Dealing with uncertainties in assessing geomorphic change. Spatially estimating structure-from-motion precisions using a block-resampling approach.
Authors: Strohmaier Florian , Goetz Jason , McColl Sam 
Published: March 2021

&lt;p&gt;Structure-from-Motion &amp;#8211; Multi-View Stereo (SfM-MVS) has become a widely used approach in the study of Earth surface processes to reconstruct high-resolution topography (HRT) models. Starting in the early 2010s, it has become a cheap, flexible and user-friendly alternative to aerial/terrestrial laser scanning in geosciences and in change detection analyses in particular. In this context, previous work has dealt with the spatial distribution of error and with appropriately accounting for uncertainty estimates of such models in change detection results. However, error distribution and propagation are still not widely accounted for in standard analyses: Various sources of error result in complex distribution of model precision and accuracy. This poses challenges on study effort and complexity.&lt;/p&gt;&lt;p&gt;In this study, we developed a novel approach for obtaining spatially distributed estimates of precision for SfM-MVS derived digital elevation models (DEM). We applied block resampling to simulate repeatedly surveyed flights. This approach allows us to create multiple independently-resampled image sets that capture the general geometry of the original survey for SfM-MVS reconstruction. In a case study of observing erosion and deposition patterns of a highly active badass gully (Mangatu fluvio&amp;#8211;mass movement gully complex, East Coast, NZ) we simulated 20 repeated flights (i.e. images sets) for images acquired from UAVs in 2018 and 2019. The subsequent precisions were used for deriving confidence intervals for sediment budgets. Overall, the precision estimates in open-terrain matched well with previous studies based on repeated surveys (~ &lt;5cm). Weaker precisions were observed in areas of vegetation or where viewing angles could be obstructed by surrounding vegetation. The simulated DEMs, which were based on the mean value for each grid cell across the simulations, were in good agreement with the original reconstructed scene: differences were mainly less than 2 cm for most of the exposed erosion and deposition areas.&lt;/p&gt;&lt;p&gt;We estimated volumetric net change to be within [&amp;#8211; 113.07;&amp;#8211;101.48]&amp;#215;1000m&amp;#179; with 95% confidence between April 2018 and April 2019. Gross sediment erosion was [&amp;#8211;123.07;&amp;#8211;111.73]&amp;#215;1000m&amp;#179;; gross deposition was [8.9;11.7]&amp;#215;1000m&amp;#179; in the same time frame. This is well within findings of previous studies. However, compared to these, we could substantially improve the precision of uncertainty estimates. While computationally intensive, our method is able to reduce field work compared to similar studies. It additionally has the advantage of computing precisions that account for uncertainties in both SfM and MVS reconstruction algorithms. This means that SfM-MVS precisions can be computed on past surveys given the images were taken with sufficient overlap, as we demonstrated in our case study.&lt;/p&gt;