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.

翻译：本研究解决了从噪声且不完整的激光雷达扫描数据中构建精确表示不确定曲面的连续三维模型的挑战。在先前利用高斯过程和高斯混合模型进行结构化建筑模型研究的基础上，我们提出了一种更通用的方法，专门针对城市场景中复杂曲面进行建模，其中采用了高斯混合模型回归和带有导数观测的高斯过程。通过使用层次化高斯混合模型优化高斯混合模型组件数量并加速其训练过程，我们在获得层次化高斯混合模型先验地图后，进一步通过高斯过程推理来优化最终地图。该方法对地理对象的隐式曲面进行建模，并能够推断出未被测量完全覆盖的区域。高斯混合模型与高斯过程的结合可在生成曲面模型的同时提供经过良好校准的不确定性估计，从而提升准确性和可靠性。通过在移动测绘系统采集的真实数据上进行评估，与高斯过程隐式曲面地图及对数高斯过程隐式曲面地图等其他方法相比，本方法在评估数据集中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。