Handbook of Medical Imaging: Processing and Analysis Management pdf

HANDBOOK OF
MEDICAL IMAGING
Editorial Advisory Board
Dr. William Brody Dr. Elias Zerhouni
President Chairman, Department of Radiology
Johns Hopkins University and Radiological Science
Johns Hopkins Medical Institutions
Section Editors
Dr. Rangaraj M. Rangayyan Dr. Richard A. Robb
Department of Electrical and Computer Engineering Director, Biomedical Imaging Resource
University of Calgary Mayo Foundation
Dr. Roger P. Woods Dr. H. K. Huang
Division of Brain Mapping Department of Radiology
UCLA School of Medicine Childrens Hospital of Los Angeles/
University of Southern California
Academic Press Series in Biomedical Engineering
Joseph Bronzino, Series Editor
The focus of this series will be twofold. First, the series will produce a set of core text/
references for biomedical engineering undergraduate and graduate courses. With
biomedical engineers coming from a variety of engineering and biomedical backgrounds,
it will be necessary to create new cross-disciplinary teaching and self-study books. Secondly,
the series will also develop handbooks for each of the major subject areas of biomedical
engineering.
Joseph Bronzino, the series editor, is one of the most renowned biomedical engineers in the
world. He is the Vernon Roosa Professor of Applied Science at Trinity College in Hartford,
Connecticut.
HANDBOOK OF
MEDICAL IMAGING
PROCESSING AND ANALYSIS
Editor-in-Chief
Isaac N. Bankman, PhD

Applied Physics Laboratory
Johns Hopkins University
Laurel, Maryland
San Diego / San Francisco / New York / Boston / London / Sydney / Tokyo
This book is printed on acid-free paper. ?
s
Copyright # 2000 by Academic Press
All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means,
electronic or mechanical, including photocopy, recording, or any information storage and retrieval
system, without permission in writing from the publisher.
Requests for permission to make copies of any part of the work should be mailed to: Permissions
Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida, 32887-6777.
ACADEMIC PRESS
A Harcourt Science and Technology Company
525 B Street, Suite 1900, San Diego, CA 92101-4495, USA

Academic Press
Harcourt Place, 32 Jamestown Road, London NW1 7BY, UK
Library of Congress Catalog Card Number: 00-101315
International Standard Book Number: 0-12-077790-8
Printed in the United States of America
00 01 02 03 04 COB 9 8 7 6 5 4 3 2 1
To Lisa, Judy, and Danny

Contents
Foreword ix
Preface xi
Contributors xiii
I Enhancement

1 Fundamental Enhancement Techniques Raman B. Paranjape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2 Adaptive Image Filtering Carl-Fredrik Westin, Hans Knutsson, and Ron Kikinis. . . . . . . . . . . . . . . . . . . . . . .
19
3 Enhancement by Multiscale Nonlinear Operators Andrew Laine and Walter Huda . . . . . . . . . . . . . . . . . . . .
33
4 Medical Image Enhancement with Hybrid Filters Wei Qian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
II Segmentation
5 Overview and Fundamentals of Medical Image Segmentation Jadwiga Rogowska . . . . . . . . . . . . . . . . . . . . .
69
6 Image Segmentation by Fuzzy Clustering: Methods and Issues Melanie A. Sutton, James C. Bezdek,
Tobias C. Cahoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
7 Segmentation with Neural Networks Axel Wismu
È
ller, Frank Vietze, and Dominik R. Dersch . . . . . . . . . . . . . .
107
8 Deformable Models Tim McInerney and Demetri Terzopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
127
9 Shape Constraints in Deformable Models Lawrence H. Staib, Xiaolan Zeng, James S. Duncan, Robert T. Schultz,
and Amit Chakraborty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
147
10 Gradient Vector Flow Deformable Models Chenyang Xu and Jerry L. Prince . . . . . . . . . . . . . . . . . . . . . . . .
159
11 Fully Automated Hybrid Segmentation of the Brain M. Stella Atkins and Blair T. Mackiewich. . . . . . . . . . . . .
171
12 Volumetric Segmentation Alberto F. Goldszal and Dzung L. Pham . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
185
13 Partial Volume Segmentation with Voxel Histograms David H. Laidlaw, Kurt W. Fleischer, and Alan H. Barr . .

195
III Quanti®cation
14 Two-Dimensional Shape and Texture Quanti®cation Isaac N. Bankman, Thomas S. Spisz, and Sotiris Pavlopoulos
215
15 Texture Analysis in Three Dimensions as a Cue to Medical Diagnosis Vassili A. Kovalev and Maria Petrou . . . .
231
16 Computational Neuroanatomy Using Shape Transformations Christos Davatzikos . . . . . . . . . . . . . . . . . . . .
249
17 Arterial Tree Morphometry Roger Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
261
18 Image-Based Computational Biomechanics of the Musculoskeletal System Edmund Y. Chao, N. Inoue, J.J. Elias,
and F.J. Frassica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
285
19 Three-Dimensional Bone Angle Quanti®cation Jens A. Richolt, Nobuhiko Hata, Ron Kikinis, Jens Kordelle,
and Michael B. Millis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
299
20 Database Selection and Feature Extraction for Neural Networks Bin Zheng . . . . . . . . . . . . . . . . . . . . . . . . .
311
21 Quantitative Image Analysis for Estimation of Breast Cancer Risk Martin J. Yaffe, Jeffrey W. Byng,
and Norman F. Boyd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
323
22 Classi®cation of Breast Lesions in Mammograms Yulei Jiang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
341
23 Quantitative Analysis of Cardiac Function Osman Ratib. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
359
24 Image Processing and Analysis in Tagged Cardiac MRI William S. Kerwin, Nael F. Osman, and Jerry L. Prince .
375
25 Image Interpolation and Resampling Philippe The
Â
venaz, Thierry Blu, and Michael Unser . . . . . . . . . . . . . . . .

