Persistent homology on LiDAR data to detect landslides

Landslides can result in loss of lives, cause damage to property, infrastructure, utilities, and residential structures and can block transportation routes. Landslide inventory maps can provide spatial-temporal information about past and recent landslides and are used for analysis to create models that can characterize susceptibility. As such, these maps are considered an essential source for risk management tasks. In this paper, we propose a persistent homology method applied on LiDAR-derived digital terrain model data to detect landslides for landslide inventory maps. In testing the hypothesis that persistent homology, a method for computing topological features of a space at different resolutions, can be used to accurately detect landslides, we applied the method on LiDARderived digital terrain models to detect shapes and patterns that are indicative of landslide surface expressions. We validated our test results by comparing them to currently available landslide inventory maps for selected locations in Pennsylvania, Oregon, Colorado and Washington. The results show a different performance for each state; the accuraces were 0.79, 0.71, 0.53, 0.69, and 0.77 for five study areas. Variations in performance are linked to varying surface roughness between different types of landslides, their size, shape, ages, composition, and a possible history of reactivations of landslides that would further pronounce surface expressions. To overcome some of these challenges that may hinder performance of our method, we recommend that other datasets, containing landslides, be considered as additional nth-order dimensions beyond the spatial and elevation dimensions inherent in topographic datasets.