Level of detail in 3D city models

The concept of level of detail (LOD) describes the content of 3D city models and it plays an essential role during their life cycle. On one hand it comes akin to the concepts of scale in cartography and LOD in computer graphics, on the other hand it is a standalone concept that requires attention. LOD has an influence on tendering and acquisition, and it has a hand in storage, maintenance, and application aspects. However, it has not been significantly researched, and this PhD thesis fills this void. This thesis reviews dozens of current LOD standards, revealing that most practitioners consider the LOD to be comprised solely of the geometric detail of data and there are disparate views on the concept as a whole. However, the research suggests that the LOD encompasses additional metrics, such as semantics and texture. The thesis formalises the concept, enabling integration and comparison of current LOD standards. The established framework may be applied to cartography and to different forms of 3D geoinformation such as point clouds. Following the formalised concept, a new LOD specification is presented improving the LOD concept in the current OGC CityGML 2.0 standard, a prominent norm in the 3D GIS industry. The specification introduces 16 LODs for buildings that are shaped after analysing the capabilities of acquisition techniques and a large number of real-world datasets. The improved LOD specification may be integrated in product portfolios and tenders, preventing misunderstandings between stakeholders, and as a better language for communicating the specifics of a dataset to be acquired. The specification also considers different approaches to realise the data. Such geometric references result in dozens of different variants of the same LOD. 3D data according to the LOD specification was generated using a procedural modelling engine that was developed over the course of the research. The engine is capable of producing 3D city models in a large number of different variants and according to the CityGML standard. The thesis also catalogues the many different ways to create 3D city models. A prominent technique for producing data in a different LOD is generalisation, i.e. simplifying a 3D city model. The inverse---augmenting the LOD of a dataset---has not been researched to a great extent, and this thesis gives an overview of the topic. This research demonstrates that it is possible to generate 3D city models without elevation measurements, inherently augmenting the LOD of coarser data (2D footprints). The method relies on machine learning: several attributes found in 2D datasets may hint at the height of a building, thus enabling extrusion and creating 3D city models suited for several applications. Some acquisition techniques may result in multi-LOD datasets, and nowadays there are some regions represented in different, independent datasets. However, it was found that possibilities to link such data are deficient. The lack of linking mechanisms inhibits acquisition, storage, and maintenance of multi-LOD data. Two methods for linking features across two or more LODs have been developed resulting in an increased consistency of multi-LOD datasets. The first method links matching geometries across multiple LODs, while the second method establishes a 4D data structure in which the LOD is modelled as the fourth (spatial) dimension. It is often believed that the more detailed 3D data the better. However, similarly as in computer graphics, dealing with data at fine LODs comes at a cost: such datasets are harder to obtain, their storage footprint is large, and their usage within a spatial analysis may be slow. Scarce research has been dedicated to investigating whether an increase in the LOD of the data brings a comparably significant increase in benefits when the data is used in a spatial analysis. First, an analysis using real-world multi-LOD data was carried out. Different LODs of spatial data covering the Netherlands was used in a spatial analysis to refine population maps, obtaining different results for each LOD. However, several problems are exposed, revealing that using real data for such investigations is not optimal. The remainder of the research focuses on using procedurally generated data for such experiments. Synthetic data in several different LODs has been generated and employed for four spatial analyses (estimation of the building shadow, envelope area, volume, and solar irradiation). The experiments result in different conclusions. Finer LODs usually bring some improvement to the quality of the spatial analysis, but not always and such may be negligible. The results of the experiments ultimately depend on the spatial analysis that is considered. The varying results between different spatial analyses make each of them unique. Furthermore, the benefit a finer LOD brings to a spatial analysis is not always clear and easily measurable. In short, striving to produce data at finer LODs may please the eye, but this is not always counter-balanced in the benefit it brings to a spatial analysis. A further addition to the equation above is that when realised, 3D city models are unavoidably burdened with acquisition errors. An error propagation analysis was performed by disturbing the procedurally generated datasets with a range of simulated positional errors. Comparisons have been made between the intentionally degraded datasets and their error-free counterparts, thus obtaining the magnitude of uncertainty the positional errors cause in a spatial analysis. Based on these experiments, several findings are discovered, most importantly: 1. How the LODs are realised (which geometric references are used) has a larger influence than the LOD. A coarse LOD produced with a favourable geometric reference may yield better results than a finer LOD realised with an unfavourable reference. 2. Positional errors considerably affect spatial analyses. The effect is comparable across similar LODs. Simpler LODs are sligthly less affected by positional errors, but they may contain a large systematic error. 3. Errors induced in the acquisition process generally cancel out the improvement provided by finer LODs. The main conclusion is that in the considered spatial analyses the positional error has a significantly higher impact than the LOD. As a consequence, it is suggested that it is pointless to acquire geoinformation at a fine LOD if the acquisition method is not accurate, and instead it is advised to focus on the improvement of accuracy of the data. The thesis proposes additional research for future work. For example, since this research focuses specifically on 3D building models, it would be worth extending the research to other urban features such as roads and vegetation. Furthermore, quality control in 3D GIS does not encompass the evaluation of the LOD of data. Hence integration of the LOD in quality standards should be a priority for future work.