Extraction of Skeletal Meshes from Volumetric Data by Sparse Polynomial Approximation

The skeletal structures of solid objects play an important role in medical and industrial applications. Given a volumetrically sampled solid object, our method extracts a well-connected and not-fragmented skeletal structure represented as a polygon mesh. The purpose is to achieve a noise-robust extraction of the skeletal mesh from a realworld object obtained using a scanning technology such as the CT scan method. We first approximate the input image intensity through a set of spherically supported polynomials that provide an adaptively smoothed intensity field, and then perform a polygonization process to find the extremal sheet of the field, which is regarded as a skeletal sheet in this research. In our polygonization, a subset of the weighted Delaunay tetrahedrization defined by a set of spherical supports is used as an adaptively sampled grid. The derivatives for detecting extremality are analytically evaluated at the tetrahedron vertices. We also demonstrate the effectiveness of our method by extracting skeletal meshes from noisy CT images.