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14 Two-Dimensional Shape and Texture Quantification 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 Quantification 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. Yajfe, Jeffrey W. Byng, and Norman F. Boyd 323

22 Classification of Breast Lesions from 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,

Neal F. Osman, and Jerry L. Prince 375

25 Image Interpolation and Resampling Phillippe Thevenaz, Thierry Blu, and Michael Unser 393

Isaac N. Bankman

Johns Hopkins University

Medical image analysis benefits significantly from the precise, fast, repeatable, and objective measurements made by computational resources. These quantitative measurements contribute to the analysis of structure and function in normal and abnormal cases by addressing many aspects of the data, such as tissue shape, size, texture, and density; musculoskeletal angle, kinematics, and stress; as well as ventricular motion, myocardial strain, and blood flow. The shape of tissue structures or organs is of particular interest in visual interpretation of images, and automated techniques provide many quantitative measures that can contribute to the examination. The smoothness or homogeneity of the tissue is also often used in visual examination to assess the state of the tissue. Chapter 14 presents fundamental techniques for shape and texture quantification in two-dimensional images, including spatial, statistical, and spectral methods. Texture information is also present in volumetric data and can be quantified by setting an appropriate framework for three-dimensional tessellation. Chapter 15 describes relatively new concepts and methods for three-dimensional texture analysis based on gradient estimation as well as a generalization of cooccurrence matrices introduced in Chapter 14. In some cases, the shape of a structure can be characterized by comparing it to a preset template. In such cases, shape is quantified with the parameters of a transformation function that needs to be applied to the template in order to match it to the image structure's shape. Shape quantification with deformable template transformations can be used on anatomical as well as functional data. Concepts and techniques used for shape transformation are explained in Chapter 16, in the context of brain imaging, where this approach is of particular interest.

Some applications in medical imaging require a specialized approach that addresses the unique structure and properties of the data. One example is the analysis of branching structures such as the arterial tree. Both segmentation and quantification techniques for analyzing arterial trees have to relate to the tubular bifurcating shapes. Chapter 17 reviews techniques used for arterial tree morphometry and presents quantitative measures obtained from three-dimensional images. Quantitative image analysis also contributes to the study of the musculoskeletal system using biomechanical models that yield static, dynamic, and stress parameters. Chapter 18 introduces biomechanical models derived from three-dimensional images, presents techniques for quantifying bone structure and material properties, and provides illustrative applications. Quantification of angles between bone structures is of interest in the study of the musculoskeletal system for diagnosis as well as planning of treatment. Chapter 19 presents a technique for bone angle quantification using three-dimensional data.

Quantitative measures obtained from medical images are typically used for making decisions regarding the structure or function of tissue. When automated techniques are used to assist such decisions, an additional layer of decisions is imposed. The user must select images for training pattern recognition algorithms and determine the measurements, often called features, that have appropriate discrimination power. These decisions also can be guided by automated techniques described in Chapter 20, which discusses database selection criteria and feature evaluation methods. This chapter also introduces two commonly used pattern recognition techniques: the feed-forward neural network and the Bayesian network.

Interpretation of mammograms is an area where detailed analysis of both shape and texture is of particular interest. Risk of breast cancer has been correlated to the density of mammograms, quantified with brightness as well as texture. Chapter 21 reviews the physical foundations of radiographic imaging in mammography, establishes the factors that dictate the optical density of mammograms, and describes techniques for characterizing their brightness and texture. Chapter 22 presents a review of lesion classification in mammograms using shape and texture quantification and discusses the evaluation of classification techniques. The contribution of automated techniques to the visual interpretation of radiologists is also addressed in Chapter 22.

Many techniques for quantification of volume, motion, and flow are available for analyzing cardiovascular images. The main parameters of interest are ventricular volume and ejection ratio, blood flow, and ventricular wall motion. Chapter 23 describes techniques for quantifying these parameters using geometric, densitometric, and spectral methods. The delineation of the left ventricular wall can be accomplished using segmentation techniques described in the previous section, and parts of the cardiovascular system can be inspected visually using visualization techniques described in the next section. The performance of the heart, especially myocardial strain, is also addressed with the tagged MRI technique that led to new computational methods for quantification of cardiac function. Chapter 24 first establishes the analytical framework for representing three-dimensional tissue motion and strain, and also describes the fundamentals of tagged MRI in the same framework. It then reviews image processing techniques for deriving motion measurements in two-dimensional images and describes the combination of these measurements to estimate the three-dimensional motion and strain of material points inside the left ventricle.

The last chapter in this section is a comprehensive survey of techniques used for an essential image processing function that has universal applicability. Interpolation and resampling, addressed in Chapter 25, are used in many applications where estimates of image values at points other than the original grid are required. Applications include zooming and coordinate transformations in two-dimensional data, rescaling, reslicing, and rendering in volumetric data, tomographic reconstructions, and image registration. Selection of a technique is often difficult because of assumptions, possible approaches, and the diversity of models involved. Chapter 25 clarifies the terminology and fundamental concepts, sets the analytical foundation of generalized linear interpolation, establishes the desirable properties that interpolation and resampling should have, describes several types of interpolation functions, and illustrates their performance.

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