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of the state of the landuse node the state of neighbouring pixels can be considered. The direction of the arrows in Figure 3 
indicate that the state of the central node, i.e. the node to be evaluated, depends on the state of the neighbouring nodes. A 
reasonable form of dependence could for instance be that a pixel has landuse forest with a high probability, if its neighbours 
are forest. As in reality also the neighbouring nodes depend on the state of the central node, i.e. as the dependence is 
also valid in the opposite direction, the notion of mutual dependence would result in an undirected graph including all 
pixels of the image. Then the Bayesian network for the classification of a single pixel would become a Markov random 
field X over the complete image whose joint pdf p(X) could be evaluated using the well-known optimization methods 
for Markov random fields (Winkler, 1995, Koch and Schmidt, 1994, Hellwich, 1997). Figure 4 shows an example of a 
Markov random field defined on a grey value image using eight-neighbourhoods. 
landuse i-1,j 
  
  
    
  
landuse i,j-1 Tanduse i,j+1 
  
landuse i+1,j 
Figure 3: Bayesian network considering spatial contextual information. The indices indicate row and column of a raster 
image. 
  
  
  
  
  
  
1 2 3 4 
5 6 7 8 
9 10 11 12 
13 14 15 16 
  
  
Figure 4: Markov random field defined on a grid (here: grey value image). 
Furthermore, the Bayesian network can be extended to accommodate grouping and hierarchy of object parts or objects, 
and relations between different types of objects !. For instance, several pixels with a certain landuse could be considered 
as components of an agricultural field. Agricultural field objects could consist of surrounding edges and roads, and pixels 
enclosed by those edges. 
In the following section a shape criterion for a group of raster elements is introduced. It is used to judge whether a 
group of pixels has a shape similar to a rectangle, usually the shape of an agricultural field, or not. If the group of 
pixels approximates a rectangle, this contributes to a high probability to be an agricultural field; otherwise this probability 
decreases. 
3 SEGMENT SHAPE PARAMETER FOR GRID DATA 
A criterion was developed which allows to judge the shape of a group of connected pixels of an image. While it is 
described in depth in (Günzl and Hellwich, 2000), here a short comment on its use in a region-growing algorithm is given. 
The purpose of the criterion is to determine the compactness of an object out of grid data by compensation of the influence 
of the imaged grid. The compensation was found to be possible using a set of geometrical parameters. The concept lead 
to a shape parameter with several advantages: 
1. The parameter is completely independent of the orientation of an object regarding the grid. 
  
! For this purpose it is advantageous to make use of dynamic Bayesian networks (Kulschewski, 1999b, Murphy, 2000). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 391