393
IV Registration
26 Physical Basis of Spatial Distortions in Magnetic Resonance Images Peter Jezzard . . . . . . . . . . . . . . . . . . . . .
425
27 Physical and Biological Bases of Spatial Distortions in Positron Emission Tomography Images Magnus Dahlbom
and Sung-Cheng (Henry) Huang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
439
28 Biological Underpinnings of Anatomic Consistency and Variability in the Human Brain N. Tzourio-Mazoyer,
F. Crivello, M. Joliot, and B. Mazoyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
449
29 Spatial Transformation Models Roger P. Woods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
465
vii
30 Validation of Registration Accuracy Roger P. Woods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
31 Landmark-Based Registration Using Features Identi®ed Through Differential Geometry Xavier Pennec,
Nicholas Ayache, and Jean-Philippe Thirion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
32 Image Registration Using Chamfer Matching Marcel Van Herk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
33 Within-Modality Registration Using Intensity-Based Cost Functions Roger P. Woods. . . . . . . . . . . . . . . . . . . . 529
34 Across-Modality Registration Using Intensity-Based Cost Functions Derek L.G. Hill and David J. Hawkes . . . . . 537
35 Talairach Space as a Tool for Intersubject Standardization in the Brain Jack L. Lancaster and Peter T. Fox . . . . . 555
36 Warping Strategies for Intersubject Registration Paul M. Thompson and Arthur W. Toga . . . . . . . . . . . . . . . . . 569
37 Optimizing the Resampling of Registered Images William F. Eddy and Terence K. Young . . . . . . . . . . . . . . . . . 603
38 Clinical Applications of Image Registration Robert Knowlton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
39 Registration for Image-Guided Surgery Eric Grimson and Ron Kikinis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
40 Image Registration and the Construction of Multidimensional Brain Atlases Arthur W. Toga
and Paul M. Thompson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
V Visualization
41 Visualization Pathways in Biomedicine Meiyappan Solaiyappan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
42 Three-Dimensional Visualization in Medicine and Biology Richard A. Robb . . . . . . . . . . . . . . . . . . . . . . . . . 685
43 Volume Visualization in Medicine Arie E. Kaufman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713

44 Fast Isosurface Extraction Methods for Large Image Data Sets Yarden Livnat, Steven G. Parker,
and Christopher R. Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
45 Morphometric Methods for Virtual Endoscopy Ronald M. Summers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747
VI Compression Storage and Communication
46 Fundamentals and Standards of Compression and Communication Stephen P. Yanek, Quentin E. Dolecek,
Robert L. Holland, and Joan E. Fetter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759
47 Medical Image Archive and Retrieval Albert Wong and Shyh-Liang Lou . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771
48 Image Standardization in PACS Ewa Pietka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783
49 Quality Evaluation for Compressed Medical Images: Fundamentals Pamela Cosman, Robert Gray,
and Richard Olshen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803
50 Quality Evaluation for Compressed Medical Images: Diagnostic Accuracy Pamela Cosman, Robert Gray,
and Richard Olshen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 821
51 Quality Evaluation for Compressed Medical Images: Statistical Issues Pamela Cosman, Robert Gray,
and Richard Olshen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
52 Three-Dimensional Image Compression with Wavelet Transforms Jun Wang and H.K. Huang . . . . . . . . . . . . . 851
53 Medical Image Processing and Analysis Software Thomas S. Spisz and Isaac N. Bankman . . . . . . . . . . . . . . . . 863
Index 895
viii
Foreword
The development of medical imaging over the past three
decades has been truly revolutionary. For example, in cardi-
ology specialized three-dimensional motion estimation
algorithms allow myocardial motion and strain measurements
using tagged cardiac magnetic resonance imaging. In mam-
mography, shape and texture analysis techniques are used to
facilitate the diagnosis of breast cancer and assess its risk.
Three-dimensional volumetric visualization of CT and MRI
data of the spine, internal organs and the brain has become the
standard for routine patient diagnostic care.
What is perhaps most remarkable about these advances in

medical imaging is the fact that the challenges have required
signi®cant innovation in computational techniques for nearly
all aspects of image processing in various ®elds. The use of
multiple imaging modalities on a single patient, for example
MRI and PET, requires sophisticated algorithms for image
registration and pattern matching. Automated recognition
and diagnosis require image segmentation, quanti®cation and
enhancement tools. Algorithms for image segmentation and
visualization are employed broadly through many applications
using all of the digital imaging modalities. And ®nally, the
widespread availability of medical images in digital format has
spurred the search for ef®cient and effective image compres-
sion and communication methods.
Advancing the frontiers of medical imaging requires the
knowledge and application of the latest image manipulation
methods. In Handbook of Medical Imaging, Dr. Bankman has
assembled a comprehensive summary of the state-of-the-art in
image processing and analysis tools for diagnostic and
therapeutic applications of medical imaging. Chapters cover
a broad spectrum of topics presented by authors who are highly
expert in their respective ®elds. For all those who are working
in this exciting ®eld, the Handbook should become a standard
reference text in medical imaging.
William R. Brody
President, John Hopkins
University
ix

Preface
The discoveries of seminal physical phenomena such as X-rays,

ultrasound, radioactivity, and magnetic resonance, and the
development of imaging instruments that harness them have
provided some of the most effective diagnostic tools in
medicine. The medical imaging community is now able to
probe into the structure, function, and pathology of the human
body with a diversity of imaging systems. These systems are
also used for planning treatment and surgery, as well as for
imaging in biology. Data sets in two, three, or more dimensions
convey increasingly vast and detailed information for clinical
or research applications. This information has to be interpreted
in a timely and accurate manner to bene®t health care. The
examination is qualitative in some cases, quantitative in others;
some images need to be registered with each other or with
templates, many must be compressed and archived. To assist
visual interpretation of medical images, the international
imaging community has developed numerous automated
techniques which have their merits, limitations, and realm of
application. This Handbook presents concepts and digital
techniques for processing and analyzing medical images after
they have been generated or digitized. It is organized into six
sections that correspond to the fundamental classes of algo-
rithms: enhancement, segmentation, quanti®cation, registra-
tion, visualization, and a section that covers compression,
storage, and communication. The last chapter describes some
software packages for medical image processing and analysis.
I Enhancement
Enhancement algorithms are used to reduce image noise and
increase the contrast of structures of interest. In images where
the distinction between normal and abnormal tissue is subtle,
accurate interpretation may become dif®cult if noise levels are

relatively high. In many cases, enhancement improves the
quality of the image and facilitates diagnosis. Enhancement
techniques are generally used to provide a clearer image for a
human observer, but they can also form a preprocessing step
for subsequent automated analysis. The chapters in this section
present diverse techniques for image enhancement including
linear, nonlinear, ®xed, adaptive, pixel-based, or multi-scale
methods.
II Segmentation
Segmentation is the stage where a signi®cant commitment is
made during automated analysis by delineating structures of
interest and discriminating them from background tissue. This
separation, which is generally effortless and swift for the
human visual system, can become a considerable challenge in
algorithm development. In many cases the segmentation
approach dictates the outcome of the entire analysis, since
measurements and other processing steps are based on
segmented regions. Segmentation algorithms operate on the
intensity or texture variations of the image using techniques
that include thresholding, region growing, deformable tem-
plates, and pattern recognition techniques such as neural
networks and fuzzy clustering. Hybrid segmentation and
volumetric segmentation are also addressed in this section.
III Quanti®cation
Quanti®cation algorithms are applied to segmented structures
to extract the essential diagnostic information such as shape,
size, texture, angle, and motion. Because the types of
measurement and tissue vary considerably, numerous techni-
ques that address speci®c applications have been developed.
Chapters in this section cover shape and texture quanti®cation

