close second place in 2005 with 2002 published pages. Add to
that the content of independent journals, such as the John Wiley & Sons Interna-
tional Journal of Imaging Systems and Technology plus numerous image processing
technical conferences. There is an enormous amount of new image processing tech-
nology to be absorbed. I have tried to act as a publishing filter by culling through the
image processing literature since the third edition was published in 2002, and then
abstracting what I think are the most important contributions. Details follow.
Another reason for publication of the fourth edition of Digital Image Processing
is to make available, at no cost, the PIKS Scientific API for educational purposes
and for industrial software development. The PIKS Scientific software is on a CD
affixed to the back cover of this book. PIKS Scientific includes implementations of
most of the high-level operators in this book.
The book is intended to be an “industrial strength” introduction to digital image
processing to be used as a text for an electrical engineering or computer science
course on the subject. Also, it can be used as a reference manual for scientists who
are engaged in image processing research, developers of image processing hardware
and software systems, and practicing engineers and scientists who use image pro-
cessing as a tool in their applications. Mathematical derivations are provided for
most algorithms. The reader is assumed to have a basic background in linear system
theory, vector space algebra and random processes. Proficiency in C language pro-
gramming is necessary for execution of the image processing programming exer-
cises using PIKS.
The book is divided into six parts. The first three parts cover the basic technolo-
gies that are needed to support image processing applications.

Part 1 contains three chapters concerned with the characterization of continuous
images. Topics include the mathematical representation of continuous images, the
psychophysical properties of human vision, and photometry and colorimetry. No
substantial changes have been made to this fundamental material.
In Part 2, image sampling and quantization techniques are explored along with
the mathematical representation of discrete images. A new section on Color Image
Sampling Systems, such as the Bayer color filter, has been added to Chapter 4.
Part 3 discusses two-dimensional signal processing techniques, including general
linear operators and unitary transforms such as the Fourier, Hadamard, Daubechies
and Karhunen–Loeve transforms. The final chapter in Part 3 analyzes and compares
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PREFACE xv
linear processing techniques implemented by direct convolution and Fourier domain
filtering.
The next two parts of the book cover the two principal application areas of image
processing: Image Improvement and Image Analysis.
Part 4 presents a discussion of image enhancement and restoration techniques,
including restoration models, point and spatial restoration and geometrical image
modification. Chapter 10 on Image Enhancement contains new material on Contrast
Manipulation, Histogram Modification Noise Cleaning and Color Image Enhance-
ment. Content on Blind Image Restoration and Multi-Plane Image Restoration has
been added to Chapter 12, Image Restoration Techniques. A new section on Polar
Coordinate Conversion has been included in the chapter on Geometrical Image
Modification.
Part 5, entitled Image Analysis, concentrates on the extraction of information
from an image. Specific topics include morphological image processing, edge
detection, image feature extraction, image segmentation, object shape analysis and
object detection. Additional material on Structuring Element Decomposition has
been included in the Morphological Image Processing chapter. The sections on First
Order Derivative Edge Detection and Color Edge Detection in Chapter 15 have

been augmented. Material has been added on Texture Features in Chapter 16. In the
chapter on Image Segmentation, material has been added on Amplitude, Region,
Boundary and Texture Segmentation. New content on Distance, Perimeter and Area
Measurements has been added to the Shape Analysis chapter. A new section on
Non-morphological Thinning and Skeletonizing has been included in the chapter.
Finally, new material has been added on Template Matching and Image Registration
in Chapter 19.
Part 6 discusses the software implementation of image processing applications.
This part describes the PIKS API and explains its use as a means of implementing
image processing algorithms. Image processing programming exercises are included
in Part 6.
Throughout the first 19 chapters on the theoretical basis of image processing, up-
to-date references of papers judged to be of significance have been included as a
guide for extended study.
Although readers should find this book reasonably comprehensive, many impor-
tant topics allied to the field of digital image processing have been omitted to limit
the size and cost of the book. Among the most prominent omissions are the topics of
pattern recognition, image reconstruction from projections, image understanding,
image coding, scientific visualization and computer graphics.
W
ILLIAM K. PRATT
Los Altos, California
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xvii
ACKNOWLEDGMENTS
The following is a cumulative acknowledgment of all who have contributed to the
four editions of Digital Image Processing.
The first edition of this book was written while I was a professor of electrical
engineering at the University of Southern California (USC). Image processing

