Grouping segments of lineaments seems obvious to a human operator, but it is not the same for an automatic process. The global vision makes it possible to easily put end to end segments leading, from a point A, towards a point B, by respecting criteria of proximity and orientation. In an automatic process, available information remains very local and it is possible to aggregate two segments which, although close, do not belong to the same lineament.

The example below shows a typical case:

Figure 16: Problems occurring when linking from local criteria.

The path passing through the bottom segment seems most regular, although it is not shortest.

STEGER and Al [C. Steger, 1997] propose to solve this type of problem, for aerial images, with a method based on fuzzy logic. A graph gathers the possible connections between segments, their opportunity is evaluated by means of three fuzzy criteria, defined in [ 0, 1 ], combined by means of one AND: the absolute distance, the relative distance and collinearity.

Absolute distance

is a function of the minimal distance which separates the two ends, closest to the two segments:

• a separation lower than 20 meters gives 1,
• a separation higher than 100 meters gives 0,
• the intermediate values are calculated by linear interpolation.
  
  

Relative distance

results from the comparison of the shortest segment of road which joins each end and the distance separating the ends. If the ratio is

• lower than 1, the value is set to 1,
• higher than 3, the fuzzy value is set to 0.
  
  

Collinearity

is calculated from the two angles formed by

• the directions of the segments of roads finishing at each end and
• the direction of the line segment likely to connect the two ends.
  

Only the minimal value of both is considered. An angle lower than gives 1, whereas an angle higher than gives 0.

Such a process gives rather good results, in particular in the slightly built zones. It has the advantage of retaining the segments which prolong the roads coming from outside, and to reject the small streets, thus the crossings of small agglomerations are continuous.

Small occlusions do not seem to pose any problem. For example, a case similar to that presented Figure 16 is correctly treated and the most regular path selected.

A problem remains for crossroads. If the preliminary low-level processing did not detect any ``seed'' point in the crossroads, the process is unable to connect the segments.

                  
  
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