Ansgar Brunn 
  
  
   
   
  
U Approximate Surfacq 
Interpretation «ez - - - - Building models 
Q(-------. L- > Reconstructions - - - Instances of 
appearance 
Y 
Reconstructed and 
interpreted building 
  
  
Observed data 
  
  
  
  
  
Figure 1: Work flow of the combined interpretation and analysis. 
1.2 Overview 
Here we assume that the problem of detecting buildings in an arbitrary 2D data set is already solved. A detection procedure 
based on bayesian nets can be found in (Brunn et al., 1998). For each building the detection algorithm gives a bounding 
polygon which encloses the complete building. 
Starting from the subparts of several data sets the work flow is a follows (cf. fig. 1): From the selected part of the data of 
some not necessary all sensor types we generate an approximate description of the building, which is a graph representa- 
tion and contains the topology of its surface. We choose the topology of the surface graph as the base representation of the 
building because the topology is independent of the used sensor type (cf. sec. 2). Each graph element is connected to a set 
of appearance models (e. g. geometric coordinates or attributes or radiometric attributes). Further steps of reconstruction 
and interpretation optimize the graph representation including the attributes. Ideally interpretation and reconstruction 
should be done in a common step. We approximate the common step by iterating separate steps of interpretation (cf. sec. 
3) and reconstruction (cf. sec. 4). 
The paper closes with some conclusions and an outlook on further research (cf. sec. 6). 
  
  
  
  
  
  
  
   
  
  
  
  
  
  
  
  
M M e 
(a) The polymorphic graph of one side of (b) Polymorphic graph of the simplex (c) Simplices are the basis elements of the 
a cube (v=vertex, e=edge, f=face). representation of one side of a cube simplicial complexes (v=vertex, e= edge 
(v=vertex, e=edge, t=triangle) and t=triangle). 
Figure 2: Representations of topology. 
2 MODELING BUILDINGS BY THEIR TOPOLOGY 
2.1 CW-complexes 
We introduce CW-complexes (Jänich, 1994) as a representation of the topology of buildings. The building surface can be 
divided in corner, bounding edge and faces. The corner are called 0-cells, the edges 1-cells and the faces 2-cells (0, 1 and 
2 are the degree of the cells). They are handled as open sets, which means that the union of all points, edges and faces 
yields the complete surface, the intersection of all pairs of elements is empty. 
We define a graph whose vertices are all cells of the three types and whose edges show neighborhood relations: Two 
cells are neighbored if the cell of lower degree is the border of the cell of higher degree. The neighborhood relation is 
  
118 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.