in two- and three-dimensional data, the use of shape
transformations to characterize structures, arterial tree mor-
phometry, image-based techniques for musculoskeletal
biomechanics, image analysis in mammography, and quanti-
®cation of cardiac function. In applications where different
kinds of tissue must be classi®ed, the effectiveness of
quanti®cation depends signi®cantly on the selection of
database and image features, as discussed in this section. A
comprehensive chapter covers the choices and pitfalls of image
interpolation, a technique included in many automated
systems and used particularly in registration.
IV Registration
Registration of two images of the same part of the body is
essential for many applications where the correspondence
between the two images conveys the desired information.
These two images can be produced by different modalities, for
example CT and MRI, can be taken from the same patient with
the same instrument at different times, or can belong to two
different subjects. Comparison of acquired images with digital
anatomic atlas templates also requires registration algorithms.
These algorithms must account for the distortions between the
two images, which may be caused by differences between the
imaging methods, their artifacts, soft tissue elasticity, and
variability among subjects. This section explains the physical
and biological factors that introduce distortions, presents
various linear and nonlinear registration algorithms, describes
the Talairach space for brain registration, and addresses
interpolation issues inherent in registration. Chapters that
describe clinical applications and brain atlases illustrate the
current and potential contributions of registration techniques

in medicine.
xi
V Visualization
Visualization is a relatively new area that is contributing
signi®cantly to medicine and biology. While automated
systems are good at making precise quantitative measurements,
the complete examination of medical images is accomplished
by the visual system and experience of the human observer.
The ®eld of visualization includes graphics hardware and
software speci®cally designed to facilitate visual inspection of
medical and biological data. In some cases such as volumetric
data, visualization techniques are essential to enable effective
visual inspection. This section starts with the evolution of
visualization techniques and presents the fundamental con-
cepts and algorithms used for rendering, display,
manipulation, and modeling of multidimensional data, as
well as related quantitative evaluation tools. Fast surface
extraction techniques, volume visualization, and virtual endo-
scopy are discussed in detail, and applications are illustrated in
two and three dimensions.
VI Compression, Storage, and
Communication
Compression, storage, and communication of medical images
are related functions for which demand has recently increased
signi®cantly. Medical images need to be stored in an ef®cient
and convenient manner for subsequent retrieval. In many cases
images have to be shared among multiple sites, and commu-
nication of images requires compression, specialized formats,
and standards. Lossless image compression techniques ensure
that all the original information will remain in the image after

compression but they do not reduce the amount of data
considerably. Lossy compression techniques can produce
signi®cant savings in storage but eliminate some information
from the image. This section covers fundamental concepts in
medical image compression, storage and communication, and
introduces related standards such as JPEG, DICOM, and HL-7.
Picture archiving and communication systems (PACS) are
described and techniques for preprocessing images before
storage are discussed. Three chapters address lossy compres-
sion issues and one introduces an ef®cient three-dimensional
image compression technique based on the wavelet transform.
Acknowledgments
This Handbook is the product of a relatively large international
team which re¯ects the diversity of the medical imaging
community. It has been a great privilege and pleasure for me to
interact with the authors. I would like to express my most
sincere thanks to the section editors, Bernie Huang, Rangaraj
Rangayyan, Richard Robb, and Roger Woods, for their
initiative, insight, coordination, and perseverance. The journey
of the Handbook was set on its course with the guidance of two
distinguished leaders who served on the advisory board of the
Handbook: William Brody, president of Johns Hopkins
University, and Elias Zerhouni, director of the Radiology and
Radiological Science Department at Hopkins. I appreciate the
vision and encouragement of Joel Claypool who initiated this
Handbook at Academic Press and allowed the journey to
progress smoothly in all its phases and for all involved. I also
thank Julie Bolduc from Academic Press and Marty Tenney
from Textbook Writers Associates for coordinating the com-
pilation of the Handbook so effectively. My deepest gratitude

goes to my wife, Lisa, and my children, Judy and Danny, for
enduring and encouraging the journey graciously.
Isaac N. Bankman
Johns Hopkins University
xii
Contributors
M. Stella Atkins
School of Computing Science
Simon Fraser University
Burnaby, BC V5A 1S6, Canada
Chapter 11
Nicholas Ayache
INRIA Sophia-Projet Epidaure
06902 Sophia Antipolis Cedex, France
Chapter 31
Isaac N. Bankman
Applied Physics Laboratory
Johns Hopkins University
Laurel, MD 20723
Chapters 14, 53
Alan H. Barr
Computer Graphics Laboratory
Department of Computer Science
Division of Engineering and Applied Science
California Institute of Technology
Pasadena, CA 91125
Chapter 13
James C. Bezdek
Computer Science Department
University of West Florida

Pensacola, FL 32514
Chapter 6
Thierry Blu
Swiss Federal Institute of Technology-
Lausanne
EPFL/DMT/IOA/Biomedical Imaging Group
CH-1015 Lausanne, Switzerland
Chapter 25
Norman F. Boyd
Division of Clinical Epidemiology and
Biostatistics
Ontario Cancer Institute
Toronto, ON, Canada
Chapter 21
Jeffrey W. Byng
Health Imaging
Eastman Kodak Company
Toronto, ON, Canada
Chapter 21
Tobias C. Cahoon
Computer Science Department
University of West Florida
Pensacola, FL 32514
Chapter 6
Amit Chakraborty
Siemens Corporate Research
Princeton, NJ 08540
Chapter 9
Edmund Y. S. Chao
Orthopaedic Biomechanics Laboratory

Johns Hopkins University School of Medicine
Baltimore, MD 21205
Chapter 18
Pamela Cosman
Department of Electrical and Computer
Engineering
University of California at San Diego
La Jolla, CA 92093-0407
Chapters 49, 50, 51
Fabrice Crivello
Groupe d'Imagerie Neurofonctionelle (GIN)
Universite
Â
de Caen
GIP Cyceron
14074 Caen Cedex, France
Chapter 28
Magnus Dahlbom
Division of Nuclear Medicine
Department of Molecular and Medical
Pharmacology
UCLA School of Medicine
Los Angeles, CA 90095-6942
Chapter 27
Christos Davatzikos
Department of Radiology
Johns Hopkins University School of Medicine
Baltimore, MD 21287
Chapter 16
Dominik R. Dersch

