Uncertainty Quantification Framework for Aerial and UAV Photogrammetry through Error Propagation

Uncertainty quantification of the photogrammetry process is essential for providing per-point accuracy credentials of the point clouds. Unlike airborne LiDAR, whose accuracy generally remains consistent with objects with varying geometric complexity, the accuracy of photogrammetric point clouds is rather object/scene-dependent, as it relies on algorithm-derived measurements. Generally, errors of the photogrammetric point clouds propagate through a two-step process: Structure-from-Motion (SfM) with Bundle adjustment (BA), followed by Multi-view Stereo (MVS). While uncertainty estimation in the SfM stage has been well studied using the first-order statistics of the reprojection error function, that in the MVS stage remains largely unsolved and non-standardized, primarily due to its non-differentiable and multi-modal nature (i.e., from pixel values to geometry). In this paper, we present an uncertainty quantification framework closing this gap by associating an error covariance matrix per point accounting for this two-step photogrammetry process. Specifically, to estimate the uncertainty in the MVS stage, we propose a novel, self-calibrating method by taking reliable n-view points (n>=6) per-view to regress the disparity uncertainty using highly relevant cues (such as matching cost values) from the MVS stage. Compared to existing approaches, our method uses self-contained, reliable 3D points extracted directly from the MVS process, with the benefit of being self-supervised and naturally adhering to error propagation path of the photogrammetry process, thereby providing a robust and certifiable uncertainty quantification across diverse scenes. We evaluate the framework using a variety of publicly available airborne and UAV imagery datasets. Results demonstrate that our method outperforms existing approaches by achieving high bounding rates without overestimating uncertainty.