research at USC began in 1962 on a very modest scale, but the program increased in
size and scope with the attendant international interest in the field. In 1971, Dr.
Zohrab Kaprielian, then dean of engineering and vice president of academic
research and administration, announced the establishment of the USC Image Pro-
cessing Institute. This environment contributed significantly to the preparation of
the first edition. I am deeply grateful to Professor Kaprielian for his role in provid-
ing university support of image processing and for his personal interest in my career.
Also, I wish to thank the following past and present members of the Institute’s
scientific staff who rendered invaluable assistance in the preparation of the first-
edition manuscript: Jean-François Abramatic, Harry C. Andrews, Lee D. Davisson,
Olivier D. Faugeras, Werner Frei, Ali Habibi, Anil K. Jain, Richard P. Kruger,
Nasser E. Nahi, Ramakant Nevatia, Keith Price, Irving S. Reed, Guner S. Robinson,
Alexander A. Sawchuk and Lloyd R. Welsh.
In addition, I sincerely acknowledge the technical help of my graduate students at
USC during preparation of the first edition: Ikram Abdou, Behnam Ashjari,
Wen-Hsiung Chen, Faramarz Davarian, Michael N. Huhns, Kenneth I. Laws, Sang
Uk Lee, Clanton Mancill, Nelson Mascarenhas, Clifford Reader, John Roese and
Robert H. Wallis.
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xviii ACKNOWLEDGMENTS
The first edition was the outgrowth of notes developed for the USC course Image
Processing. I wish to thank the many students who suffered through the early ver-
sions of the notes for their valuable comments. Also, I appreciate the reviews of the
notes provided by Harry C. Andrews, Werner Frei, Ali Habibi and Ernest L. Hall,
who taught the course.
With regard to the first edition, I wish to offer words of appreciation to the
Information Processing Techniques Office of the Advanced Research Projects
Agency, directed by Larry G. Roberts, which provided partial financial support of
my research at USC.
During the academic year 1977–1978, I performed sabbatical research at the

Institut de Recherche d’Informatique et Automatique in LeChesney, France, and at
the Université de Paris. My research was partially supported by these institutions,
USC and a Guggenheim Foundation fellowship. For this support, I am indebted.
I left USC in 1979 with the intention of forming a company that would put some
of my research ideas into practice. Toward that end, I joined a startup company,
Compression Labs, Inc., of San Jose, California. There I worked on the development
of facsimile and video coding products with Dr. Wen-Hsiung Chen and Dr. Robert
H. Wallis. Concurrently, I directed a design team that developed a digital image
processor called VICOM. The early contributors to its hardware and software design
were William Bryant, Howard Halverson, Stephen K. Howell, Jeffrey Shaw and
William Zech. In 1981, I formed Vicom Systems, Inc., of San Jose, California, to
manufacture and market the VICOM image processor. Many of the photographic
examples in this book were processed on a VICOM.
Work on the second edition began in 1986. In 1988, I joined Sun Microsystems,
of Mountain View, California. At Sun, I collaborated with Stephen A. Howell and
Ihtisham Kabir on the development of image processing software. During my time
at Sun, I participated in the specification of the Programmers Imaging Kernel
application program interface, which was made an ISO standard in 1994. Much of
the PIKS content is present in this book. Some of the principal contributors to the
PIKS standard include Timothy Butler, Adrian Clark, Patrick Krolak and Gerard A.
Paquette. The second edition of Digital Image Processing was published in 1991.
In 1993, I formed PixelSoft, Inc., of Los Altos, California, to commercialize the
PIKS standard. PixelSoft developed an implementation of the PIKS Foundation
version of the PIKS standard in 1994. PIKS Foundation is the base subset of the
image processing technology in the standard. Contributors to its development
include Timothy Butler, Larry R. Hubble and Gerard A. Paquette.
I joined Photon Dynamics, Inc., of San Jose, California, a manufacturer of
machine vision equipment for the inspection of electronics displays and printed
circuit boards in 1996. There, I collaborated with Larry R. Hubble, Sunil S. Sawkar
and Gerard A. Paquette on the development of several hardware and software

products based on PIKS.
In 1998, I began writing the third edition of Digital Image Processing. The major
purpose for that edition was to incorporate the significant amount of research
advancement in digital image processing since publication of the second edition. A
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ACKNOWLEDGMENTS xix
secondary purpose was to entice users to adopt PIKS for educational purposes and
application development. Toward that end, PixelSoft developed an implementation
of the PIKS Core version of the standard. PIKS Core incorporates all of the basic
software building blocks for application development. PIKS Core was included with
each copy of the third edition. Larry R. Hubble and Gerard A. Paquette contributed
significantly to PixelSoft’s PIKS Core implementation.
I began to write a fourth edition of Digital Image Processing in late 2004. The
principal purpose for the fourth edition was to chronicle research advances since
publication of the third edition. Another motivating factor was to further promote
the PIKS standard. PixelSoft has developed the PIKS Scientific version of the stan-
dard. PIKS Scientific implements most of the high-level PIKS operators. It is
included with the fourth edition. Gerard A. Paquette was instrumental in coding the
bulk of PIKS Scientific. His effort is gratefully acknowledged.
I offer my appreciation to Ray Schmidt, who was responsible for many photo-
graphic reproductions in the first edition of the book. I thank Kris Pendelton, who
created much of the line art of the first and second editions. The third edition, and
this fourth edition, were “type set” using Adobe’s FrameMaker product. Tarlochan
Nahal did the bulk of the initial type setting of the third edition. The company Laser
Words performed the final publication rendering. Starting with this base, I com-
posed most of the fourth edition text. FrameMaker help was provided by Louis
Angulo and Paul McJones. Many thanks to Larry R. Hubble, who developed the
PIKS software CDs for the third and fourth editions.
Also, thanks are given to readers of the first three editions who reported errors
both typographical and mental.