Crux Cybernetics
Sydney, Australia
Chapter 7
Quentin E. Dolecek
Applied Physics Laboratory
Johns Hopkins University
Laurel, MD 20723
Chapter 46
James S. Duncan
Image Processing and Analysis Group
Departments of Diagnostic Radiology and
Electrical Engineering
Yale University
New Haven, CT 06520-8042
Chapter 9
William F. Eddy
Department of Statistics
Carnegie Mellon University
Pittsburgh, PA 15213
Chapter 37
John J. Elias
Orthopaedic Biomechanics Laboratory
Johns Hopkins University
Baltimore, MD 21205-2196
Chapter 18
Joan E. Fetter
Applied Physics Laboratory
Johns Hopkins University
Laurel, MD 20723
Chapter 46

Kurt W. Fleischer
Pixar Animation Studios
Richmond, CA 94804
Chapter 13
Peter T. Fox
Research Imaging Center
University of Texas Health Science Center at
San Antonio
San Antonio, TX 78232
Chapter 35
Frank J. Frassica
Orthopaedic Biomechanics Laboratory
Johns Hopkins University
Baltimore, MD 21205-2196
Chapter 18
Alberto F. Goldszal
Imaging Sciences Program, Clinical Center
National Institutes of Health
Bethesda, MD 20892
Chapter 12
Robert Gray
Stanford University
Palo Alto, CA
Chapters 49, 50, 51
Eric Grimson
Arti®cal Intelligence Laboratory
Massachusetts Institute of Technology
Cambridge, MA 02139
Chapter 39
xiii

Nobuhiko Hata
Surgical Planning Lab
Department of Radiology
Brigham & Women's Hospital
Harvard Medical School
Boston, MA 02115
Chapters 6, 19
David J. Hawkes
Radiological Sciences
King's College London
Guy's Hospital
London SE1 9RT, United Kingdom
Chapter 34
Derek L.G. Hill
Radiological Sciences
King's College London
Guy's Hospital
London SE1 9RT, United Kingdom
Chapter 34
Robert L. Holland
Applied Physics Laboratory
Johns Hopkins University
Laurel, MD 20723
Chapter 46
Sung-Cheng (Henry) Huang
Division of Nuclear Medicine
Department of Molecular and Medical
Pharmacology
UCLA School of Medicine
Los Angeles, CA 90095-6942

Chapter 27
H.K. Huang
Department of Radiology
Childrens Hospital of Los Angeles/University
of Southern California
Los Angeles, CA 90027
Chapter 52
Walter Huda
Director, Radiological Physics
Department of Radiology
SUNY Upstate Medical University
Syracuse, NY 13210
Chapter 3
Nozomu Inoue
Orthopaedic Biomechanics Laboratory
Johns Hopkins University
Baltimore, MD 21205-2196
Chapter 18
Peter Jezzard
FMRIB Centre
John Radcliffe Hospital
Headington, Oxford OX3 9DU, United
Kingdom
Chapter 26
Yulei Jiang
Department of Radiology
The University of Chicago
Chicago, IL 60637
Chapter 22
Roger Johnson

Biomedical Engineering Department
Marquette University
Milwaukee, WI 53233-1881
Chapter 17
Christopher R. Johnson
Center for Scienti®c Computing and Imaging
Department of Computer Science
University of Utah
Salt Lake City, UT 84112
Chapter 44
Marc Joliot
Groupe d'Imagerie Neurofonctionelle (GIN)
Universite
Â
de Caen
GIP Cyceron
14074 Caen Cedex, France
Chapter 28
Arie E. Kaufman
Department of Computer Science
State University of New York at Stony Brook
Stony Brook, NY 11794-4400
Chapter 43
William S. Kerwin
Center for Imaging Science
Department of Electrical and Computer
Engineering
Johns Hopkins University
Baltimore, MD 21218
Chapter 24

Ron Kikinis
Surgical Planning Laboratory
Brigham & Women's Hospital
Harvard Medical School
Boston, MA 02115
Chapters 2, 19, 39
Robert Knowlton
Epilepsy Center
University of Alabama School of Medicine
Birmingham, AL 35205
Chapter 38
Hans Knutsson
Computer Vision Lab
Department of Electrical Engineering
Linko
È
ping University
Linko
È
ping, Sweden
Chapter 2
Jens Kordelle
Surgical Planning Lab
Department of Radiology
Brigham & Women's Hospital
Harvard Medical School
Boston, MA 02115
Chapter 19
Vassili A. Kovalev
Institute of Engineering Cybernetics

Belarus Academy of Sciences
220012 Minsk, Belarus
Chapter 15
David H. Laidlaw
Computer Science Department
Brown University
Providence, RI 02912
Chapter 13
Andrew Laine
Department of Biomedical Engineering
Columbia University
New York, NY 10027
Chapter 3
Jack L. Lancaster
Research Imaging Center
University of Texas Health Science Center at
San Antonio
San Antonio, TX 78232
Chapter 35
Yarden Livnat
Center for Scienti®c Computing and Imaging
Department of Computer Science
University of Utah
Salt Lake City, UT 84112
Chapter 44
Shyh-Liang Lou
Laboratory for Radiological Informatics
Department of Radiology
University of California at San Francisco
San Francisco, CA 94903

Chapter 47
Blair T. Mackiewich
School of Computing Science
Simon Fraser University
Burnaby, BC V5A 1S6, Canada
Chapter 11
Bernard Mazoyer
Groupe d'Imagerie Neurofonctionelle (GIN)
Universite
Â
de Caen
GIP Cyceron
14074 Caen Cedex, France
Chapter 28
xiv
Tim McInerney
Department of Computer Science
University of Toronto
Toronto, ON M5S 3H5, Canada
Chapter 8
Michael B. Millis
Department of Orthopaedic Surgery
Children's Hospital
Boston, MA 02115
Chapter 19
Richard Olshen
Stanford University
Palo Alto, CA
Chapters 49, 50, 51
Nael F. Osman

Center for Imaging Science
Department of Electrical and Computer
Engineering
Johns Hopkins University
Baltimore, MD 21218
Chapter 24
Raman B. Paranjape
Electronic Systems Engineering
University of Regina
Regina, SASK S4S 0A2, Canada
Chapter 1
Steven G. Parker
Center for Scienti®c Computing and Imaging
Department of Computer Science
University of Utah
Salt Lake City, UT 84112
Chapter 44
Sotiris Pavlopoulos
Institute of Communication and Computer
Systems
National Technical University of Athens
Athens 157-73, Greece
Chapter 14
Xavier Pennec
INRIA Sophia-Projet Epidaure
06902 Sophia Antipolis Cedex, France
Chapter 31
Maria Petrou
School of Electronic Engineering
Information Technologies and Maths

