Multilevel T-spline Approximation for Scattered Observations with Application to Land Remote Sensing

TL;DR

This paper introduces a multilevel T-spline approximation method for fitting scattered point clouds efficiently, especially useful in land remote sensing, demonstrating comparable accuracy to traditional methods but with improved computational efficiency.

Contribution

The paper presents a novel multilevel T-spline approximation technique that improves efficiency and robustness in fitting large, noisy, and unevenly distributed point clouds.

Findings

Comparable accuracy to global least-squares fitting.

Enhanced computational efficiency for large datasets.

Effective handling of noisy and uneven point densities.

Abstract

In this contribution, we introduce a multilevel approximation method with T-splines for fitting scattered point clouds iteratively, with an application to land remote sensing. This new procedure provides a local surface approximation by an explicit computation of the control points and is called a multilevel T-splines approximation (MTA). It is computationally efficient compared with the traditional global least-squares (LS) approach, which may fail when there is an unfavourable point density from a given refinement level. We validate our approach within a simulated framework and apply it to two real datasets: (i) a surface with holes scanned with a terrestrial laser scanner, and (ii) a patch on a sand-dune in the Netherlands. Both examples highlight the potential of the MTA for rapidly fitting large and noisy point clouds with variable point density and with similar results compared to the global LS approximation.