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, and Tobias C. Cahoon 87

7 Segmentation with Neural Networks Axel Wismiller, Frank Vietze, and

Dominik R. Dersch 107

8 Deformable Models Tim Mclnerney 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

Isaac N. Bankman

Johns Hopkins University

Segmentation, separation of structures of interest from the background and from each other, is an essential analysis function for which numerous algorithms have been developed in the field of image processing. In medical imaging, automated delineation of different image components is used for analyzing anatomical structure and tissue types, spatial distribution of function and activity, and pathological regions. Segmentation can also be used as an initial step for visualization and compression. Typically, segmentation of an object is achieved either by identifying all pixels or voxels that belong to the object or by locating those that form its boundary. The former is based primarily on the intensity of pixels, but other attributes, such as texture, that can be associated with each pixel, can also be used for segmentation. Techniques that locate boundary pixels use the image gradient, which has high values at the edges of objects. Chapter 5 presents the fundamental concepts and techniques used for region-based and edge-based segmentation, including global and adaptive thresholding, watershed segmentation, gradient operators, region growing, and segmentation using multiple images.

Since segmentation requires classification of pixels, it is often treated as a pattern recognition problem and addressed with related techniques. Especially in medical imaging, where variability in the data maybe high, pattern recognition techniques that provide flexibility and convenient automation are of special interest. One approach is fuzzy clustering, a technique based on fuzzy models and membership functions. Chapter 6 introduces the concept of fuzzy sets, establishes the distinction between membership and probability, and describes image segmentation with fuzzy clustering. Both supervised and unsupervised methods are presented and illustrated with several applications. Another approach is neural networks, where the classification is based on distributed nonlinear parallel processing. Numerous neural network structures and training algorithms are available and can be applied to medical image segmentation.

Chapter 7 focuses on a particularly effective class of neural networks, the generalized radial basis functions, and presents an approach that combines unsupervised and supervised techniques.

A relatively new segmentation approach based on deformable models provides a mechanism that is considerably different from fundamental techniques and pattern recognition methods. In this approach a flexible boundary model is placed in the vicinity of the structure to be segmented, and the model is iteratively adjusted to fit the contour of the structure. Deformable models are particularly suited for segmentation of images that have artifacts, noise, and weak boundaries between structures. Chapter 8 presents a comprehensive review of deformable models and their use for medical image segmentation. Since the formulation of deformable models lends itself well to shape representation, matching, and motion tracking, these three applications are also addressed in Chapter 8. An important aspect of segmentation with deformable models is the possibility of incorporating prior information on the shape of the object. Chapter 9 describes shape constraints that facilitate segmentation with deformable templates. Specific shape information can be used when the shapes of structures of interest are consistent. In cases where shapes are likely to vary significantly, generic shape constraints are needed. Chapter 9 presents integrated techniques that use a maximum a posteriori formulation and related distributions for specific shape constraints, while the generic shape constraints are addressed with the level set method and a thickness constraint. The application of specific and generic shape constraints for deformable models is illustrated on heart and brain images in Chapter 9. Segmentation with deformable models has been successful in many images that cannot be segmented well with other techniques; however, two main limitations of deformable templates must be noted. Deformable models can converge to a wrong boundary if the initial position is not close enough to the desired boundary, and they also can refuse to converge into concave regions of the desired boundary. Chapter 10 describes gradient vector flow fields that can provide a solution for both problems. This technique allows the initial model to be placed inside, outside, or even across the boundary, and it converges well if other structures do not interfere with the progress of the model.

In some medical image analysis applications, the presence of various structures with different properties suggests the use of a specifically designed sequence of multiple segmentation techniques. For example, initial steps can use fundamental techniques to reduce the data, and subsequent steps can apply more elaborate techniques that are robust but more time consuming. The best choice of techniques and their order depends typically on the problem as well as computational resources. Chapter 11 presents a hybrid approach designed for fully automated segmentation of brain MRI images. The algorithm includes histogram analysis, thresholding, nonlinear anisotropic diffusion, and deformable templates. The paradigm of this chapter can guide the design of other hybrid methods for use on different image data.

Recent advances in the speed and resolution of medical imaging instruments provide valuable volumetric data for numerous clinical applications. Practically all segmentation techniques described in this chapter were first developed for 2D image analysis but can also be extended to 3D images. Chapter 12 presents a comparative study of eight different techniques that can be used for volumetric segmentation. The evaluation is based on identification of white matter, gray matter, and cerebrospinal fluid in brain MRI images. Many segmentation algorithms may have difficulties at the boundary of different tissue types in volumetric data. This can be due to the fact that a voxel can contain a mixture of materials. Segmentation with fuzzy clustering provides one solution based on its membership functions. Another possibility is obtained by modeling each voxel as a region and computing the proportion of materials in each voxel. Chapter 13 presents this approach, which is based on a probabilistic Bayesian approach, to determine the most likely mixture within each voxel. The discrete 3D sampled data are used to produce a continuous measurement function. and the distribution of this function within each voxel leads to the mixture information. The technique is illustrated on volumetric data of brain, hand, and tooth.

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