3D Uncertain Distance Field Mapping using GMM and GP

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning data. Building upon our prior work, which utilized the Gaussian Process (GP) and Gaussian Mixture Model (GMM) for structured building models, we introduce a more generalized approach tailored for complex surfaces in urban scenes, where four-dimensional (4D) GMM Regression and GP with derivative observations are applied. A Hierarchical GMM (HGMM) is employed to optimize the number of GMM components and speed up the GMM training. With the prior map obtained from HGMM, GP inference is followed for the refinement of the final map. Our approach models the implicit surface of the geo-object and enables the inference of the regions that are not completely covered by measurements. The integration of GMM and GP yields well-calibrated uncertainty estimates alongside the surface model, enhancing both accuracy and reliability. The proposed method is evaluated on the real data collected by a mobile mapping system. Compared to the performance in mapping accuracy and uncertainty quantification of other methods such as Gaussian Process Implicit Surface map (GPIS) and log-Gaussian Process Implicit Surface map (Log-GPIS), the proposed method achieves lower RMSEs, higher log-likelihood values and fewer computational costs for the evaluated datasets.