Level of Detail Generation of 3d Building Groups by Aggregation and Typification

The real-time visualisation of 3D city models requires the representation of the buildings in different levels of detail (LoD). This LoDs should be generated automatically by specific generalisation procedures. In this article we propose two approaches which extents cartographic generalisation algorithm for the application to 3D building groups generalisation. The problem of generalisation of object groups leads directly to the topic of aggregation and typification. Typification denotes the process of replacing a number of objects in a group by a smaller number of new objects, while leaving the main visual structure unchanged. We describe a typification approach which is able to detect grid like building structures to preserve this structure when reducing the number of involved objects. For the aggregation of 3D building groups we describe an approach based on the 2D aggregation program CHANGE. INTRODUCTION The fast visualisation of large 3D city models requires the representation of the buildings in different levels of detail (LoD). This LoDs should be generated automatically by specific generalisation procedures. Nowadays the main focus of research in 3D building generalisation is on the generalisation of single buildings (Thiemann 2003, Forberg 2004, Thieman and Sester 2004, Kada 2005). However less research activities can be found on the topic of aggregation and typification of 3D building groups. Typification denotes the process of replacing a number of objects by a smaller number of new objects. Simplifying each building by itself is one big step to reduce the number of surfaces to be displayed, but we can continue to reduce the number of surfaces if we take into account that the visible distance between buildings depends on the viewing distance. That means we have to aggregate building geometries if they are too narrow to distinguish between them. The result of the aggregation is a reduced number of building objects and yet another reduction of the number of building surfaces. Current methods to generate different LoDs like edge collapsing, vertex clustering or wavelet transformations work well for all kind of singular objects. The main drawback of all this approaches is that they ignore the structure of architectural data, which is very important for the visualisation of large city models. The institute of cartography and geoinformatics (ikg) at the university of Hannover has experience since a long time in map generalisation of building ground plans by rule based approaches (software CHANGE) and least square adjustment approaches (Sester 2000). In this work we describe an extension of these 2D approaches to 3D objects, which is based on the aggregation of 2D projections of the 3D objects. For typification we can directly adopt approaches from 2D map generalisation. We describe a typification approach based on the so called relative neighbourhood graph (RNG) which is usable to detect grid structures in building groups. TYPIFICATION Generalisation is needed in order to limit the amount of information on a map by enhancing the important information and dropping the unimportant one. Triggers for generalisation are on the one hand limited space to present all the information and on the other hand but also the fact that different scales of an object are needed in order to reveal its internal structure. Typification is a generalisation operation that replaces a large number of similar objects by a small number – while ensuring that the typical spatial structure of the objects is preserved. Consider e.g. a set of buildings in a city: when looking at this spatial situation at a different scale or resolution, the typical distribution and structure of the buildings should still be preserved. In general there are two classes of typification approaches:  typification with structural knowledge and  typification without structural knowledge. Approaches with structural knowledge try to detect geometrical structures in the object groups which should be preserved by the generalisation process. Typification for linear structures is proposed by (Regnauld 1996). Based on a minimum spanning tree (MST) clustering groups are detected; then the relevant objects within these groups are replaced by typical exemplars. This approach for building typification is motivated by the phenomenological property of buildings being aligned along streets – thus a one-dimensional approach is feasible. Another approach which tries to find linear building structures is described in (Christophe and Ruas 2002). In (Anders and Sester 2000) we describe an approach to detect two dimensional structures, but in contrast to the following described algorithm we don’t consider the inner structure of the found cluster. The above described clustering is applied to buildings, thus delineating buildings clusters, and their respective densities (or mean distances, respectively). After clustering, the number of objects within the clusters has to be reduced. The reduction factor can be derived using e.g. the black-and-white–ratio, which is to be preserved before and after generalization, or Töpfer’s radical law. The problem now is to decide which object has to be removed. This question is decisive, since the removal of one object results in gaps. a) b) c) Figure 1: Reduction of a larger data set (a): reduction to 60% (b) and 40% (c) Approaches without explicit structural knowledge try to preserve the overall distribution and structure. (Müller and Wang 1992) use mathematical morphology to typify natural areal objects. Their principle is to enhance big objects and reduce small ones – unless they are important. (Sester and Brenner 2000) describe an approach based on Kohonen Feature Maps. Kohonen Feature Maps are self organising maps which try to preserve the original structure by moving the remaining objects in the direction of the removed one to minimise a certain error measure. In most cases this approach produces excellent results (Figures 1). The drawback of the approaches without structural knowledge is that dominant structures, like linear or grid structures are often destroyed. In cases of regular structures like grids, the approach presented in this paper will be needed (Figure 2). a) b) c) Figure 2: Regular grid structure of objects, which cannot be preserved: initial situation (a), result (b), overlay of initial situation and result (c).