Image Processing with MATLAB® Applications in Medicine and Biology 9246_C000.indd 2 12/3/08 6:39:08 PM Image Processing with MATLAB ® Applications in Medicine and Biology Omer Demirkaya Musa Hakan Asyali Prasanna K.indd 3 12/3/08 6:39:08 PM CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2009 by Taylor and Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-0893-7 (Ebook-PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained.
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Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.com and the CRC Press Web site at http://www.com Dedicated by Ömer Demirkaya to his parents Nehabat and Mehmet and his wife Semra, and children Meryem, Hatice and Abdullah, and Musa Hakan Asyalı to his parents, Kiraz and Yas¸ ar Asyalı and his wife Elçin and daughters Ahsen Nur and Ays¸ e Nur, and Prasanna Sahoo in memory of his mother Sairendry and to his wife Sadhna and son Amit 9246_C000.indd 6 12/3/08 6:39:08 PM Contents Preface.xv 1 Medical Imaging Systems. 1 2 Fundamental Tools for Image Processing and Analysis. 49 3 Probability Theory for Stochastic Modeling of Images.115 4 Two-Dimensional Fourier Transform.167 5 Nonlinear Diffusion Filtering.
189 6 Intensity-Based Image Segmentation. 223 7 Image Segmentation by Markov Random Field Modeling. 327 Application 1: Quantification of Green Fluorescent Protein eXpression in Live Cells: ProXcell. 371 Application 2: Calculation of Performance Parameters of Gamma Cameras and SPECT Systems.
379 Application 3: Analysis of Islet Cells Using Automated Color Image Analysis. 405 Appendix B: Working with Dicom Images. 407 Appendix C: Medical Image Processing Toolbox. 421 Appendix D: Description of Image Data.indd 8 12/3/08 6:39:08 PM Preface Imaging, mainly due to its impact on medicine and biology, has been selected as one of the greatest achievements of the twentieth century by the National Academy of Engineering.
In the last several decades, medical imaging systems have advanced in quantum leaps. There have been substantial improvements on their characteristics such as sensitivity, resolution and acquisition speed. Multislice, 320-slice cur- rently, computer tomography (CT) scanners, for instance, allow the visualization of the entire coronary tree, even atherosclerotic plaques within the coronaries with extremely high accuracy and detail. Similar advances have occurred in the other medical imaging modalities such as magnetic resonance imaging (MRI) and positron emission tomog- raphy (PET).
Substantial effort has been put into the integration of different modalities. These systems are also called hybrid systems. The inte- gration of CT and PET scanners has enabled physicians to localize biochemical activity (functional) with a high degree of certainty in the human body. As a result of the significant advances in small ani- mal imaging, a new research discipline known as molecular imaging, which can be defined as in-vivo imaging of biochemical or molecu- lar activity in an organ, is emerging.
In-vitro molecular imaging has already been contributing to the advancement of the study of genome and efficacy of new drugs. With the help of imaging, now biologists can get a snapshot of almost the entire genomic activity (expression or disexpression of genes) within a diseased tissue in a matter of days. It will not be long before physicians can visualize, in-vivo, the biochemi- cal processes triggered by a disease. All of this may soon result in a paradigm shift in healthcare.
It may open up the possibility of design- ing drugs as per a patient’s individual genetic profile (i., personal- ized medicine). Advanced techniques of image processing and analysis find wide- spread use in biology and medicine. In medical and biological fields, image data are ubiquitously used in clinical as well as scientific stud- ies to infer details regarding the process under investigation whether it be a disease process or a biochemical pathway. Today, perhaps, health care institutions alone produce the largest amount of image data which are used in diagnosis and treatment of patients.
Information provided by medical images has become an indispensable part of today’s patient care. As the number of images produced increases, utilization, and han- dling of image data are becoming an increasingly formidable task for engineers, scientists, and medical physicists.indd 9 12/3/08 6:39:08 PM x Preface There are two main issues that concern the field of image processing and analysis applied to medical applications. • Improving the quality of the acquired image data • Extraction of information (i., feature) from medical image data in a robust, efficient and accurate manner Image enhancement techniques such as noise filtering, contrast, and edge enhancement; and image restoration techniques that focus on removing degradations in images, all fall within the former category, whereas image analysis methods deal primarily with the latter issue. The shear size of images in medical applications has been increasing rapidly with the advent of imaging technologies; hence, transfer and stor- age issues are also challenging tasks.
