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 approximating the exact solution. 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. Working together with an adaptive sampling algorithm, the HRBF-based implicits can also reconstruct surfaces from point clouds with non-uniformity and noises. Robust and efficient reconstruction has been observed in our experimental tests on real data captured from a variety of scenes.
@article{arxiv.1507.02860,
title = {A Closed-Form Formulation of HRBF-Based Surface Reconstruction},
author = {Shengjun Liu and Charlie C. L. Wang and Guido Brunnett and Jun Wang},
journal= {arXiv preprint arXiv:1507.02860},
year = {2015}
}