A two-level approach to implicit surface modeling with compactly supported radial basis functions

TL;DR

This paper introduces a two-level method for implicit surface modeling using compactly supported radial basis functions, improving efficiency and surface quality for point cloud reconstruction.

Contribution

It presents a novel two-level approach combining coarse and fine basis functions to accurately reconstruct surfaces from scattered points.

Findings

Produces accurate signed distance functions for surface reconstruction

Reduces extra zero-level sets compared to global RBF methods

Efficiently handles set operations between shapes

Abstract

We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear combination of compactly supported radial basis functions (CSRBFs). The method preserves the simplicity and efficiency of implicit surface interpolation with CSRBFs and the reconstructed implicit surface owns the attributes, which are previously only associated with globally supported or globally regularized radial basis functions, such as exhibiting less extra zero-level sets, suitable for inside and outside tests. First, in the coarse scale approximation, we choose basis function centers on a grid that covers the enlarged bounding box of the given point set and compute their signed distances to the underlying surface using local quadratic approximations of the nearest surface points. Then a fitting to the residual errors on the surface points and additional off-surface points is performed with fine scale basis functions. The final function is the sum of the two intermediate functions and is a good approximation of the signed distance field to the surface in the bounding box. Examples of surface reconstruction and set operations between shapes are provided.