RBF Your SDF: Radial Basis Function Interpolation of Signed Distance Fields with Implied Tangent Points

Abstract

Signed distance fields (SDFs) are a popular implicit representation of geometry. Converting a discrete set of SDF samples into an explicit surface is a fundamental problem in geometry processing. Traditional reconstruction methods such as marching cubes and dual contouring ignore the geometric information carried by samples far from the surface. Recently, Sell\'an et al.[2023] and several follow-up works leveraged the tangent-sphere structure of SDFs; every sample implies a point on a sphere tangent to the surface. However, these approaches extract the zero-level set via surface reconstruction, which considers only points and normals on the surface and ignores the remaining samples. We propose an approach that marries the tangent-sphere observation with radial basis function interpolation of all data, the implied surface points and the original data. By detecting spheres with extremely constrained tangent points, a configuration geometrically forced at sharp surface features, we identify and preserve surface corners that surface reconstruction-based methods systematically round. A partition-of-unity decomposition allows our method to scale efficiently to large grid resolutions. Our reconstructions improve both Chamfer and Hausdorff accuracy at every tested resolution.