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In the past four decades, computerized image segmentation has played an increasingly important role in medical imaging. Segmented images are now used routinely in a multitude of different applications, such as the quantification of tissue volumes [1], diagnosis [2], localization of pathology [3], study of anatomical structure [4, 5], treatment planning [6], partial volume correction of functional imaging data [7], and computer-integrated surgery [8, 9]. Image segmentation remains a difficult task, however, due to both the tremendous variability of object shapes and the variation in image quality (see Fig. 3.1). In particular, medical images are often corrupted by noise and sampling artifacts, which can cause considerable difficulties when applying classical segmentation techniques such as edge detection and thresholding. As a result, these techniques either fail completely or require some kind of postprocessing step to remove invalid object boundaries in the segmentation results.
To address these difficulties, deformable models have been extensively studied and widely used in medical image segmentation, with promising results. Deformable models are curves or surfaces defined within an image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data. The internal forces are designed to keep the model smooth during deformation. The external forces are defined to move the model toward an object boundary or other desired features within an image. By constraining extracted boundaries to be smooth and incorporating other prior information about the object shape, deformable models offer robustness to both image noise and boundary gaps and allow integrating boundary elements into a coherent and consistent mathematical description. Such a boundary description can then be readily used by subsequent applications. Moreover, since deformable models are implemented on the continuum, the resulting boundary representation can achieve subpixel accuracy, a highly desirable property for medical imaging applications. Figure 3.2 shows two examples of using deformable models to extract object boundaries from medical images. The result is a parametric curve in Fig. 3.2(a) and a parametric surface in Fig. 3.2(b).
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