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Thomas Vógtle 
  
4.1 Segmentation of roof planes 
In section 3 the extraction of building hypotheses was described. These regions define the areas where roof planes have 
to be detected. For this purpose a special segmentation algorithm is used which is capable of estimating (oblique) planes 
in 3D space from laser DEM. The used algorithm is described in detail in (Quint & Landes, 1996). Therefore, only a 
short summarization will be given. It is a specific region growing algorithm with a homogeneity predicate that is based 
on the maximum a-posteriori principle. Originally it was developed for aerial colour images but it has proved to be 
suitable for a laser DEM as well. In this case the laser DEM has to be stored as an intensity image, where the grey 
values represent the respective elevations. The homogeneity parameter is the special characteristic of this method. It is 
based on the assumption that each pixel value can be expressed as 
Lx. y) =U f (5. X) + VY GW) + WC (x,y) k=1,....N (2) 
ie. a pixel value I at position (X,,y,) can be expressed as a combination of three well-defined functions 
(£4x.7.)y (0.1) (x.y) ); each depending on the position of this pixel. They define a so-called image model, 
i.e. a mathematical description of the grey value distribution. These functions are constant for each individual plane, but 
differ from plane to plane. The parameters u, v and w are realizations of a random process; they describe a systematic 
difference of the pixel grey values of an image from the theoretical image model. Beside this, noise has to be taken into 
account that additionally affect the intensities. Because of these noise effects, it is not possible to verify the 
homogeneity criteria directly, i.e. the fulfillment of equation (2). This problem is solved by making some assumptions 
about noise and random process (e.g. normal distribution of noise) and computing a probability value for the fulfillment 
of this criteria. If the computed probability for the membership of a pixel to a certain region is higher than a defined 
threshold, the pixel is regarded as belonging to this region. 
In principle, an arbitrary image model can be chosen. For this application, a linear approach, an oblique plane in the 
object space, is used for segmentation of planar parts of the roofs: 
z=ax+by+c G) 
EN EA sc A 
The parameters a, b, c of these planes are estimated by means of this formula during segmentation process and can be 
used for subsequent processing. 
Figure 8 shows some segmentation examples of the DEM regions regarded as building hypotheses. Inside each region 
planes are estimated representing the shape of the building. Generally, the roof planes are extracted correctly, except the 
building in Figure 8 (a) where small plane areas at the ends of the house are missing. Also the penthouse in Figure 8 (b) 
is detected correctly as separate part inside the main roof. In Figure 8 (a) and (c) some small gaps by rejected pixels can 
be observed. These are caused either by disturbing objects on the roof (e.g. antennas, dormers, chimneys etc.) or by 
errors in laser measurement, but do not affect the subsequent intersection procedure. 
4.2 Determination of contour lines and corner points 
After segmentation of roof planes, contour lines and corner points can be derived by intersection of two neighbouring 
planes and intersection of plane and contour line respectively. This is determined by solving the well-known linear 
equation system (derived from eq. 3): 
z=ax+by+c, (4) 
= a,x+b,y+c, 
N 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 931