Discriminative Parameter Estimation for Random Walks Segmentation

In the following, we present the principal methods addressing the segmentation of skeletal muscles. Muscle Segmentation using Simplex meshes with medial representations A skele-tal muscle segmentation method was presented in [8] based on simplex meshes [6]. Considering a 3D surface model, simplex meshes are discrete meshes where each vertex has exactly 3 neighbors. Having a constant connectivity allows to simply parametrize the location of one vertex with respect to its neighbors, and thus parametrize deformation of the shape – translation, rotation, scaling – in a lo-cal manner. Indeed, the location of a pixel, denoted as x can be expressed as a linear combination of the locations of the three neighbors plus a local elevation term parallel to the local normal: x = ε1x1 + ε2x2 + (1 − ε1 − ε2)x3 + hn. As a result, many local measurements – including curvature and cell surface – can be computed efficiently and global energy terms enforcing local constraints come up naturally. Here, the authors impose local smoothing via curvature averaging, which does not tend to reduce the surface like 1-order operators typically do. Prior knowledge is imposed by constraining the local scale changes on the elevation parameter with respect to a reference shape. Denoting the surface of the tri-angle formed by the three neighbors of a pixel as S, given the reference shape parameters ε̃1, ε̃2, h̃, S̃, the new location of the considered pixel is expressed as: x = ε̃1x1 + ε̃2x2 + (1 − ε̃1 − ε̃2)x3 + h