Fourier-based modeling of topologically complex bone data using various alternatives of 3D scalar fields

This article presents a new approach for Fourier-based modeling of bone anatomies for compression and smoothing. By treating the bone surface as a level set of a 3D scalar field, we can model topologically complex models such as bones. In particular, we experiment with five different alternatives, and prove that 3D scalar field which allows monotonous continuity around the boundary can be a good choice for volumetric description of the surface. This allows avoiding Gibbs phenomena which previous volume-based methods have suffered from, returning better results in compression and smoothing than other scalar fields. We demonstrate the efficacy of the proposed method by showing results with various bone data.