geospatial engineers

Abstract: We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the proposed kernel estimator first parallel transports nearby responses to the target tangent space and then forms a volume-corrected local average. We first derive its uniform second-order bias, finite-bandwidth covariance, and stochastic rate. For simultaneous inference, the tangent norm is written as a supremum over the unit tangent bundle. Exact covariance whitening gives a unit-variance Gaussian field whose correlation length is of order $h$ along the base manifold and of order one along the fibre. Its local covariance geometry leads to a Gumbel limit with an explicit intrinsic constant. Combining this limit with Gaussian approximation and cross-fitted covariance estimation yields a feasible simultaneous confidence tube for the regression field. We further discuss improved finite-sample inference with bandwidth selection and high-order bias corrections. Simulations on various manifolds support the proposed inference procedure. A randomized reconstruction of global wind data illustrates how the tube's cross-sections describe spatially varying uncertainty.

Abstract: A Digital Surface Model (DSM) is a fundamental geospatial data product for representing the elevation of the Earth's surface. Recently, 3D Gaussian Splatting (3DGS) has shown considerable potential for DSM reconstruction from multi-view optical satellite imagery due to its explicit scene representation and efficient optimization. However, in 3DGS-based DSM generation, alpha-weighted aggregation of Gaussian altitudes may blend splats from different height layers at the same rendered pixel or DSM sampling location, producing non-physical intermediate elevations and height-layer mixing errors. To address this problem, we propose HLC-GS, a risk-map-guided height-layer consistency Gaussian Splatting method for DSM reconstruction from optical satellite imagery. HLC-GS consists of a risk map module, a dominant-layer reliability correction module, and a secondary-layer suppression module. The risk map localizes high-risk pixels with abnormal height dispersion and unreliable dominant-layer responses, while the latter two modules regularize unreliable dominant-layer responses and suppress weakly supported far secondary-layer responses. Extensive experiments are conducted on the DFC2019 and IARPA2016 datasets. Compared with six state-of-the-art DSM reconstruction methods, HLC-GS achieves better overall accuracy. Compared with the latest and precision-enhanced EOGS, HLC-GS reduces the average MAE from 1.46 m to 1.18 m and the average RMSE from 2.78 m to 2.58 m over the evaluated scenes, while improving PAG$_{2.5}$ from 86.09\% to 88.61\%. Overall, these results demonstrate that explicitly modeling per-pixel height-layer consistency alleviates height-layer mixing and improves the geometric quality of 3DGS-based DSM reconstruction from optical satellite imagery.