Determining Vertical Displacement of Agricultural Areas Using UAV-Photogrammetry and a Heteroscedastic Deep Learning Model

Abstract

This article introduces an algorithm that uses a U-Net architecture to determine vertical ground surface displacements from unmanned aerial vehicle (UAV)-photogrammetry point clouds, offering an alternative to traditional ground filtering methods. Unlike con-ventional ground filters that rely on point cloud classification, the proposed approach em-ploys heteroscedastic regression. The U-Net model predicts the conditional expected val-ues of the elevation corrections, aiming to reduce the impact of vegetation on determined ground surface elevations. Concurrently, it estimates the logarithm of the elevation cor-rection variance, allowing for direct quantification of the uncertainty associated with each elevation correction value. The algorithm was evaluated using three metrics: the root mean square error (RMSE) of vertical displacements, the percentage of nodes with deter-mined displacement values, and the percentage of outliers among those values. Perfor-mance was assessed using the technique for order of preference by similarity to ideal so-lution (TOPSIS) method and compared against several ground-filter-based algorithms across four datasets, each including at least two time intervals. In most cases, the U-Net-based approach demonstrated a slight performance advantage over traditional ground filtering techniques. For example, for the U-Net-based algorithm, for one of the test da-tasets, the RMSE of the determined subsidences was 6.1 cm, the percentage of nodes with determined subsidences was 80.5%, and the percentage of outliers was 0.2%. For the same case, the algorithm based on the next best model (SMRF) allowed an RMSE of 7.7 cm to be obtained; for 77.3% of nodes, the subsidences were determined; and the percentage of outliers was 0.3%.