University of Surrey
Guildford GU2 7XH, United Kingdom
Chapter 15
Dzung L. Pham
Laboratory of Personality and Cognition
National Institute on Aging
National Institutes of Health
Baltimore, MD
Chapter 12
Ewa Pietka
Silesian University of Technology
Division of Biomedical Electronics
PL. 44-101 Gliwice, Poland
Chapter 48
Jerry L. Prince
Center for Imaging Science
Department of Electrical and Computer
Engineering
Johns Hopkins University
Baltimore, MD 21218
Chapters 10, 24
Wei Qian
Department of Radiology
College of Medicine and the H. Lee Mof®tt
Cancer and Research Institute
University of South Florida
Tampa, FL 33612
Chapter 4
Osman Ratib
Department of Radiological Sciences

UCLA School of Medicine
Los Angeles, CA 90095-1721
Chapter 23
Jens A. Richolt
Orthopaedic University Clinic
"Friedrichsheim"
D-60528 Frankfurt, Germany
Chapter 19
Richard A. Robb
Director, Biomedical Imaging Resource
Mayo Foundation
Rochester, MN 55905
Chapter 42
Jadwiga Rogowska
McLean Brain Imaging Center
Harvard Medical School
Belmont, MA 02478
Chapter 5
Robert T. Schultz
Yale University Child Study Center
New Haven, CT 06520
Chapter 9
Meiyappan Solaiyappan
Department of Radiology
Johns Hopkins University School of Medicine
Baltimore, MD 21210
Chapter 41
Thomas S. Spisz
Applied Physics Laboratory
Johns Hopkins University

Laurel, MD 20723
Chapter 53
Lawrence H. Staib
Image Processing and Analysis Group
Departments of Diagnostic Radiology and
Electrical Engineering
Yale University
New Haven, CT 06520-8042
Chapter 9
Ronald M. Summers
Diagnostic Radiology Department
Warren Grant Magnuson Clinical Center
National Institutes of Health
Bethesda, MD 20892-1182
Chapter 45
Melanie A. Sutton
Computer Science Department
University of West Florida
Pensacola, FL 32514
Chapter 6
Demetri Terzopoulos
Department of Computer Science
University of Toronto
Toronto, ON M5S 3H5, Canada
Chapter 8
Philippe The
Â
venaz
Swiss Federal Institute of Technology-
Lausanne

EPFL/DMT/IOA/Biomedical Imaging Group
CH-1015 Lausanne, Switzerland
Chapter 25
Jean-Philippe Thirion
INRIA Sophia-Projet Epidaure
06902 Sophia Antipolis Cedex, France
Chapter 31
Paul M. Thompson
Department of Neurology
Lab of Neuro-Imaging and Brain Mapping
Division
UCLA School of Medicine
Los Angeles, CA 90095-1769
Chapters 36, 40
Arthur W. Toga
Department of Neurology
Lab of Neuro-Imaging and Brain Mapping
Division
UCLA School of Medicine
Los Angeles, CA 90095-1769
Chapters 36, 40
Nathalie Tzourio-Mazoyer
Groupe d'Imagerie Neurofonctionelle (GIN)
Universite
Â
de Caen
GIP Cyceron
14074 Caen Cedex, France
Chapter 28
xv

Michael Unser
Swiss Federal Institute of Technology-
Lausanne
EPFL/DMT/IOA/Biomedical Imaging Group
CH-1015 Lausanne, Switzerland
Chapter 25
Marcel Van Herk
Radiotherapy Department
The Netherlands Cancer Institute
1066 CX Amsterdam, The Netherlands
Chapter 32
Frank Vietze
Institut fu
È
r Radiologische Diagnostik
Ludwig-Maximilians-Universita
È
tMu
È
nchen
Klinikum Innenstadt
80336 Mu
È
nchen, Germany
Chapter 7
Jun Wang
Collabria
Menlo Park, CA
Chapter 52
Carl-Fredrik Westin

Surgical Planning Lab
Brigham & Women's Hospital
Harvard Medical School
Boston, MA 02115
Chapter 2
Axel Wismu
È
ller
Institut fu
È
r Radiologische Diagnostik
Ludwig-Maximilians-Universita
È
tMu
È
nchen
Klinikum Innenstadt
80336 Mu
È
nchen, Germany
Chapter 7
Albert Wong
Laboratory for Radiological Informatics
Department of Radiology
University of California at San Francisco
San Francisco, CA 94903
Chapter 47
Roger P. Woods
Division of Brain Mapping
Department of Neurology

Neuropsychiatric Institute
UCLA School of Medicine
Los Angeles, CA 90095-7085
Chapters 29, 30, 33
Chenyang Xu
Center for Imaging Science
Department of Electrical and Computer
Engineering
Johns Hopkins University
Baltimore, MD 21218
Chapter 10
Martin J. Yaffe
Department of Medical Imaging
University of Toronto
Toronto, ON M4N 3M5, Canada
Chapter 21
Stephen P. Yanek
Applied Physics Laboratory
Johns Hopkins University
Laurel, MD 20723
Chapter 46
Terence K. Young
Mobil Exploration & Producing Technical
Center
Dallas, TX 75265-0232
Chapter 37
Xiaolan Zeng
Image Processing and Analysis Group
Departments of Diagnostic Radiology and
Electrical Engineering

Yale University
New Haven, CT 06520-8042
Chapter 9
Bin Zheng
Radiological Imaging Division
University of Pittsburgh
Pittsburgh, PA 15261
Chapter 20
xvi
I
Enhancement
1 Fundamental Enhancement Techniques Raman B. Paranjape 3
2 Adaptive Image Filtering Carl-Fredrik Westin, Hans Knutsson,
and Ron Kikinis 19
3 Enhancement by Multiscale Nonlinear Operators Andrew Laine
and Walter Huda 33
4 Medical Image Enhancement with Hybrid Filters Wei Qian 57
Rangaraj M. Rangayyan
University of Calgary
M
edical images are often deteriorated by noise due to various sources of interference and other
phenomena that affect the measurement processes in imaging and data acquisition systems.
The nature of the physiological system under investigation and the procedures used in
imaging also diminish the contrast and the visibility of details. For example, planar projection nuclear
medicine images obtained using a gamma camera as well as single-photon emission computed
tomography (SPECT) are severely degraded by Poisson noise that is inherent in the photon emission and
counting processes. Although mammograms (X-ray images of the breast) are not much affected by noise,
they have limited contrast because of the nature and superimposition of the soft tissues of the breast,
which is compressed during the imaging procedure. The small differences that may exist between normal
and abnormal tissues are confounded by noise and artifacts, often making direct analysis of the acquired

