Model Based Segmentation

Incorporation of a priori knowledge of the object such as shape, location, and orientation using deformable models (also known as active contour models) is one of the possible solutions to constrain the segmentation of organ structures. The term deformable models was coined by Terzopoulos and his collaborators [45,46] in the 1980s, but the idea of using a deformable template for feature extraction dated back to the work of Fischler and Elschlager on spring-loaded templates [47] and the work ofWidrow on rubber mask technique [48] in the early 1970s. Deformable models are analytically or parametrically defined curves or surfaces that move under the influence of forces, which have two components: internal forces and external forces. The internal forces are used to assure the smoothness of the model during deformation process and the external forces are defined to push/pull the model toward the boundaries of the structure. Parametric representations of the models allow accurate and compact description of the object shape, while the continuity, connectivity, and smoothness of the models can compensate for the irregularities and noise in the object boundaries. Model-based approaches treat the problem of finding object boundaries as an optimization problem of searching the best fit for the image data to the model. In the case of boundary finding via optimization in image space, a fairly extensive review on various deformable model methods can be found in Ref. [49].

Mykkanen et al. [50] investigated automatic delineation of brain structures in FDG-PET images using generalized snakes with promising results. Chiao et al. [51] proposed using model-based approach for segmenting dynamic cardiac PET or SPECT data. The object model consists of two parts: a heart and the rest of the body. The heart is geometrically modeled using a polygonal model [52] and the myocardial boundaries are parameterized by the endocardial radii and a set of angular thicknesses. Kinetic parameters in the compartment model and the endocardial and epicardial radii are estimated by maximizing a joint log-likelihood function using nonlinear parameter estimation. Tissue and blood TACs are extracted simultaneously with estimated kinetic parameters. Chiao et al. [51] proposed that some forms of regularization can be applied, including auxiliary myocardial boundary measurements obtained by MRI or CT and registering the auxiliary measurements with the emission tomographic data, if the kinetic parameter estimation failed.

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