Formalisation of the level of detail in 3D city modelling
Introduction
The concept of level of detail (LOD) is essential in 3D city modelling. It is used to define a series of different representations of real world objects, and to suggest how thoroughly they have been acquired and modelled. Although the background and intention of the concept are intuitively recognised, in 3D city modelling the term LOD has been borrowed from 3D computer graphics and accepted without much discussion. In this paper we argue that the term of LOD in 3D city modelling is currently incoherent, and that it is different from the one in computer graphics. It does not have a significant overlap other than the goal of the selection of a model sufficient for accomplishing a required task while balancing computational, economical and cognitive limitations (Çöltekin and Reichenbacher, 2011, Luebke et al., 2003, Mao, 2011).
While the term is prevalent in several papers in the GIS research community, it is influenced by computer graphics and its meaning often differs. For instance, Meng and Forberg (2007) define LOD as a uniform number of milestones along the scale space when taking the scale space as a linear continuum. For Glander and Döllner (2008) it is a degree of generalisation. Forberg (2007) expresses that it as a common way to enhance the performance of interactive visualisation of polyhedral data. According to Sester, 2007, Goetz, 2013 LODs are multi-scale models for different applications. Lemmens (2011) equals it to the term of resolution and states that it is related to how much detail is present in the data and may refer to space, time and semantics.
As explained in Section 2, the LOD in 3D city modelling serves as a specification-related instruction for the acquisition, modelling, generalisation and exchange of spatial data. This is in contrast with computer graphics where models are simplified to their coarser counterparts in a dynamic process. Moreover, LODs of 3D city models do not differ only by the amount of data, richness of details and visual properties, but may also define the semantics, and the complexity of buildings and other city objects required for different applications (Gröger & Plümer, 2012). While researchers recognise that there are no universally agreed LODs for 3D buildings and other objects comparably to the 2D topographic maps that have official scale series (Meng & Forberg, 2007), there is still not much work on the formalisation of LOD, i.e. a fundamental discussion that would standardise and unify the different approaches.
The CityGML 2.0 standard of the Open Geospatial Consortium (2012) contains the de facto LOD concept of 3D city modelling, developed by a Special Interest Group 3D (SIG3D) initiative (Albert et al., 2003, Gröger et al., 2004, Gröger et al., 2005). The specification of LOD for CityGML establishes quality classes for data acquisition, and the model’s LOD roughly reflects the model’s complexity and accuracy (Kolbe et al., 2005, Kolbe et al., 2009). However, as it is the case with other standards, the LOD concept of CityGML has deficiencies, and discussions for its improvement are undergoing (Benner et al., 2013, Löwner et al., 2013).
The goal of this paper is to formalise the concept of LOD in 3D city modelling, and to provide a framework for specifying LODs. Lacking a definition, specification, and a universal standard, the current LODs cannot be compared, translated, sorted, and evaluated. This leads to ambiguity in the communication of the acquisition–modelling properties of a 3D city model between users and producers.
We define the LOD of a 3D city model as the degree of its adherence to its corresponding subset of reality. In this paper we decompose the LOD into six metrics that may be defined by continuous functions (Section 3), yielding a continuous LOD approach. In this view, the LODs are discretisations from a series of functions of such metrics (Section 4). We argue that in such case the traditional term LOD might be misleading. However, we do not propose linguistic modifications because we are aware that the current term is deeply ingrained in the GIS community. We show the example of the implementation of the framework resulting in ten discrete LODs. Finally, a proposal for the integration within CityGML is made (Section 5).
Section snippets
Analysis of existing concepts and the need for an LOD definition
We have evaluated different 3D city model representations and LOD concepts found in academia, standards, products and guidelines (Section 2.1), and we have made an analysis and summarised their shortcomings in Section 2.2. We have found that these standards are essentially different not only by their specification, but also by their driving metrics, targeted usage, and arrangement of thematic classes and elements. In total, 26 level of detail paradigms comprising 79 mutually exclusive LODs have
Composition of the design characteristics of a 3D city model (metrics)
By analysing the standards presented in Section 2, by discussing with other researchers and practitioners, based on own experience, we have composed a list of 6 metrics (quantifiable ingredients) that constitute a 3D city model from the design and specification perspective. These metrics may be applied separately to all data in a spatial extent (or dataset), to a class of city objects (thematic class), and to their elements (features which cannot be semantically further decomposed). The
Proposal of a formalised LOD framework
We define the LOD of a 3D city model as the degree of its spatio-semantic adherence to its corresponding subset of reality. The values through which the adherence is assessed are the metrics introduced in Section 3.1. When an LOD is decomposed into these quantifiable components, a straightforward comparison of two or more LODs is possible. Each such different combination of the values of metrics is a different LOD, and a small difference results in a change in the LOD, making this framework
Realisation of our proposed framework in CityGML
We have implemented our framework in CityGML since it is currently the most relevant standard for 3D city modelling, and it is undergoing discussions for the extension of the LOD concept for the upcoming version (Machl, 2013). There are three main points to translate to CityGML: (1) how to map the presented extended and nested semantic classes; (2) how to integrate the specification of the metrics of a discrete LOD; and (3) how to integrate the geometry of non-CityGML discrete LODs.
However,
Conclusion and future work
In this paper we have given a comprehensive LOD analysis with a list of most shortcomings of current paradigms, and we have discussed the concept of LOD in 3D city modelling thoroughly.
We have defined and formalised the concept, and we have established a harmonised LOD framework which is applicable to any format in 3D city modelling, not just CityGML. We see the LOD as the degree of correspondence between the model and the real-world object, being driven by the geometry, appearance, semantics
Acknowledgements
We wish to thank the reviewers for their constructive comments which helped us to improve the manuscript. The discussions and useful advices of fellow researchers in the 3D city modelling community are gratefully acknowledged. Thanks are also due to companies and institutions that provided us with the information about their internal practices, and to Peter James Morton for the access to his comprehensive database of 3D city models. This research is supported by (1) the Dutch Technology
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