# A Closed-Form Formulation of HRBF-Based Surface Reconstruction

arXiv: https://arxiv.org/abs/1507.02860 · HTML: https://mlsanity.com/paper/1507.02860/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2015.

## Built on by (most cited first, 5 of 5)

- [MIPS-Fusion: Multi-Implicit-Submaps for Scalable and Robust Online Neural RGB-D Reconstruction](https://mlsanity.com/paper/2308.08741/) (2023)
- [HRBF-Fusion: Accurate 3D reconstruction from RGB-D data using on-the-fly implicits](https://mlsanity.com/paper/2202.01829/) (2022)
- [LISR: Learning Linear 3D Implicit Surface Representation Using Compactly Supported Radial Basis Functions](https://mlsanity.com/paper/2402.07301/) (2024)
- [Approximating Signed Distance Fields With Sparse Ellipsoidal Radial Basis Function Networks: A Dynamic Multi-Objective Optimization Strategy](https://mlsanity.com/paper/2505.02350/) (2025)
- [Wavelet-based Global Orientation and Surface Reconstruction for Point Clouds](https://mlsanity.com/paper/2506.16299/) (2025)

## Abstract (arXiv)

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.