Monte Carlo-based 3D surface point cloud volume estimation by exploding local cubes faces

Abstract

This article proposes a state-of-the-art algorithm for estimating the 3D volume enclosed in a surface point cloud via a modified extension of the Monte Carlo integration approach. The algorithm consists of a pre-processing of the surface point cloud, a sequential generation of points managed by an affiliation criterion, and the final computation of the volume. The pre-processing phase allows a spatial re-orientation of the original point cloud, the evaluation of the homogeneity of its points distribution, and its enclosure inside a rectangular parallelepiped of known volume. The affiliation criterion using the explosion of cube faces is the core of the algorithm, handles the sequential generation of points, and proposes the effective extension of the traditional Monte Carlo method by introducing its applicability to the discrete domains. Finally, the final computation estimates the volume as a function of the total amount of generated points, the portion enclosed within the surface point cloud, and the parallelepiped volume. The developed method proves to be accurate with surface point clouds of both convex and concave solids reporting an average percentage error of less than 7 %. It also shows considerable versatility in handling clouds with sparse, homogeneous, and sometimes even missing points distributions. A performance analysis is presented by testing the algorithm on both surface point clouds obtained from meshes of virtual objects as well as from real objects reconstructed using reverse engineering techniques.