images dif®cult.
In all of the cases just mentioned, some improvement in the appearance and visual quality of the
images, even if only subjective, may assist in their interpretation by a medical specialist.
Image enhancement techniques are mathematical techniques that are aimed at realizing improvement
in the quality of a given image. The result is another image that demonstrates certain features in a manner
that is better in some sense as compared to their appearance in the original image. One may also derive or
compute multiple processed versions of the original image, each presenting a selected feature in an
enhanced appearance. Simple image enhancement techniques are developed and applied in an ad hoc
manner. Advanced techniques that are optimized with reference to certain speci®c requirements and
objective criteria are also available.
Although most enhancement techniques are applied with the aim of generating improved images for
use by a human observer, some techniques are used to derive images that are meant for use by a
subsequent algorithm for computer processing. Examples of the former category are techniques to
remove noise, enhance contrast, and sharpen the details in a given image. The latter category includes
many techniques in the former, but has an expanded range of possibilities, including edge detection and
object segmentation.
If used inappropriately, enhancement techniques themselves may increase noise while improving
contrast, they may eliminate small details and edge sharpness while removing noise, and they may
produce artifacts in general. Users need to be cautious to avoid these pitfalls in the pursuit of the best
possible enhanced image.
1
The ®rst chapter, by Paranjape, provides an introduction to basic techniques, including histogram
manipulation, mean and median ®ltering, edge enhancement, and image averaging and subtraction, as
well as the Butterworth ®lter. Applications illustrate contrast enhancement, noise suppression, edge
enhancement, and mappings for image display systems. Dental radiographic images and CT images of the
brain are used to present the effects of the various operations. Most of the methods described in this
chapter belong to the ad hoc category and provide good results when the enhancement need is not very
demanding. The histogram equalization technique is theoretically well founded with the criterion of
maximal entropy, aiming for a uniform histogram or gray-level probability density function. However,
this technique may have limited success on many medical images because they typically have details of a

wide range of size and small gray-level differences between different tissue types. The equalization
procedure based on the global probability with a quantized output gray scale may obliterate small details
and differences. One solution is the locally adaptive histogram equalization technique described in this
chapter. The limitations of the fundamental techniques motivated the development of adaptive and
spatially variable processing techniques.
The second chapter by Westin et al. presents the design of the adaptive Wiener ®lter. The Wiener ®lter is
an optimal ®lter derived with respect to a certain objective criterion. Westin et al. describe how the
Wiener ®lter may be designed to adapt to local and spatially variable details in images. The ®lter is cast as a
combination of low-pass and high-pass ®lters, with factors that control their relative weights. Application
of the techniques to CT and MR images is illustrated.
The third chapter by Laine et al. focuses on nonlinear contrast enhancement techniques for
radiographic images, in particular mammographic images. A common problem in contrast or edge
enhancement is the accompanying but undesired noise ampli®cation. A wavelet-based framework is
described by Laine et al. to perform combined contrast enhancement and denoising, that is, suppression
of the noise present in the input image and/or control of noise ampli®cation in the enhancement process.
The basic unsharp masking and subtracting Laplacian techniques are included as special cases of a more
general system for contrast enhancement.
The fourth and ®nal chapter of the section, by Qian, describes a hybrid ®lter incorporating an adaptive
multistage nonlinear ®lter and a multiresolution/multiorientation wavelet transform. The methods
address image enhancement with noise suppression, as well as decomposition and selective reconstruc-
tion of wavelet-based subimages. Application of the methods to enhance microcalci®cation clusters and
masses in mammograms is illustrated.
Together, the chapters in this section present an array of techniques for image enhancement: from
linear to nonlinear, from ®xed to adaptive, and from pixel-based to multiscale methods. Each method
serves a speci®c need and has its own realm of applications. Given the diverse nature of medical images
and their associated problems, it would be dif®cult to prescribe a single method that can serve a range of
problems. An investigator is well advised to study the images and their enhancement needs, and to
explore a range of techniques, each of which may individually satisfy a subset of the requirements. A
collection of processed images may be called for in order to meet all the requirements.
2 I Enhancement

1
Fundamental Enhancement
Techniques
Raman B. Paranjape
University of Regina
1 Introduction . 3
2 Preliminaries and De®nitions 3
3 Pixel Operations 4
3.1 Compensation for Nonlinear Characteristics of Display or Print Media

3.2 Intensity Scaling

3.3 Histogram Equalization
4 Local Operators 7
4.1 Noise Suppression by Mean Filtering

4.2 Noise Suppression by Median Filtering

4.3 Edge Enhancement

4.4 Local-Area Histogram Equalization
5 Operations with Multiple Images 15
5.1 Noise Suppression by Image Averaging

5.2 Change Enhancement by Image Subtraction
6 Frequency Domain Techniques 16
7 Concluding Remarks 16
References . . . 17
1 Introduction
Image enhancement techniques are used to re®ne a given

image, so that desired image features become easier to perceive
for the human visual system or more likely to be detected by
automated image analysis systems [1, 13]. Image enhancement
allows the observer to see details in images that may not be
immediately observable in the original image. This may be the
case, for example, when the dynamic range of the data and that
of the display are not commensurate, when the image has a
high level of noise or when contrast is insuf®cient [4, 5, 8, 9].
Fundamentally, image enhancement is the transformation or
mapping of one image to another [10, 14]. This transformation
is not necessarily one-to-one, so that two different input
images may transform into the same or similar output images
after enhancement. More commonly, one may want to generate
multiple enhanced versions of a given image. This aspect also
means that enhancement techniques may be irreversible.
Often the enhancement of certain features in images is
accompanied by undesirable effects. Valuable image informa-
tion may be lost or the enhanced image may be a poor
representation of the original. Furthermore, enhancement
algorithms cannot be expected to provide information that is
not present in the original image. If the image does not contain
the feature to be enhanced, noise or other unwanted image
components may be inadvertently enhanced without any
bene®t to the user.
In this chapter we present established image enhancement
algorithms commonly used for medical images. Initial con-
cepts and de®nitions are presented in Section 2. Pixel-based
enhancement techniques described in Section 3 are trans-
formations applied to each pixel without utilizing speci®cally
the information in the neighborhood of the pixel. Section 4

presents enhancement with local operators that modify the
value of each pixel using the pixels in a local neighborhood.
Enhancement that can be achieved with multiple images of the
same scene is outlined in Section 5. Spectral domain ®lters that
can be used for enhancement are presented in Section 6. The
techniques described in this chapter are applicable to dental
and medical images as illustrated in the ®gures.
2 Preliminaries and De®nitions
We de®ne a digital image as a two-dimensional array of
numbers that represents the real, continuous intensity dis-
tribution of a spatial signal. The continuous spatial signal is
Copyright # 2000 by Academic Press.
All rights of reproduction in any form reserved.
3
sampled at regular intervals and the intensity is quantized to a
®nite number of levels. Each element of the array is referred to
as a picture element or pixel. The digital image is de®ned as a
spatially distributed intensity signal f m; n, where f is the
intensity of the pixel, and m and n de®ne the position of the
pixel along a pair of orthogonal axes usually de®ned as
horizontal and vertical. We shall assume that the image has M
rows and N columns and that the digital image has P quantized
levels of intensity (gray levels) with values ranging from 0 to
P À1.
The histogram of an image, commonly used in image
enhancement and image characterization, is de®ned as a vector
that contains the count of the number of pixels in the image at
each gray level. The histogram, hi, can be de®ned as
hi


