Full four-dimensional change analysis of topographic point cloud time series using Kalman filtering

Abstract

Four-dimensional (4D) topographic point clouds contain information on surface change processes and their spatial and temporal characteristics, such as the duration, location, and extent of mass movements. To automatically extract and analyze changes and patterns in surface activity from this data, methods considering the spatial and temporal properties are required. The commonly used model-to-model cloud comparison (M3C2) point cloud distance reduces uncertainty through spatial averaging for bitemporal analysis. To extend this concept into the full spatiotemporal domain, we use a Kalman filter for change analysis in point cloud time series. The filter incorporates M3C2 distances together with uncertainties obtained through error propagation as Bayesian priors in a dynamic model. The Kalman filter yields a smoothed estimate of the change time series for each spatial location in the scene, again associated with an uncertainty. Through the temporal smoothing, the Kalman filter uncertainty is generally lower than the individual bitemporal uncertainties, which therefore allows the detection of more changes as significant. We apply our method to a dataset of tri-hourly terrestrial laser scanning point clouds of around 90 d (674 epochs) showcasing a debris-covered high-mountain slope affected by gravitational mass movements and snow cover dynamics in Tyrol, Austria. The method enables us to almost double the number of points where change is detected as significant (from 24 % to 47 % of the area of interest) compared to bitemporal M3C2 with error propagation. Since the Kalman filter interpolates the time series, the estimated change values can be temporally resampled. This provides a solution for subsequent analysis methods that are unable to deal with missing data, as may be caused by, e.g., foggy or rainy weather conditions or temporary occlusion. Furthermore, noise in the time series is reduced by the spatiotemporal filter. By comparison to the raw time series and temporal median smoothing, we highlight the main advantage of our method, which is the extraction of a smoothed best estimate time series for change and associated uncertainty at each location. A drawback of the Kalman filter is that it is ill-suited to accurately model discrete events of large magnitude. It excels, however, at detecting gradual or continuous changes at small magnitudes. In conclusion, the combined consideration of temporal and spatial information in the data enables a notable reduction in the associated uncertainty in quantified change values for each point in space and time, in turn allowing the extraction of more information from the 4D point cloud dataset.