Olaf Hellwich 
  
expressed by a landuse node on the real world level. On the sensor level multispectral data and interferometric synthetic 
aperture radar (/NSAR) data nodes are shown. The connecting geometry and material level consists of green vegetation, 
wood, and soil nodes for the evaluation of multispectral data, and small-scale roughness and large-scale roughness for 
INSAR data. The states of the landuse node are landuse classes, e.g. forest, agricultural vegetation, and build-up areas. 
The states of the sensor nodes are for instance grey value vectors; those of the material nodes numerical degrees of 
presence. The direction of the arrows indicates that the objects to be extracted from the observations are introduced as 
root nodes and the observations as leaf nodes (cf. (Pearl, 1988, page 157ff.) versus (Kulschewski, 1999b, Kulschewski, 
1999a, page 28f.)). This means that the observations are considered functions of the material properties of the object, and 
that the material itself is seen as a function of the object. In this way the direct sensor model is implemented through the 
a priori probability density function (pdf) of the root node and the conditional pdf's of the leaf nodes and all remaining 
nodes. Thus, the /anduse node is described by the a priori pdf, i.e. by probability values for landuse variable & such as 
p(e = forest) = 0.3. The multispectral image data node is given a conditional pdf p(z,,|m,, m,,,m,) where x, is 
the grey value vector of the multispectral image data, m, the degree of presence of green vegetation, 7n,, the degree of 
presence of wood, and m, the degree of presence of soil. 
real world 
    
  
  
   
material 
  
(C wood 7j C soll small rough large rough. 
Figure 1: Bayesian network for multisensor landuse classification. (small rough.: small-scale roughness, large rough.: 
large-scale roughness) 
For the classification of a pixel the leaf nodes are instantiated with the corresponding grey value vectors from the im- 
age data sets. Then the Bayesian network is evaluated, i.e. the probabilities are propagated according to the respective 
formulas, e.g. given by (Pearl, 1988, Koch, 2000, Kulschewski, 1999b), using the pdf’s. 
The model for pixel-based classification is extended to process multitemporal data allowing changes of the landuse node 
in time. Figure 2 shows the corresponding Bayesian network, in this case for one multispectral data set and multitemporal 
INSAR data sets acquired at later points in time. The arrows between the landuse nodes indicate the dependence of the 
state of the node at time #; on the state of the node at time 1; 1. In the Bayesian network this dependence is implemented 
with the help of conditional pdf's p(c;|e; ,). In the extreme cases this function either does not allow any changes or 
it does not favor any particular state c; with respect to the previous state c; ,. In the first case, for the function values 
p(eilei—1) = 0 holds whenever e; # €i—1 which means that the landuse nodes could be united. In the second case, 
p(eilei—1) = const., independent of the state of £; ; which means that all classes are equally probable, i.e. that the 
landuse nodes could be disconnected. In general the conditional pdf’s of the landuse nodes give transition probabilities of 
landuse in time (Bruzzone and Serpico, 1997). For example, when in a certain area a change from forest to built-up land 
is to be expected this is expressed by the pdf. The conditional pdf's between landuse nodes developing in time can also 
include models describing dynamic developments such as growth and harvest models. 
SON. 
Figure 2: Bayesian network for multitemporal multisensor landuse classification. 
  
The Bayesian network can be extended to incorporate spatial contextual information. For instance for the determination 
  
390 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.