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

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.