GENERALIZATION OF 3D BUILDING DATA 
BASED ON A SCALE-SPACE APPROACH 
Andrea Forberg 
Institute for Photogrammetry and Cartography, Bundeswehr University Munich, 85577 Neubiberg, Germany 
andrea. forberg@unibw-muenchen.de 
Commission IV, WG IV/3 
KEY WORDS: Multiresolution Representation, Generalization, Three-dimensional Building Model, Image Analysis, Rectification 
ABSTRACT: 
In image analysis, scale-space theory is used, e.g., for object recognition. A scale-space is obtained by deriving coarser 
representations at different scales from an image. With it, the behaviour of image features over scales can be analysed. One example 
of a scale-space is the reaction-diffusion-space, a combination of linear scale-space and mathematical morphology. As scale-spaces 
have an inherent abstraction capability, they are used here for the development of an automatic generalization procedure for three- 
dimensional (3D) building models. It can be used to generate level of detail (LOD) representations of 3D city models. Practically, it 
works by moving parallel facets towards each other until a 3D feature under a certain extent is eliminated or a gap is closed. As not 
all building structures consist of perpendicular facets, means for a squaring of non-orthogonal structures are given. Results for 
generalization and squaring are shown and remaining problems are discussed. 
1 INTRODUCTION 
The Level of Detail (LOD) concept is a common way to 
enhance the performance of interactive visualization of 
polyhedral data. To reduce the number of polygons to be 
displayed, objects, that are closer, are represented with more 
detail than objects that are far away (cf. Fig. 1). 
  
  
  
  
  
Figure 1: Different Levels of Detail (LOD) of a building 
automatically generated by scale-space based generalization 
The focus of this work lies on the simplification of three 
dimensional (3D) building data for the generation of LOD 
representations of city models. For the automatic derivation of 
coarser models from a fine-scale model, ie, for 3D 
generalization, different approaches from computer graphics 
and computational geometry exist. Most of them are developed 
for general objects and do not consider the specific structure of 
buildings, which consist mainly of right angles. (Heckbert and 
Garland 1997) give a summary of common approaches for 
surface simplification. Approaches for automatic LOD 
194 
generation are represented by (Varshney et al. 1995) and 
(Schmalstieg 1996). An important approach for the 
simplification of objects with perpendicular structures is given 
by (Ribelles et al. 2001). In order to obtain a coarser 
representation. for computer aided design (CAD) models, 
features of polyhedra are found and removed based on planar 
cuts. The approach can be generalized to deal with quadric and 
other implicit surfaces. 
Approaches from cartography or Geographic Information 
Systems (GIS) take into account the properties of buildings, but 
mostly focus on 2D generalization. Some of them are described 
by (Staufenbiel 1973, Mackaness et al. 1997, Meng 1997, and 
Weibel and Jones 1998). An approach, which applies least 
squares adjustment for generalization of building ground plans, 
can be found in (Sester 2000). (Kada 2002) presents one of the 
rare approaches for automatic 3D generalization of buildings. A 
least-squares adjustment is combined with an elaborate set of 
surface classification and simplification operations. Another 
work on 3D generalization of buildings is (Thieman 2002), 
which proposes to decompose a building into basic 3D- 
primitives. Primitives with a small volume are eliminated. 
In this paper 3D generalization is realized based on scale-space 
theory. In image analysis, a scale-space is obtained by deriving 
representations at different scale from an image. In Section 2 
scale-spaces for 2D images are investigated. Their application 
to 2D ground plans, i.e., vector data, is described and an 
approach for a 3D-generalization of orthogonal structures is 
introduced. As not all buildings consist only of right angles, in 
Section 3 meanings for squaring non-orthogonal 3D structures 
are given. The focus lies on the squaring of inclined roof- 
structures. Results for the simplification of orthogonal 
structures as well as for the roof-squaring are presented. The 
paper ends up with conclusions and an outlook. 
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