I wish to thank all those previously cited, and many others too numerous to
mention, for their assistance in the academic and industrial phases of my career. I
spent the first 14 years of my post doctoral career as a professor of electrical
engineering at USC. It was an exciting period of research investigation. I then
moved on to the challenges of industry. Having participated in the design of
hardware and software products has been an arduous but intellectually rewarding
task. This combination of academic and industrial experience, I believe, has
significantly enriched this fourth edition.
Most of all, I wish to thank my wife, Shelly, for her support in the writing of the
fourth edition.
W. K. P.
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PART 1
CONTINUOUS IMAGE
CHARACTERIZATION
Although this book is concerned primarily with digital, as opposed to analog, image
processing techniques. It should be remembered that most digital images represent
continuous natural images. Exceptions are artificial digital images such as test
patterns that are numerically created in the computer and images constructed by
tomographic systems. Thus, it is important to understand the “physics” of image
formation by sensors and optical systems including human visual perception.
Another important consideration is the measurement of light in order quantitatively
to describe images. Finally, it is useful to establish spatial and temporal
characteristics of continuous image fields, which provide the basis for the
interrelationship of digital image samples. These topics are covered in the following
chapters.

3
1

Digital Image Processing: PIKS Scientific Inside, Fourth Edition, by William K. Pratt
Copyright © 2007 by John Wiley & Sons, Inc.
CONTINUOUS IMAGE
MATHEMATICAL CHARACTERIZATION
In the design and analysis of image processing systems, it is convenient and often
necessary mathematically to characterize the image to be processed. There are two
basic mathematical characterizations of interest: deterministic and statistical. In
deterministic image representation, a mathematical image function is defined and
point properties of the image are considered. For a statistical image representation,
the image is specified by average properties. The following sections develop the
deterministic and statistical characterization of continuous images. Although the
analysis is presented in the context of visual images, many of the results can be
extended to general two-dimensional time-varying signals and fields.
1.1. IMAGE REPRESENTATION
Let represent the spatial energy distribution of an image source of radi-
ant energy at spatial coordinates (x, y), at time t and wavelength . Because light
intensity is a real positive quantity, that is, because intensity is proportional to the
modulus squared of the electric field, the image light function is real and nonnega-
tive. Furthermore, in all practical imaging systems, a small amount of background
light is always present. The physical imaging system also imposes some restriction
on the maximum intensity of an image, for example, film saturation and cathode ray
tube (CRT) phosphor heating. Hence it is assumed that
(1.1-1)
Cxytλ,,,()
λ
0 Cxytλ,,,()A≤<
4 CONTINUOUS IMAGE MATHEMATICAL CHARACTERIZATION
where A is the maximum image intensity. A physical image is necessarily limited in
extent by the imaging system and image recording media. For mathematical sim-
plicity, all images are assumed to be nonzero only over a rectangular region

for which
(1.1-2a)
(1.1-2b)
The physical image is, of course, observable only over some finite time interval.
Thus, let
(1.1-2c)
The image light function is, therefore, a bounded four-dimensional
function with bounded independent variables. As a final restriction, it is assumed
that the image function is continuous over its domain of definition.
The intensity response of a standard human observer to an image light function is
commonly measured in terms of the instantaneous luminance of the light field as
defined by
(1.1-3)
where represents the relative luminous efficiency function, that is, the spectral
response of human vision. Similarly, the color response of a standard observer is
commonly measured in terms of a set of tristimulus values that are linearly propor-
tional to the amounts of red, green and blue light needed to match a colored light.
For an arbitrary red–green–blue coordinate system, the instantaneous tristimulus
values are
(1.1-4a)
(1.1-4b)
(1.1-4c)
where , , are spectral tristimulus values for the set of red, green
and blue primaries. The spectral tristimulus values are, in effect, the tristimulus
values required to match a unit amount of narrowband light at wavelength . In a
multispectral imaging system, the image field observed is modeled as a spectrally
L
x
– xL
x

≤≤
L
y
– yL
y
≤≤
T– tT≤≤
Cxytλ,,,()
Yxyt,,() Cxytλ,,,()V λ()λd
0
∞
∫
=
V λ()
Rxyt,,() Cxytλ,,,()R
S
λ() λd
0
∞
∫
=
Gxyt,,() Cxytλ,,,()G
S
λ() λd
0
∞
∫
=
Bxyt,,() Cxytλ,,,()B
S

λ() λd
0
∞
∫
=
R
S
λ() G
S
λ() B
S
λ()
λ