Deformable triangular surfaces using fast 1-D radial Lagrangian dynamics-segmentation of 3-D MR and CT images of the wrist

We developed a new triangulated deformable surface model, which is used to detect the boundary of the bones in three-dimensional magnetic resonance (MR) and computed tomography (CT) images of the wrist. This surface model is robust to initialization and provides wide geometrical coverage and quantitative power. The surface is deformed by applying one-dimensional (1-D) radial Lagrangian dynamics. For initialization a tetrahedron is placed within the bone to be segmented. This initial surface is inflated to a binary approximation of the boundary. During inflation, the surface is refined by the addition of vertices. After the surface is fully inflated, a detailed, accurate boundary detection is obtained by the application of radial scale-space relaxation. In this optimization stage, the image intensity is filtered with a series of 1-D second-order Gaussian filters. The resolution of the triangulated mesh is adapted to the width of the Gaussian filter. To maintain the coherence between the vertices, a resampling technique is applied which is based on collapsing and splitting of edges. We regularized the triangulated mesh by a combination of volume-preserving vertex averaging and equi-angulation of edges. In this paper, we present both qualitative and quantitative results of the surface segmentations in eight MR and ten CT images.