I  m  a  g  e      P  r  o  c  e  s  s  i  n  g        w  i  t  h          M  A  T  L  A  B

A p p l i c a t i o n s     in   M e d i c i n e   a n d    B i o l o g y
Table Of Contens
Contents
Preface............................................................................................................... vii
Acknowledgments.................................................................................................. xi
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.................................................. 279
8 Deformable Models.............................................................................................. 311
9 Image Analysis................................................................................................... 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............................ 397
Appendix A: Notation............................................................................................. 405
Appendix B: Working with Dicom Images...................................................................... 407
Appendix C: Medical Image Processing Toolbox.............................................................. 421
Appendix D: Description of Image Data........................................................................ 425
Index................................................................................................................. 429
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 in characteristics such as sensitivity, resolution, and acquisition speed. Multislice, 64-Slice, and very soon, 256-Slice 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 other medical imaging modalities such as magnetic resonance imaging (MRI) and positron emission tomography (PET).


      Substantial effort has been put into the integration of different modalities. These systems are also called hybrid systems. The integration of CT and PET scanners has enabled physicians to localize biochemical activity (functional) with a high degree of certainty in the human body and will significantly impact molecular imaging, which can be defined as in vivo imaging of biochemical or molecular activity in the organ. There is also significant development in small animal imaging modalities. In vivo and in vitro molecular imaging has already been contributing to the advancement of the study of the genome and efficacy of new drugs. With the help of imaging, now biologists can get a snapshot of almost the entire range of 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 biochemical processes triggered by a disease. All of this may soon result in a paradigm shift in healthcare. It may open up the possibility of designing drugs as per a patient’s individual genetic profile.


     Advanced techniques of image processing and analysis find widespread use in biology and medicine. In medical and biological fields, image data are ubiquitously used in clinical as well as scientific studies to infer details regarding the process under investigation whether it be a disease process or a biological or biochemical process. 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 handling of image data are becoming an increasingly formidable task for engineers, scientists, and medical physicists.


     There are two main issues that concern the field of image processing and analysis applied to medical applications. These are the following:
  • Improving the quality of the acquired image data 
  • Extraction of information (i.e., 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 sheer size of images in medical applications has been increasing rapidly with the advent of imaging technologies; hence, transfer and storage issues are also challenging tasks. The main goal of developing efficient image data compression techniques is to address these two issues.


   Unlike the images produced in industrial applications, the images generated in medical and biological applications are complex and vary substantially 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 topics that we consider important in the fields of medicine and biology.


   Some concepts in image processing and analysis are theory-intensive and may be difficult for beginners to grasp. Explaining complex topics in image processing through examples and MATLAB algorithms is the principal 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 shallow nor complex, so that readers from diverse fields would comprehend without 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 a 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 the 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 as 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 advanced topics such as segmentation methods based on Markov random field (MRF) modeling. Statistical and stochastic modeling in image processing are 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 3D are no longer a prohibitive factor. Therefore, we have described applications to 3-D volume images. We tried to extend the techniques (algorithms) in this book to 3D 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 comprehend.

 
  The content of this book can be summarized as follows. 


  Chapter 1 discusses major imaging modalities in diagnostic radiology. They include CT, MRI, gamma cameras, 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, and are hence unique. Some of these techniques have also be 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 them help follow the other chapters such as chapters 6 and 7.


    Chapter 4 introduces the 2-D fast 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 of the Fourier transform.

   
    Chapter 5 deals with nonlinear diffusion filtering as well as some of the PDE-based image denoising techniques. This relatively recent class of filters has found many applications in medical imaging because of their superior performance in removing noise and preserving edge sharpness. 


    Chapter 6 discusses most of the intensity-based image segmentation methods. It discusses the thresholding techniques based on betweenclass variance, the Kullback function, entropy, and mixture modeling. We also discuss K-means and fuzzy C-means clustering techniques and their application to image segmentation.

  
    Chapter 7 discusses the image segmentation method based on MRF in detail. By MRF modeling, we model the spatial dependency of the intensities in a local neighborhood. The conditional density of the intensities and the MRF local dependency model is combined under the Bayesian framework in which the MRF model is viewed as a prior. This formulation leads to the maximum a posteriori (MAP) estimate of the true image (i.e., the image not deteriorated by the noise and the imaging system). We have discussed both the deterministic and probabilistic methods of finding the MAP estimate. 


    Chapter 8 describes fundamental image analysis methods applicable to a wide range of problems in image analysis. These methods include, for example, regions’ properties, boundary analysis, curvature analysis, and line and circle detection using the Hough transform.


    Chapter 9 discusses deformable models and their application to image segmentation. The theory of both parametric and geometric deformable models has been covered. Chapter 10 includes three applications of image processing and analysis. Unique approaches to image processing and analysis problems have been described. Through these applications, we wish that the reader will also gain experience in tackling a problem at hand.


Acknowledgments
We would like to thank Dr. Ersin Bayram for contributing the Deformable Model chapter and the MRI section of Chapter 1. We are thankful to Mr. Kostas Chantziantoniou for contributing to the Computer Tomography section in Chapter 1. We would also like to thank Edward D. Carroll and John Schneider for proofreading some chapters and for pointing out places where the text was very clear.
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