Estimates of Spatial Variability of Digital Elevation Models from Ensemble Neural Networks

New surveying methods such as terrestrial lidar (TLS) and unmanned aerial systems (UAS) coupled with structure from motion (SfM) algorithms generate point clouds with tens to hundreds of millions points. Of great interest is to extract digital elevation models (DEMs) of the observed scene. Challenges include the presence of various types of vegetation or uneven surfaces. Adding a field survey component can help calibrate the remote observations and generate more accurate DEMs with quantified uncertainties. Field surveys are however time consuming and best kept to a limited number of measurements. In this work, a coastal marsh is measured by both an array (5) of terrestrial lidar sensors and a gridded Real Time Kinematic (RTK) survey. Machine learning techniques are a great fit to extract and quantify information from such point clouds. An ensemble neural network (NN) model is first calibrated to predict the differences between TLS and the reference RTK survey. The NN ensemble is comprised of 1000 different single members. Model outputs include median of the 1000 model for each point as well as the upper 95% or 97.5% upper range and the lower 5% or 2.5% lower range to quantify for each point 90% or 95% confidence intervals. The precision of the predictions for the RTK points and then for the rest of the scene are estimated from the spreads of the ensemble. The ensemble variability quantifies both the model calibration variability as well as the spatial variability of the scene. The latter is included by randomly selecting different training, validation and testing portion of the data set representing different portions of the scene. The predicted uncertainties are compared first to the RTK measurements and then to the marsh scene environments, from smooth tidal flats to different types of vegetations. Uncertainties range from a few centimeters, x cm on average, to 6-8cm to larger than 8 cm depending on the environment with a very high degree of correlation to the scene features. The ensemble model is finally used to predict the DEM for the overall scene including estimates of the precision of the predictions for each raster point. Portions of the scene with high degree of DEM confidence can be retained for further analysis while other areas can be further processed differently. While the method was developed and tested for the combination of TLS and RTK measurements the process can be implemented to other paired survey methods which include a sufficient number of distributed measurements describing a scene.