  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 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 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 lower
computational costs for the evaluated datasets.