MÀ1
m0

NÀ1
n0
df m; nÀi; i  0; 1; ; P À 1;
where
dw
1 w  0;
0 otherwise:
&
A useful image enhancement operation is convolution using
local operators, also known as kernels. Considering a kernel
wk; l to be an array of 2K 162L  1 coef®cients where
the point k; l0; 0 is the center of the kernel, convolution
of the image with the kernel is de®ned by:
gm; nwk; lÃf m; n

K
kÀK

L
lÀL
wk; l? f m À k; n Àl;
where gm; n is the outcome of the convolution or output
image. To convolve an image with a kernel, the kernel is
centered on an image pixel m; n, the point-by-point products
of the kernel coef®cients and corresponding image pixels are
obtained, and the subsequent summation of these products is
used as the pixel value of the output image at m; n. The

complete output image gm; n is obtained by repeating the
same operation on all pixels of the original image [4, 5, 13]. A
convolution kernel can be applied to an image in order to effect
a speci®c enhancement operation or change in the image
characteristics. This typically results in desirable attributes
being ampli®ed and undesirable attributes being suppressed.
The speci®c values of the kernel coef®cients depend on the
different types of enhancement that may be desired.
Attention is needed at the boundaries of the image where
parts of the kernel extend beyond the input image. One
approach is to simply use the portion of the kernel that
overlaps the input image. This approach can, however, lead to
artifacts at the boundaries of the output image. In this chapter
we have chosen to simply not apply the ®lter in parts of the
input image where the kernel extends beyond the image. As a
result, the output images are typically smaller than the input
image by the size of the kernel.
The Fourier transform Fu; v of an image f m; n is de®ned
as
Fu; v
1
MN

MÀ1
m0

NÀ1
n0
f m; ne
À2pj

um
M

vn
N

;
u  0; 1; 2; ; M À 1 v  0; 1; 2; ; N À 1;
where u and v are the spatial frequency parameters. The Fourier
transform provides the spectral representation of an image,
which can be modi®ed to enhance desired properties. A spatial-
domain image can be obtained from a spectral-domain image
with the inverse Fourier transform given by
f m; n

MÀ1
u0

NÀ1
v0
Fu; ve
2pj
um
M

vn
N

;
m  0; 1; 2; ; M À1; n  0; 1; 2; ; N À 1:

The forward or inverse Fourier transform of an N 6N image,
computed directly with the preceding de®nitions, requires a
number of complex multiplications and additions propor-
tional to N
2
. By decomposing the expressions and eliminating
redundancies, the fast Fourier transform (FFT) algorithm
reduces the number of operations to the order of N log
2
N [5].
The computational advantage of the FFT is signi®cant and
increases with increasing N.WhenN  64 the number of
operations are reduced by an order of magnitude and when
N  1024, by two orders of magnitude.
3 Pixel Operations
In this section we present methods of image enhancement that
depend only upon the pixel gray level and do not take into
account the pixel neighborhood or whole-image character-
istics.
3.1 Compensation for Nonlinear Characteristics
of Display or Print Media
Digital images are generally displayed on cathode ray tube
(CRT) type display systems or printed using some type of
photographic emulsion. Most display mechanisms have non-
linear intensity characteristics that result in a nonlinear
intensity pro®le of the image when it is observed on the
display. This effect can be described succinctly by the equation
em; nCf m; n;
where f m; n is the acquired intensity image, em; n
represents the actual intensity output by the display system,

and C() is a nonlinear display system operator. In order to
correct for the nonlinear characteristics of the display, a
transform that is the inverse of the display's nonlinearity must
be applied [14, 16].
4 I Enhancement
gm; nTem; n%C
À1
Cf m; n
gm; n%f m; n;
where T is a nonlinear operator which is approximately equal
to C
À1
, the inverse of the display system operator, and
gm; n is the output image.
Determination of the characteristics of the nonlinearity
could be dif®cult in practice. In general, if a linear intensity
wedge is imaged, one can obtain a test image that captures the
complete intensity scale of the image acquisition system.
However, an intensity measurement device that is linear is then
required to assess the output of the display system, in order to
determine its actual nonlinear characteristics.
A slightly exaggerated example of this type of a transform is
presented in Fig.1. Figure 1a presents a simulated CRT display
with a logarithmic characteristic. This characteristic tends to
suppress the dynamic range of the image decreasing the
contrast. Figure 1b presents the same image after an inverse
transformation to correct for the display nonlinearity.
Although these operations do in principle correct for the
display, the primary mechanism for review and analysis of
image information is the human visual system, which is

fundamentally a nonlinear reception system and adapts locally
to the intensities presented.
3.2 Intensity Scaling
Intensity scaling is a method of image enhancement that can be
used when the dynamic range of the acquired image data
signi®cantly exceeds the characteristics of the display system, or
vice versa. It may also be the case that image information is
present in speci®c narrow intensity bands that may be of
special interest to the observer. Intensity scaling allows the
observer to focus on speci®c intensity bands in the image by
modifying the image such that the intensity band of interest
spans the dynamic range of the display [14, 16]. For example, if
f
1
and f
2
are known to de®ne the intensity band of interest, a
scaling transformation may be de®ned as
e 
ff
1
f f
2
0 otherwise
@
g 
e Àf
1
f
2

À f
1
&'
? f
max
;
where e is an intermediate image, g is the output image, and
f
max
is the maximum intensity of the display.
These operations may be seen through the images in Fig. 2.
Figure 2a presents an image with detail in the intensity band
from 90 to 170 that may be of interest to, for example a gum
specialist. The image, however, is displayed such that all gray
levels in the range 0 to 255 are seen. Figure 2b shows the
histogram of the input image and Fig. 2c presents the same
image with the 90-to-170 intensity band stretched across the
output band of the display. Figure 2d shows the histogram of
the output image with the intensities that were initially between
90 and 170, but are now stretched over the range 0 to 255. The
detail in the narrow band is now easily perceived; however,
details outside the band are completely suppressed.
(a) (b)
FIGURE 1 (a) Original image as seen on a poor-quality CRT-type display. This image has poor contrast, and details are dif®cult to perceive Ð
especially in the brighter parts of the image such as in areas with high tooth density or near ®lling material. (b) The nonlinearity of the display is reversed
by the transformation, and structural details become more visible. Details within the image such as the location of amalgam, the cavity preparation liner,
tooth structures, and bony structures are better visualized.
1 Fundamental Enhancement Techniques 5
3.3 Histogram Equalization
Although intensity scaling can be very effective in enhancing

