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a) Hough-lines (black) b) Hypotheses for trunks 
Figure 4: Result of Hough transformation and Hypotheses for trunks 
  
results in basic hypotheses for trunks. Unfortunately, they can also correspond to the shadow projections of disturbing 
objects such as poles or street-lamps (cf. Fig. 4b). The result demonstrates that the extraction of the trunk is feasible, 
though it still has to be refined. For example, hypotheses for trunks can be tracked in sun direction to search for lines with 
low contrast. 
42 Direct Projection of the Trunk in Nadir Direction 
An important evidence for a hypothesis for a trunk is the existence of a trunk in direct projection. Additionally, the base 
of the trunk can be determined more robustly and more accurately based on the direct projection. Contrary to the shadow, 
which is always darker than the surroundings, the direct projection of the trunk can be both, lighter and darker. Therefore, 
we extract dark as well as light lines. Then, we use the same procedure based on the Hough transformation as described 
above for the selection of lines in nadir direction. Ideally, finally one single long line represents the direct projection of the 
trunk. As search area, a parallelogram is chosen. Figure 5a) shows in black the search areas for the hypotheses for trunks 
presented in white. One direction of the parallelogram is determined by the shadow projection, the other by the direction 
to the nadir point. The lengths are the same as for the hypotheses for the trunks. The extracted lines within the search 
areas and the extracted lines pointing in nadir direction are illustrated in grey and white, respectively. The procedure 
is successful for the street-lamp on the top-left and for the trunk on the bottom-right. However, a refinement is still 
necessary. Figure 5b) demonstrates the procedure in another part of the image, showing good results for the street-lamp 
on the bottom-right. 
      
a) Example 1 b) Example 2 
Figure 5: Direct projection of trunks in nadir direction (Hypotheses for trunks from shadow projection = white; search 
area = black parallelogram; lines = grey; lines in nadir direction = white) 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 55