Geographical point cloud modelling with the 3D medial axis transform

A geographical point cloud is a detailed three-dimensional representation of the geometry of our geographic environment. Using geographical point cloud modelling, we are able to extract valuable information from geographical point clouds that can be used for applications in asset management, crisis management, city and landscape planning, and environmental simulations.
During this process the point cloud is semantically enriched, e.g. by performing classification, and structurally enriched, e.g. by performing segmentation or surface reconstruction. In this thesis I propose a new approach to geographical point cloud modelling based on the 3D Medial Axis Transform (MAT), a skeleton-like representation of shapes that explicitly models both the topology and the geometry of shapes. While the 3D MAT has been used before in other fields, its application to geographical point clouds is novel. Advantages of the MAT over existing mostly 2.5D and boundary representation-based methods include that 1) it is fully 3D, 2) it can be used to intuitively structure and decompose a point cloud into objects, 3) it clearly separates a point cloud into interior and exterior volumes, and 4) it is able to compactly characterise geometrical properties of a shape though its local medial geometry. I make three core contributions. First, I explain how to robustly approximate the 3D MAT for large real-world geographical point clouds. This is critical for geographical point clouds because they are inherently noisy due to the challenging acquisition conditions and the fact that the MAT in itself is highly sensitive to noise. Second, I show how to structure the MAT into a connected set of medial sheets that form so-called 'medial clusters' that give us a natural decomposition of the point cloud into objects. Third, I demonstrate how the MAT can be applied for feature aware point cloud simplification and visualisation, visibility analysis, watercourse detection, and building detection. Due to noise and limitations in the point density of geographical point clouds, the MAT performs best for objects that have a clearly defined volume in the point cloud such as for example houses and landscape features. It is less suitable for object like trees and thin street furniture. The core result of this thesis is that I prove that the 3D MAT is a useful and practically viable tool for geographical point cloud modelling.