3D Surface Reconstruction and Volume Approximation via the meshless methods

TL;DR

Three meshless methods including the interpolation-based method by RBF, PDE-based approach by Kansa's method and the Method of Fundamental Solutions are employed and compared for the optimal recovery of the surfaces and the volume estimation strategy is proposed.

Abstract

In this paper, we propose several mathematical models for 3D surface reconstruction and volume estimation from a set of scattered cloud data. Three meshless methods including the interpolation-based method by RBF, PDE-based approach by Kansa's method and the Method of Fundamental Solutions are employed and compared. For the optimal recovery of the surfaces, the selection of free parameters in related PDE models are further studied and analyzed. Besides, several criteria like distance are employed in above methods instead of the classical parameter lambda determination strategy, which leads to a more reliable reconstruction performance. Finally, the volume estimation of 3D irregular objects is proposed based on the optimal reconstructed geometric models via proposed meshless methods. Numerous numerical examples are presented to demonstrate the effectiveness of the proposed surface reconstruction methods and the volume estimation strategy.

Figures (10)

• Figure 1: The reconstruction comparisons among PDE Model I and II with different $\lambda$ in MFS.
• Figure 2: The optimal $\lambda^{*}$ found by different criteria measure when $\hat{N}$ = 50 via PDE-based method by MFS in Example 2.
• Figure 3: The error distribution of surface reconstruction in Example 2. (Plotted by MeshLab)
• Figure 4: Volume under different methods and criteria for Example 2.
• Figure 5: Different criteria measure for various $\lambda$ when $\hat{N}$ = 50 via PDE-based method by MFS in Example 3.