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  • 1. H A N D B O O K O F MEDICAL IMAGING
  • 2. 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.
  • 3. H A N D B O O K O F MEDICAL IMAGING P R O C E S S I N G A N D A N A LY S I S 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
  • 4. 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 http://www.academicpress.com 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
  • 5. To Lisa, Judy, and Danny
  • 6. 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 WismuÈller, 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 TheÂvenaz, 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
  • 7. 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
  • 8. 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
  • 9. 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
  • 10. 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
  • 11. 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 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
  • 12. 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 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 LinkoÈping University LinkoÈping, 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 de Caen GIP Cyceron 14074 Caen Cedex, France Chapter 28 xiv
  • 13. 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 TheÂvenaz 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 de Caen GIP Cyceron 14074 Caen Cedex, France Chapter 28 xv
  • 14. 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 fuÈr Radiologische Diagnostik Ludwig-Maximilians-UniversitaÈt MuÈnchen Klinikum Innenstadt 80336 MuÈnchen, 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 WismuÈller Institut fuÈr Radiologische Diagnostik Ludwig-Maximilians-UniversitaÈt MuÈnchen Klinikum Innenstadt 80336 MuÈnchen, 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
  • 15. 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
  • 16. 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
  • 17. 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
  • 18. 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 À 1. 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† ˆ ˆMÀ1 mˆ0 ˆNÀ1 nˆ0 d…f …m; n† À i†; i ˆ 0; 1; . . . ; P À 1; where d…w† ˆ 1 w ˆ 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† ˆ …0; 0† is the center of the kernel, convolution of the image with the kernel is de®ned by: g…m; n† ˆ w…k; l† à f …m; n† ˆ ˆK kˆÀK ˆL lˆÀL w…k; l† ? f …m À k; n À l†; 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† ˆ 1 MN ˆMÀ1 mˆ0 ˆNÀ1 nˆ0 f …m; n†eÀ2pj…um M ‡vn N † ; u ˆ 0; 1; 2; . . . ; M À 1 v ˆ 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† ˆ ˆMÀ1 uˆ0 ˆNÀ1 vˆ0 F…u; v†e2pj um M ‡vn N… †; m ˆ 0; 1; 2; . . . ; M À 1; n ˆ 0; 1; 2; . . . ; N À 1: The forward or inverse Fourier transform of an N6N image, computed directly with the preceding de®nitions, requires a number of complex multiplications and additions propor- tional to N2 . By decomposing the expressions and eliminating redundancies, the fast Fourier transform (FFT) algorithm reduces the number of operations to the order of N log2N [5]. The computational advantage of the FFT is signi®cant and increases with increasing N. When N ˆ 64 the number of operations are reduced by an order of magnitude and when N ˆ 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† ˆ 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
  • 19. g…m; n† ˆ T…e…m; n††%CÀ1 …C…f …m; n††† g…m; n†%f …m; n†; where T…† is a nonlinear operator which is approximately equal to CÀ1 …†, 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 f1 and f2 are known to de®ne the intensity band of interest, a scaling transformation may be de®ned as e ˆ f f1 f f2 0 otherwise @ g ˆ e À f1 f2 À f1 & ' ? …fmax†; where e is an intermediate image, g is the output image, and fmax 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
  • 20. 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
  • 21. pro®le of the image, each bin of the histogram should have a pixel count of …M à N†=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 à N†=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† ˆ 1 M ? N ˆj iˆ0 h…i†; j ˆ 0; 1; . . . P À 1: 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† ˆ …P À 1† ? 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 À 1; 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 ˆ K ˆ 1, we obtain w…k; l† ˆ 1=9 1=9 1=9 1=9 1=9 1=9 1=9 1=9 1=9 V b` bX W ba bY ; 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
  • 22. (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