A Non-Stationary Subdivision Scheme for the Construction of Deformable Models with Sphere-Like Topology

We present an affine-invariant non-stationary subdivision scheme for the recursive refinement of any triangular mesh that is regular or has extraordinary vertices of valence 4. In particular, when applied to an arbitrary convex octahedron, it produces a $G ^{ 1 }$ -continuous surface with a blob-like shape as the limit of the recursive subdivision process. In case of a regular octahedron, the subdivision process provides an accurate representation of ellipsoids. Our scheme allows us to easily construct a new interactive 3D deformable model for use in the delineation of biomedical images, which we illustrate by examples that deal with the characterization of 3D structures with sphere-like topology such as embryos, nuclei, or brains.