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 uncertainties 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 state-of-the-art methods, the proposed method achieves lower RMSEs, higher log-likelihood values and lower computational costs for the evaluated datasets.

翻译：本研究针对从含噪声且不完整的激光雷达扫描数据中构建能精确表示不确定曲面的连续三维模型这一挑战。基于我们先前利用高斯过程与高斯混合模型处理结构化建筑模型的工作，本文提出一种更通用的方法，专门适用于城市场景中的复杂曲面，其中应用了GMM回归与带导数观测的高斯过程。采用分层高斯混合模型以优化GMM分量数量并加速GMM训练。利用从HGMM获得的先验地图，随后进行GP推断以细化最终地图。我们的方法对地理对象的隐式曲面进行建模，并能够推断未被测量完全覆盖的区域。GMM与GP的融合在曲面模型之外还产生了经过良好校准的不确定性，从而提升了准确性与可靠性。所提方法在移动测绘系统采集的真实数据上进行了评估。与其他先进方法在建图精度和不确定性量化方面的性能相比，所提方法在评估数据集上实现了更低的均方根误差、更高的对数似然值以及更低的计算成本。