A generalized Gauss–Helmert framework for point cloud fitting and registration using raw measurements

Abstract

Three-dimensional (3D) laser scanning technology plays an increasingly critical role in fields such as 3D reality modeling, cultural heritage conservation, and structural health monitoring, relying on accurate point cloud fitting and registration as its essential supporting technologies. However, most registration and fitting methodologies depend on Cartesian coordinates, overlooking that they are transformed from the raw polar coordinates (range, horizontal angle, vertical angle), which can inherently preserve the native measurement characteristics of laser scanning systems and provide a theoretically proper foundation for error propagation. To bridge this gap, this study formulates the point cloud fitting and registration problems within a generalized nonlinear Gauss–Helmert (NGH) model that directly utilizes the raw measurements for parameter estimation. Furthermore, to address the common challenge of unavailable or uncertain prior information on measurement precision, we propose a non-negative least-squares variance component estimation method for NGH model (NNLS-VCE_NGH), which introduces non-negativity constraints to ensure the physical validity and numerical stability of the estimated variance components. Superior performance of the proposed approach is demonstrated in both simulated and real-world experiments, where it achieves significantly more accurate parameter estimation than conventional NGH model-based approaches using Cartesian coordinates. This new framework enables direct weighted processing of raw measurements, yielding higher accuracy in point cloud fitting and registration even when prior precision information is missing or inaccurate, thereby demonstrating considerable application potential.