Geometric Properties Estimation from Line Point Clouds Using Gaussian-Weighted Discrete Derivatives

Abstract

A line point cloud is a series of sequential discrete points acquired by a laser ranging sensor. Geometric properties estimation from line point clouds plays a crucial role in many applications, such as reverse engineering, industrial inspection, and autonomous navigation. This article proposes a new method for estimating the geometric properties, such as tangent, normal, curvature, and torsion, from line point clouds based on derivative estimation. According to the geometric meaning of the derivative, the derivative of a discrete function at a point is defined by using the Gaussian-weighted least squares, which is called the Gaussian-weighted discrete derivative (GDD) for short. By using the GDDs, classical differential geometry is discretized, and the geometric properties are estimated from a line point cloud based on its parametrized expression. Moreover, the noise intensity of the line point cloud is computed by using the Gaussian process regression for adaptive neighborhood adjustment to improve the estimation accuracy. The proposed method introduces the Gaussian weight into derivative estimation and estimates the geometric properties directly from line point clouds, which makes the estimation process reliable and understandable. The experimental results show that the proposed method is accurate, robust to noise, and suitable for different shapes.