Ken Arroyo Ohori

Automatically enhancing CityGML LOD2 models with a corresponding indoor geometry

The international standard CityGML defines five levels of detail (LODs) for 3D city models, but only the highest of these (LOD4) supports modelling the indoor geometry of a building, which must be acquired in correspondingly high detail and therefore at a high cost. Whereas simple 3D city models of the exterior of buildings (e.g. CityGML LOD2) can be generated largely automatically, and are thus now widely available and have a great variety of applications, similarly simple models containing their indoor geometries are rare. In this paper we present two contributions: (i) the definition of a level of detail LOD2+, which extends the CityGML LOD2 specification with indoor building geometries of comparable complexity to their exterior geometries in LOD2; and more importantly (ii) a method for automatically generating such indoor geometries based on existing CityGML LOD2 exterior geometries. We validate our method by generating LOD2+ models for a subset of the Rotterdam 3D data set and visually comparing these models to their real counterparts in building blueprints and imagery from Google Street View and Bing Maps. Furthermore, we use the LOD2+ models to compute the net internal area of each dwelling and validate our results by comparing these values to the ones registered in official government data sets.

Modeling a 3D City Model and Its Levels of Detail as a True 4D Model

The various levels of detail (LODs) of a 3D city model are often stored independently, without links between the representations of the same object, causing inconsistencies, as well as update and maintenance problems. One solution to this problem is to model the LOD as an extra geometric dimension perpendicular to the three spatial ones, resulting in a true 4D model in which a single 4D object (a polychoron) represents a 3D polyhedral object (e.g., a building) at all of its LODs and a multiple-LOD 3D city model is modeled as a 4D cell complex. While such an approach has been discussed before at a conceptual level, our objective in this paper is to describe how it can be realized by appropriately linking existing 3D models of the same object at different LODs. We first present our general methodology to construct such a 4D model, which consists of three steps: (1) finding corresponding 0D–3D cells; (2) creating 1D–4D cells connecting them; and (3) constructing the 4D model. Because of the complex relationships between the objects in different LODs, the creation of the connecting cells can become difficult. We therefore describe four different alternatives to do this, and we discuss the advantages and disadvantages of each in terms of their feasibility in practice and the properties that the resulting 4D model has. We show how the different linking schemes result in objects with different characteristics in several use cases. We also show how our linking method works in practice by implementing the linking of matching cells to construct a 4D model.

A dimension-independent extrusion algorithm using generalised maps

One solution to the integration of additional characteristics, for example, time and scale, into GIS data sets is to model them as extra geometric dimensions perpendicular to the spatial ones, creating a higher-dimensional model. While this approach has been previously described and advocated, it is scarcely used in practice because of a lack of high-level construction algorithms and accompanying implementations. We present in this paper a dimension-independent extrusion algorithm permitting us to construct from any (n–1)-dimensional linear cell complex represented as a generalised map, an n-dimensional one by assigning to each (n–1)-cell one or more intervals where it exists along the nth dimension. We have implemented the algorithm in C++11 using CGAL, made the source code publicly available and tested it in experiments using real-world 2D GIS data sets which were extruded to construct up to 5D models.

Population Estimation Using a 3D City Model : A Multi-Scale Country-Wide Study in the Netherlands

The remote estimation of a region’s population has for decades been a key application of geographic information science in demography. Most studies have used 2D data (maps, satellite imagery) to estimate population avoiding field surveys and questionnaires. As the availability of semantic 3D city models is constantly increasing, we investigate to what extent they can be used for the same purpose. Based on the assumption that housing space is a proxy for the number of its residents, we use two methods to estimate the population with 3D city models in two directions: (1) disaggregation (areal interpolation) to estimate the population of small administrative entities (e.g. neighbourhoods) from that of larger ones (e.g. municipalities); and (2) a statistical modelling approach to estimate the population of large entities from a sample composed of their smaller ones (e.g. one acquired by a government register). Starting from a complete Dutch census dataset at the neighbourhood level and a 3D model of all 9.9 million buildings in the Netherlands, we compare the population estimates obtained by both methods with the actual population as reported in the census, and use it to evaluate the quality that can be achieved by estimations at different administrative levels. We also analyse how the volume-based estimation enabled by 3D city models fares in comparison to 2D methods using building footprints and floor areas, as well as how it is affected by different levels of semantic detail in a 3D city model. We conclude that 3D city models are useful for estimations of large areas (e.g. for a country), and that the 3D approach has clear advantages over the 2D approach.

