Uwe Bacher 
  
  
        
a) Part of the image b) Distinct dark lines 
Figure 3: Extraction of dark lines with high contrast 
4.1 Hypotheses for Trunks 
First, we extract distinct dark lines (cf. Fig. 3b), with a line extractor based on differential-geometry and the Gaussian 
scale-space (Steger, 1998). The parameters for smoothing and hysteresis thresholding were chosen in a way that only dark 
lines with high contrast were extracted. 
To sort out the hypotheses for trunks, we make use of the following properties of their shadow projection: a) Trunks are 
represented by relatively long straight lines. b) The lines representing trunks are oriented in sun direction. As position 
and attitude of the image as well as the date and time of its acquisition are known, the sun direction could be computed. 
We have estimated it directly from the image. The detection of straight lines in a specific direction is a typical application 
of the Hough transform (Ballard and Brown, 1982). We apply it with the two parameters distance from the origin and 
orientation. For every pixel the orientation and the corresponding distance from the origin of all lines passing through it 
are stored in a two-dimensional (2D) array. In this array long and approximately straight lines with the same distance to 
the origin can be found as local maxima. Hypotheses for trunks are local maxima of an interval around the sun direction. 
In Figure 4a) the local maxima have been projected back into the image as straight lines. Here, the dark lines are oriented 
in sun direction and are called "Hough-lines" for the remainder of the paper. The light straight lines indicate those local 
maxima who are not oriented in sun direction. 
Next, the lines in the image window which are represented by the Hough-lines are selected, connected by morphological 
closing (Serra, 1982), and thinned to their medial axes. The closing allows to link disconnected lines. Short lines are 
eliminated because they cannot correspond to trunks. For the remaining lines approximately straight lines are computed 
by linear regression. The begin and the end of a line is determined from the extent of the connected component. This 
  
54 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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