11 Jan 2022
11 Jan 2022
Status: a revised version of this preprint is currently under review for the journal ESurf.

Full 4D Change Analysis of Topographic Point Cloud Time Series using Kalman Filtering

Lukas Winiwarter1, Katharina Anders1, Daniel Schröder2,3, and Bernhard Höfle1,4 Lukas Winiwarter et al.
  • 13DGeo Research Group, Institute of Geography, Heidelberg University, Germany
  • 2Department of Civil and Mining Engineering, DMT GmbH Co. KG, Essen, Germany
  • 3Faculty of Geoscience, Geotechnology and Mining, University of Mining and Technology Freiberg, Germany
  • 4Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Germany

Abstract. 4D topographic point cloud data contain information on surface change processes and their spatial and temporal characteristics, such as the duration, location, and extent of mass movements, e.g., rockfalls or debris flows. To automatically extract and analyse change and activity patterns from this data, methods considering the spatial and temporal properties are required. The commonly used M3C2 point cloud distance reduces uncertainty through spatial averaging for bitemporal analysis. To extend this concept into the full 4D domain, we use a Kalman filter for point cloud change analysis. 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, again associated with an uncertainty. Through the temporal smoothing, the Kalman filter uncertainty is, in general, lower than the individual bitemporal uncertainties, which therefore allows detection of more change as significant. In our example time series of bi-hourly terrestrial laser scanning point clouds of around 6 days (71 epochs) showcasing a rockfall-affected high-mountain slope in Tyrol, Austria, we are able to almost double the number of points where change is deemed significant (from 14.9 % to 28.6 % of the area of interest). Since the Kalman filter allows interpolation and, under certain constraints, also extrapolation of the time series, the estimated change values can be temporally resampled. This can be critical for subsequent analyses that are unable to deal with missing data, as may be caused by, e.g., foggy or rainy weather conditions. We demonstrate two different clustering approaches, transforming the 4D data into 2D map visualisations that can be easily interpreted by analysts. By comparison to two state-of-the-art 4D point cloud change methods, we highlight the main advantage of our method to be the extraction of a smoothed best estimate time series for change at each location. A main disadvantage of not being able to detect spatially overlapping change objects in a single pass remains. In conclusion, the consideration of combined temporal and spatial data enables a notable reduction in the associated uncertainty of the quantified change value for each point in space and time, in turn allowing the extraction of more information from the 4D point cloud dataset.

Lukas Winiwarter et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esurf-2021-103', Roderik Lindenbergh, 04 Mar 2022
  • RC2: 'Comment on esurf-2021-103', Dimitri Lague, 19 Mar 2022
  • AC1: 'Authors' comment in response to the RCs', Lukas Winiwarter, 25 Apr 2022

Lukas Winiwarter et al.

Model code and software

lwiniwar/kalman4d: v0.0.2 Lukas Winiwarter

Lukas Winiwarter et al.


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Short summary
We present a method to extract surface change information from 4D time series of topographic point clouds, recorded with a terrestrial laser scanner. The method uses information on the sensor to spatially and temporally smooth the data, reducing uncertainties. The Kalman filter used for the temporal smoothing also allows to interpolate over data gaps or extrapolate into the future. Clustering areas where change histories are similar allows us to identify processes that may have the same causes.