An evaluation and classification of nD topological data structures for the representation of objects in a higher-dimensional GIS

One solution to the integration of additional characteristics, e.g. time and scale, into geographic information system (GIS) datasets is to model them as extra geometric dimensions perpendicular to the spatial ones, creating a higher-dimensional model. Previous work has been mostly limited to higher-dimensional rasters and hierarchies of trees, which grow exponentially with the dimension. As representations with limited topological relationships quickly become intractable in higher dimensions, a topological vector approach seems most suitable for this purpose, requiring the use of higher-dimensional topological data structures. We therefore present in this paper an evaluation and classification of the possible data structures for an nD GIS, including how they can be implemented to support real-world data aspects, such as holes, disconnected components and attributes, as well as practical issues that affect their feasibility, like the availability of algorithms, libraries and software.

A triangulation-based approach to automatically repair GIS polygons

Although the validation of a single GIS polygon can be considered as a solved issue, the repair of an invalid polygon has not received much attention and is still in practice a semi-manual and time-consuming task. We investigate in this paper algorithms to automatically repair a single polygon. Automated repair algorithms can be considered as interpreting ambiguous or ill-defined polygons and returning a coherent and clearly defined output (the definition of the international standards in our case). We present a novel approach, based on the use of a constrained triangulation, to automatically repair invalid polygons. Our approach is conceptually simple and easy to implement as it is mostly based on labelling triangles. It is also flexible: it permits us to implement different repair paradigms (we describe two in the paper). We have implemented our algorithms, and we report on experiments made with large real-world polygons that are often used by practitioners in different disciplines. We show that our approach is faster and more scalable than alternative tools. HighlightsThe repair of invalid polygons is still in practice a manual and time-consuming task.We investigate methods to automatically repair invalid polygons (according to the international standards).We propose a constrained triangulation-based approach, and show that in practice, with typical real-world polygons used by practitioners in disciplines related to the geosciences, it is fast, stable and scales to massive polygons.Our implementation is open-source and freely available under a GPL licence.

Representing the Dual of Objects in a Four-Dimensional GIS

The concept of duality is used to understand and characterise how geographical objects are spatially related. It has been used extensively in 2D to qualify the boundaries between different types of terrain, and in 3D for navigation inside buildings, among others. In this chapter, we explore duality in four dimensions, in the context where space and other characteristics (e.g. time) are modelled as being in four dimensional space. We explain what duality in 4D entails, and we present two data structures that can be used to store the dual graph of a set of 4D objects. We also discuss applications where such data structures could be useful in the future.

Voxelization Algorithms for Geospatial Applications : Computational methods for voxelating spatial datasets of 3D city models containing 3D surface, curve and point data models

Graphical abstract

Automatic semantic-preserving conversion between OBJ and CityGML

We investigate the automatic conversion between two substantially different formats used in 3D city models: the ubiquitous but semantically poor Wavefront OBJ and the semantically rich but less used OGC standard CityGML. We elaborate on their differences and on the challenges involved in their conversion, such as the inference of semantics in an OBJ file for their use in CityGML, and the storage of these semantics back in OBJ. We implement two software prototypes: a conversion of 3D building models from CityGML to OBJ (CityGML2OBJs), and one from OBJ to CityGML (OBJ2CityGML). By presenting both methods and implementations, we aim at increasing the availability of CityGML datasets and the possibility to create them in powerful 3D modelling software.

Modelling higher dimensional data for GIS using generalised maps

Real-world phenomena have traditionally been modelled in 2D/3D GIS. However, powerful insights can be gained by integrating additional non-spatial dimensions, such as time and scale. While this integration to form higher-dimensional objects is theoretically sound, its implementation is problematic since the data models used in GIS are not appropriate. In this paper, we present our research on one possible data model/structure to represent higher-dimensional GIS datasets: generalised maps. It is formally defined, but is not directly applicable for the specific needs of GIS data, e.g. support for geometry, overlapping and disconnected regions, holes, complex handling of attributes, etc. We review the properties of generalised maps, discuss needs to be modified for higher-dimensional GIS, and describe the modifications and extensions that we have made to generalised maps. We conclude with where this research fits within our long term goal of a higher dimensional GIS, and present an outlook on future research.