image information present in speci®c intensity bands, often
information is not available a priori to identify the useful
intensity bands. In such cases, it may be more useful to
maximize the information conveyed from the image to the user
by distributing the intensity information in the image as
uniformly as possible over the available intensity band [3, 6, 7].
This approach is based on an approximate realization of an
information-theoretic approach in which the normalized
histogram of the image is interpreted as the probability density
function of the intensity of the image. In histogram equaliza-
tion, the histogram of the input image is mapped to a new
maximally-¯at histogram.
As indicated in Section 2, the histogram is de®ned as hi,
with 0 to P À 1 gray levels in the image. The total number of
pixels in the image, M*N, is also the sum of all the values in
hi. Thus, in order to distribute most uniformly the intensity
(b)(a)
(c) (d)
FIGURE 2 (a) Input image where details of interest are in the 90-to-170 gray level band. This intensity band identi®es the bony structures in this image
and provides an example of a feature that may be of dental interest. (b) Histogram of the input image in (a). (c) This output image selectively shows the
intensity band of interest stretched over the entire dynamic range of the display. This speci®c enhancement may be potentially useful in highlighting
features or characteristics of bony tissue in dental X-ray imagery. This technique may be also effective in focusing attention on other image features such
as bony lamina dura or recurrent caries. (d) Histogram of the output image in (c). This histogram shows the gray levels in the original image in the 90-to-
170 intensity band stretched over 0 to 255.
6 I Enhancement
pro®le of the image, each bin of the histogram should have a
pixel count of M ÃN=P.
It is, in general, possible to move the pixels with a given
intensity to another intensity, resulting in an increase in the
pixel count in the new intensity bin. On the other hand, there is

no acceptable way to reduce or divide the pixel count at a
speci®c intensity in order to reduce the pixel count to the
desired M ÃN=P. In order to achieve approximate unifor-
mity, the average value of the pixel count over a number of
pixel values can be made close to the uniform level.
A simple and readily available procedure for redistribution
of the pixels in the image is based on the normalized
cumulative histogram, de®ned as
Hj
1
M ? N

j
i0
hi; j  0; 1; P À1:
The normalized cumulative histogram can be used as a
mapping between the original gray levels in the image and
the new gray levels required for enhancement. The enhanced
image gm; n will have a maximally uniform histogram if it is
de®ned as
gm; nP À1? Hf m; n:
Figure 3a presents an original dental image where the gray
levels are not uniformly distributed, while the associated
histogram and cumulative histogram are shown in Figs 3b and
3c, respectively. The cumulative histogram is then used to map
the gray levels of the input images to the output image shown
in Fig. 3d. Figure 3e presents the histogram of Fig. 3d, and Fig.
3f shows the corresponding cumulative histogram. Figure 3f
should ideally be a straight line from 0; 0 to P À1; P À 1,
but in fact only approximates this line to the extent possible

given the initial distribution of gray levels. Figure 3g through 1
show the enhancement of a brain MRI image with the same
steps as above.
4 Local Operators
Local operators enhance the image by providing a new value
for each pixel in a manner that depends only on that pixel and
others in a neighborhood around it. Many local operators are
linear spatial ®lters implemented with a kernel convolution,
some are nonlinear operators, and others impart histogram
equalization within a neighborhood. In this section we present
a set of established standard ®lters commonly used for
enhancement. These can be easily extended to obtain slightly
modi®ed results by increasing the size of the neighborhood
while maintaining the structure and function of the operator.
4.1 Noise Suppression by Mean Filtering
Mean ®ltering can be achieved by convolving the image with a
2K 162L  1 kernel where each coef®cient has a value
equal to the reciprocal of the number of coef®cients in the
kernel. For example, when L  K  1, we obtain
wk; l
1=91=91=9
1=91=91=9
1=91=91=9
V
b
`
b
X
W
b

a
b
Y
;
referred to as the 363 averaging kernel or mask. Typically, this
type of smoothing reduces noise in the image, but at
the expense of the sharpness of edges [4, 5, 12, 13]. Examples
of the application of this kernel are seen in Fig. 4(a±d). Note
that the size of the kernel is a critical factor in the successful
application of this type of enhancement. Image details that are
small relative to the size of the kernel are signi®cantly
suppressed, while image details signi®cantly larger than the
kernel size are affected moderately. The degree of noise
suppression is related to the size of the kernel, with greater
suppression achieved by larger kernels.
4.2 Noise Suppression by Median Filtering
Median ®ltering is a common nonlinear method for noise
suppression that has unique characteristics. It does not use
convolution to process the image with a kernel of coef®cients.
Rather, in each position of the kernel frame, a pixel of the input
image contained in the frame is selected to become the output
pixel located at the coordinates of the kernel center. The kernel
frame is centered on each pixel m; n of the original image,
and the median value of pixels within the kernel frame is
computed. The pixel at the coordinates m; n of the output
image is set to this median value. In general, median ®lters do
not have the same smoothing characteristics as the mean ®lter
[4, 5, 8, 9, 15]. Features that are smaller than half the size of the
median ®lter kernel are completely removed by the ®lter. Large
discontinuities such as edges and large changes in image

intensity are not affected in terms of gray level intensity by the
median ®lter, although their positions may be shifted by a few
pixels. This nonlinear operation of the median ®lter allows
signi®cant reduction of speci®c types of noise. For example,
``shot noise'' may be removed completely from an image
without attenuation of signi®cant edges or image character-
istics. Figure 5 presents typical results of median ®ltering.
4.3 Edge Enhancement
Edge enhancement in images is of unique importance because
the human visual system uses edges as a key factor in the
comprehension of the contents of an image [2, 4, 5, 10,13, 14].
Edges in different orientations can be selectively identi®ed and
1 Fundamental Enhancement Techniques 7
(c)
(b)
(d)
(a)
FIGURE 3 (a) Original image where gray levels are not uniformly distributed. Many image details are not well visualized in this image because of the
low contrast. (b) Histogram of the original image in (a). Note the nonuniformity of the histogram. (c) Cumulative histogram of the original image in (a).
(d) Histogram-equalized image. Contrast is enhanced so that subtle changes in intensity are more readily observable. This may allow earlier detection of
pathological structures. (e) Histogram of the enhanced image in (d). Note that the distribution of intensity counts that are greater than the mean value
have been distributed over a larger gray level range. (f ) Cumulative histogram of the enhanced image in (d). (g) Original brain MRI image (courtesy of
Dr. Christos Dzavatzikos, Johns Hopkins Radiology Department). (h) through (l) same steps as above for brain image.
8 I Enhancement
(g)
(f )
(h)
(e)
FIGURE 3 (Continued).
1 Fundamental Enhancement Techniques 9