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and the distance along the extracted network (network distance; ) are calculated between all pairs (i, j), # j, of points 
which are connected in both networks. The ratio r; ; between these two distances is calculated for each pair (1, j): 
network distance’ 
ref 
ij 
Tj 2j = 
network distance 
If r;,; is larger than one, the distance between points P; and Pj along the extracted network is larger than the respective 
distance along the reference network. In this case it is referred to as detour factor’, (detour factor with respect to the 
reference network). The mean detour factor is defined as the mean of all values detour factor’, ; 
The optimum value for the mean detour factor is 1.0. The mean detour factor increases with the amount of missing 
connections within connected components of the extracted network and with the degree of “wiggling” extraction (see 
Fig. 3). 
Reference 
    
   
Extraction 
Figure 3: Wiggling extraction 
For the evaluation of the connectivity of the extracted network, a number of points P; are defined equally distributed within 
the reference network. All possible pairs of these points are examined if they are connected in the reference network, i.e., 
if they lie within the same connected component. For these CR pairs connected in the reference it is checked whether 
they are connected in the extracted network as well. This yields CB pairs which are connected in both networks. Based 
on CR and CB, connectivity is defined as 
CB # of pairs connected in both networks 
  
connectivity = — = : 
> CR  # of pairs connected in reference network 
The optimum value of the connectivity is 100%. The connectivity decreases with an increasing fragmentation of the 
extracted network with respect to the reference network. 
The mean detour factor can be used to quantify the improvements achieved by the completion within connected com- 
ponents, whereas the connectivity quantifies the improvements achieved by the completion between different connected 
components. 
5 RESULTS 
In this section, results of the approach proposed in this paper are presented. The calculation of the network distance is 
performed based on the actual length of the road segments along which the shortest path has been found. No weighting 
of the roads according to their class or width is done. The optimal distance is calculated simply as the Euclidean distance 
between the respective points, i.e., no additional information like topography, land use or environmental conservation is 
taken into account until now. The check of the link hypotheses is performed automatically as described in Sect. 3. In 
this step, the geometry of the accepted hypotheses is improved according to the image data. To reduce the amount of 
computation time, the search for a road which connects the two end points of a link hypothesis is performed only in a 
restricted region of interest (ROI) which contains both end points and which is assumed to contain the connecting road 
as well. The following results were obtained using an elliptical ROI with the two end points as focuses and a numerical 
eccentricity of 0.75. The iterative process of determining link hypotheses and checking them is broken off automatically 
if no unchecked link hypothesis has a detour factor higher than the mean plus three times the standard deviation of the 
detour factors of the whole network. 
The distance between the equally spaced auxiliary nodes (see Sect. 2.4) was set to 100 m. The maximum optimal distance 
was set to 300 m. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 983