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Structure-from-motion (SfM) photogrammetry is revolutionising the collection of detailed topographic data, but insight into geomorphological processes is currently restricted by our limited understanding of SfM survey uncertainties. Here, we present an approach that, for the first time, specifically accounts for the spatially variable precision inherent to photo-based surveys, and enables confidence-bounded quantification of 3-D topographic change. The method uses novel 3-D precision maps that describe the 3-D photogrammetric and georeferencing uncertainty, and determines change through an adapted state-of-the-art fully 3-D point-cloud comparison (M3C2; Lague, et al., 2013), which is particularly valuable for complex topography. We introduce this method by: (1) using simulated UAV surveys, processed in photogrammetric software, to illustrate the spatial variability of precision and the relative influences of photogrammetric (e.g. image network geometry, tie point quality) and georeferencing (e.g. control measurement) considerations; (2) we then present a new Monte Carlo procedure for deriving this information using standard SfM software and integrate it into confidence-bounded change detection; before (3) demonstrating geomorphological application in which we use benchmark TLS data for validation and then estimate sediment budgets through differencing annual SfM surveys of an eroding badland. We show how 3-D precision maps enable more probable erosion patterns to be identified than existing analyses, and how a similar overall survey precision could have been achieved with direct survey georeferencing for camera position data with precision half as good as the GCPs’. Where precision is limited by weak georeferencing (e.g. camera positions with multi-metre precision, such as from a consumer UAV), then overall survey precision can scale as n-½ of the control precision (n = number of images). Our method also provides variance-covariance information for all parameters. Thus, we now open the door for SfM practitioners to use the comprehensive analyses that have underpinned rigorous photogrammetric approaches over the last half-century. |
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