Dual Active Contour Models for Medical Image Segmentation

Deformable Models, which includes the popular snake models (Kass et al., 1988) and deformable surfaces (McInerney & Terzopoulos, 1996; Suri & Editors, 2006), are well known techniques for boundary extraction and tracking in 2D/3D images. Basically, these models can be classified into three categories: parametric, geodesic snakes and implicit models. The relationships between these models have been demonstrated in several works in the literature (Sapiro, 1997). Parametric Deformable Models consist of a curve (or surface) which can dynamically conform to object shapes in response to internal (elastic) forces and external forces (image and constraint ones) (Suri & Editors, 2006). Snake models, also called active contour models, are 2D deformable models proposed by Kass at al. (Kass et al., 1988) which have been successfully applied in a variety of problems in computer vision and image analysis. Its mathematical formulation makes easier to integrate image data, an initial estimated, desired contour properties and knowledge-based constraints, in a single extraction process (Suri & Editors, 2006). In fact, despite of the mentioned capabilities, parametric models in general can not deal with topological changes. Among the approaches to deal with the topological limitations of the traditional snake model (Bischoff & Kobbeit, 2004; Oliveira et al., 2004), the T-Snakes has the advantage of being a general one (McInerney & Terzopoulos, 1999). Besides, parametric models are too sensitive to their initial conditions due to nonconvexity problems (see (Davatzikos & Prince, 1999) and references therein). To address this limitation some authors have proposed multiscale techniques (Leymarie & Levine, 1993), dynamic program (DP) (Amini et al., 1990)and dual methods, also called dual snakes (Gunn & Nixon, 1997). The non-invariance under affine transformations is another limitation of the traditional snake models. As a consequence, the internal energy is sensitive to distortions due to changes in viewing geometry. From a dynamical point of view, it means that the elastic forces may