A closed-form formulation of HRBF-based surface reconstruction by approximate solution

• A closed-form formulation for computing the approximate solution of HRBF-based surface reconstruction from scattered data points.
• The computation based on compact support is local and numerically stable.
• Errors between the quasi-solution and the exact one are bounded.
• Our formulation to find the approximate solution of HRBF-based surface reconstruction is robust.
• As a local approach, our method is efficient and scalable.

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution to approximate the exact one. A scheme is developed to automatically adjust the support sizes of basis functions to hold the error bound of a quasi-solution. Our method can generate an implicit function from positions and normals of scattered points without taking any global operation. Robust and efficient reconstructions are observed in our experimental tests on real data captured from a variety of scenes.