Segmentation of medical images is an important step in various applications such as visualization, quantitative analysis and image-guided surgery. Numerous segmentation methods have been developed in the past two decades for extraction of organ contours on medical images. Low-level segmentation methods, such as pixel-based clustering, region growing, and filter-based edge detection, require additional pre-processing and post-processing as well as considerable amounts of expert intervention or information of the objects of interest. Furthermore the subsequent analysis of segmented objects is hampered by the primitive, pixel or voxel level representations from those region-based segmentation . Deformable models, on the other hand, provide an explicit representation of the boundary and the shape of the object. They combine several desirable features such as inherent connectivity and smoothness, which counteract noise and boundary irregularities, as well as the ability to incorporate knowledge about the object of interest [2, 3] . However, parametric deformable models have two main limitations. First, in situations where the initial model and desired object boundary differ greatly in size and shape, the model must be re-parameterized dynamically to faithfully recover the object boundary. The second limitation is that it has difficulty dealing with topological adaptation such as splitting or merging model parts, a useful property for recovering either multiple objects or objects with unknown topology. This difficulty is caused by the fact that a new parameterization must be constructed whenever topology change occurs, which requires sophisticated schemes [5, 6]. Level set deformable models [7, 8], also referred to as geometric deformable models, provide an elegant solution to address the primary limitations of parametric deformable models. These methods have drawn a great deal of attention since their introduction in 1988. Advantages of the contour implicit formulation of the deformable model over parametric formulation include: (1) no parameterization of the contour, (2) topological flexibility, (3) good numerical stability, (4) straightforward extension of the 2D formulation to n-D. Recent reviews on the subject include papers from Suri [9, 10]. In this chapter we give a general overview of the level set segmentation methods with emphasize on new frameworks recently introduced in the context of medical imaging problems. We then introduce novel approaches that aim at combining segmentation and registration in a level set formulation. Finally we review a selective set of clinical works with detailed validation of the level set methods for several clinical applications.
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