The main goal of developing effi- cient image data compression techniques is to address these two issues. Unlike the images produced in industrial applications, the images gener- ated in medical and biological applications are complex and vary substan- tially from application to application. In addition, as one can imagine, the field of image processing and analysis has to tackle a diverse and complex set of problems. Because this is such a vast subject, we focus on certain top- ics that we consider important in the fields of medicine and biology.
Some concepts in image processing and analysis are theory-laden and may be difficult for the beginners to grasp. Explaining complex topics in image processing through examples and MATLAB algorithms is the prin- ciple aim of this book. While working on this book, we tried to strike a balance between theory and practice. We wanted to keep it neither too shallow nor too complex so readers from diverse fields could benefit with- out difficulty.
Image processing techniques in general are ad-hoc in the sense that they are optimized and tailored to solve a particular problem in hand, although they are based on solid mathematical theories. That is, they are not applicable to wide range of applications or situations. This lack of generalizability often forces scientists and researchers to resort to the method of trial-and-error. The algorithms provided in this book will help scientists and researchers to quickly identify the most effective method of solution for a particular problem at hand.
This book will help readers understand advanced concepts through algorithms applied to real-world problems in medicine and biology. The examples and exercises included in every chapter will make the book suitable for use as a textbook for students at the senior undergraduate or graduate level, who are studying image processing and analysis for the first time; or a reference book for researchers, scientists, and biologists in the related fields. In addition to fundamental topics in image processing and analysis, the book covers new areas such as nonlinear diffusion filtering (NDF) or partial differential equation (PDE) based image filtering, and relatively 9246_C000.indd 10 12/3/08 6:39:08 PM Preface xi advanced topics such as segmentation methods based on Markov Random Field (MRF) modeling. Statistical and stochastic modeling in image pro- cessing is also emphasized in this book.
In the past, computation times and memory demand for 3-D algorithms were unrealistic, but with the advent of computer (or CPU) technology, processing time and memory needs in 3-D are no longer a prohibitive fac- tor. Therefore, we discussed the applications for 3-D volumetric images. We tried to expand the techniques (algorithms) to 3-D whenever we could. Finally, the reader with a moderate level of calculus, linear algebra, and probability and statistics background will find this book reasonably easy to follow.
The content of this book can be summarized as follows: Chapter 1 discusses major imaging modalities in diagnostic radiol- ogy. They include CT, MRI, gamma camera, and single photon emission tomography (SPECT) systems, and PET. In Chapter 2, we discuss fundamental image processing techniques. We have presented basic but useful as well as advanced image processing and analysis techniques with MATLAB codes or functions.
Most of these techniques are not available in the image processing toolbox; hence are unique. Some of these techniques have also been used in the subsequent chapters of the book. Chapter 3 covers the theory of probability and statistics on which some image processing and analysis methods are built. This chapter will help the readers build a background that may help them follow the other chap- ters such as Chapters 6 and 7.
Chapter 4 introduces the 2-D Fourier Transform with unique examples. We also briefly discuss the tomographic image reconstruction method, filtered back projection, as it is one of the medical applications in which the Fourier transform is used. Chapter 5 deals with nonlinear diffusion filtering as well as some of the partial differential equation (PDE) based image denoising techniques. This relatively recent class of filters has found many applications in medi- cal imaging because of their superior performance in removing noise and preserving the edge sharpness.
Chapter 6 discusses most of the intensity-based image segmentation methods. It discusses the thresholding techniques based on between- class variance, the Kullback function, and the entropy. We also discuss K-means, fuzzy C-means clustering, and mixture modeling-based tech- niques and their application to image segmentation. Chapter 7 discusses the image segmentation method based on MRF mod- eling.
In this approach, we model the spatial dependency of the intensities in a local neighborhood. The conditional density of the intensities and the MRF local dependency model are combined under the Bayesian framework, where the MRF model is viewed as a priori. This formulation leads to the maximum a posteriori (MAP) estimate of the true image (i., the image not 9246_C000.indd 11 12/3/08 6:39:09 PM xii Preface deteriorated by the noise and the imaging system). We have discussed both the deterministic and probabilistic methods of finding the MAP estimate.
Chapter 8 discusses deformable models and their application to image segmentation. The theory of both parametric and geometric deformable models has been covered. Chapter 9 talks about the fundamental image analysis methods that are applicable to wide range of problems. These methods include, for exam- ple, regions properties, boundary analysis, curvature analysis, and line and circle detection using Hough transform.
Chapters 10, 11, and 12 include three applications of image processing and analysis. Through these applications, we wish that the reader will also gain the experience that one requires to tackle a problem at hand.