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

• Published in: Remote sensing (Basel, Switzerland) Vol. 17; no. 18; p. 3259
• Main Authors: Gruszczyński, Wojciech, Puniach, Edyta, Ćwiąkała, Paweł, Matwij, Wojciech
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.09.2025
• Subjects: Accuracy; Aerial photography; Algorithms; Classification; Datasets; Deep learning; Drone aircraft; Filters; Filtration; ground filters; heteroscedastic regression; Machine learning; Neural networks; Nodes; performance ranking; Photogrammetry; point cloud; Risk assessment; Root-mean-square errors; Subsidence; U-Net; Uncertainty; Unmanned aerial vehicles; Vegetation; vertical displacements; Poland
• ISSN: 2072-4292; 2072-4292
• DOI: 10.3390/rs17183259

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 conventional ground filters that rely on point cloud classification, the proposed approach employs heteroscedastic regression. The U-Net model predicts the conditional expected values of the elevation corrections, aiming to reduce the impact of vegetation on determined ground surface elevations. Concurrently, it estimates the logarithm of the elevation correction 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 determined displacement values, and the percentage of outliers among those values. Performance was assessed using the technique for order of preference by similarity to ideal solution (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 datasets, 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%.