A Closed-Form Formulation of HRBF-Based Surface Reconstruction

TL;DR

This paper introduces a closed-form approach for surface reconstruction using Hermite radial basis functions, enabling efficient, robust implicit surface generation from scattered, noisy point cloud data without global operations.

Contribution

It presents a novel closed-form formulation and an adaptive scheme for HRBF-based surface reconstruction that handles non-uniform and noisy data efficiently.

Findings

Robust surface reconstruction demonstrated on real-world data.

Method avoids global operations, improving efficiency.

Supports adaptive sampling for non-uniform point clouds.

Abstract

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.