Unsupervised change detection between airborne LiDAR data points, taken at separate times over the same location, can be difficult due to unmatching spatial support and noise from the acquisition system. Most current approaches to detect changes in point clouds rely heavily on the computation of Digital Elevation Models (DEM) images and supervised methods. Obtaining a DEM leads to LiDAR informational loss due to pixelisation, and supervision requires large amounts of labelled data often unavailable in real-world scenarios. We propose an unsupervised approach based on the computation of the transport of 3D LiDAR points over two temporal supports. The method is based on unbalanced optimal transport and can be generalised to any change detection problem with LiDAR data. We apply our approach to publicly available datasets for monitoring urban sprawling in various noise and resolution configurations that mimic several sensors used in practice. Our method allows for unsupervised multi-class classification and outperforms the previous state-of-the-art unsupervised approaches by a significant margin.
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