A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction

TL;DR

This paper introduces a semi-Lagrangian scheme with radial basis function interpolation for surface reconstruction from sparse, noisy data, enabling efficient, accurate, and robust surface modeling on unstructured grids.

Contribution

It presents a novel explicit semi-Lagrangian method coupled with radial basis functions for surface reconstruction, allowing flexible grid use and focused computation near data points.

Findings

Accurate reconstruction of curves and surfaces from sparse data.

Robustness to noisy data sets.

Reduced computational effort through localized reconstruction.

Abstract

We propose a Semi-Lagrangian scheme coupled with Radial Basis Function interpolation for approximating a curvature-related level set model, which has been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces from sparse, possibly noisy data sets. The main advantages of the proposed scheme are the possibility to solve the level set method on unstructured grids, as well as to concentrate the reconstruction points in the neighbourhood of the data set, with a consequent reduction of the computational effort. Moreover, the scheme is explicit. Numerical tests show the accuracy and robustness of our approach to reconstruct curves and surfaces from relatively sparse data sets.