The rapid development and proliferation of medical imaging technologies is revolutionizing medicine. Medical imaging allows scientists and physicians to glean potentially life-saving information by peering noninvasively into the human body. The role of medical imaging has expanded beyond the simple visualization and inspection of anatomic structures. It has become a tool for surgical planning and simulation, intraoperative navigation, radiotherapy planning, and tracking the progress of disease. For example, ascertaining the detailed shape and organization of anatomic structures enables a surgeon preoperatively to plan an optimal approach to some target structure. In radiotherapy, medical imaging allows the delivery of a necrotic dose of radiation to a tumor with minimal collateral damage to healthy tissue.

With medical imaging playing an increasingly prominent role in the diagnosis and treatment of disease, the medical image analysis community has become preoccupied with the challenging problem of extracting, with the assistance of computers, clinically useful information about anatomic structures imaged through CT, MR, PET, and other modalities [6,7,13,41,67,118,129,143,152]. Although modern imaging devices provide exceptional views of internal anatomy, the use of computers to quantify and analyze the embedded structures with accuracy and efficiency is limited. Accurate, repeatable, quantitative data must be efficiently extracted in order to support the spectrum of biomedical investigations and clinical activities from diagnosis, to radiotherapy, to surgery.

For example, segmenting structures from medical images and reconstructing a compact geometric representation of these structures is difficult because of the sheer size of the datasets and the complexity and variability of the anatomic shapes of interest. Furthermore, the shortcomings typical of sampled data, such as sampling artifacts, spatial aliasing, and noise, may cause the boundaries of structures to be indistinct and disconnected. The challenge is to extract boundary elements belonging to the same structure and integrate these elements into a coherent and consistent model of the structure. Traditional low-level image processing techniques that consider only local information can make incorrect assumptions during this integration process and generate infeasible object boundaries. As a result, these model-free techniques usually require considerable amounts of expert intervention. Furthermore, the subsequent analysis and interpretation of the segmented objects is hindered by the pixel- or voxel-level structure representations generated by most image processing operations.

This chapter, an updated version of McInerney and Terzopoulos [97], surveys deformable models, a promising and vigorously researched model-based approach to computerassisted medical image analysis. The widely recognized potency

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of deformable models stems from their ability to segment, match, and track images of anatomic structures by exploiting (bottom-up) constraints derived from the image data together with (top-down) a priori knowledge about the location, size, and shape of these structures. Deformable models are capable of accommodating the often significant variability of biological structures over time and across different individuals. Furthermore, deformable models support highly intuitive interaction mechanisms that allow medical scientists and practitioners to bring their expertise to bear on the modelbased image interpretation task when necessary. We will review the basic formulation of deformable models and survey their application to fundamental medical image analysis problems, including segmentation, shape representation, matching, and motion tracking (see also the compilation [124]).

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