Peter Lohmann 
  
points. For an average flat terrain at a spacing of 1m per pixel, a threshold-value of approximately 1,8m has been shown 
to be appropriate and was used in the further processing. The detected and marked areas are stored as a region (Figure 2 
Upper right). 
Since this region represents just the height-discontinuities, it contains only the edges of interrelated areas like the walls 
of buildings. For this reason, the holes within the single areas are filled in the next step using a HALCON-Operator 
(Figure 2 Mid left). The interesting areas (region of interest, ROI) are now marked, like buildings and forest-areas in 
their outline. These ROl's, however, can not yet be removed in total, because clearings within forest-areas and inner 
courtyards of buildings are filled by this procedure. In order to avoid the unwanted elimination of true ground-points an 
additional step is necessary. 
The total of the ROI's is split into its separate components that are examined sequentially in the following. An automatic 
procedure, which divides the observed ROI in sub-regions, is executed (Figure 2 Mid). In order to do so, the gray value- 
histogram for this ROI is smoothed using a Gaussian filter and the minima are subsequently determined. These minima 
serve as threshold-values for the subdivision into separate different height levels to be found within a ROI. The 
resulting sub-regions contain areas with homogeneous gray values. In the ideal case, this would be a single region, for 
example a building. Since frequently more than one sub-region is formed, for example by remaining ground-points, the 
sub-region of the darkest gray values is eliminated from the further procedure, as a candidate of a most likely ground- 
point region. 
The largest of the remaining regions contains the object to be removed with best probability. A rectangle is fitted to this 
region (see Figure 2 Mid right). The length of the shorter side of the rectangle is used to size the mask of the now 
following dual-rank-filtering. 
The dual-rank-filter (Eckstein et al., 1995)first sorts all gray values within a mask (a circular mask is used to achieve 
rotation invariance) in ascending order and chooses the value, that corresponds to a preset rank k. 
Single rank: Rd, sl lm, I : image (5) 
The value of k determines the gray-value to be selected at a position in percent above the lowest gray value in the sorted 
list. The process is repeated for a position from (100-k)%. This action is comparable to a morphological gray-opening 
or gray-closing, combining a gray-scale erosion and dilatation dependent on the used rank k. 
Erosion: e,myr,cys-RGlo- 5e- 1G Dem) m: filtering mask (6) 
r,c: row, column of image 
Dilatation: LO mr.) ER. 5c-DIG;em) (7) 
Dual rank: (om), =(IO, m)®, m (10) 
Within the dual rank the gray values within an object are replaced by values, which follow the surrounding topology 
and terrain. The resulting image is subtracted from the original. This results in an image which contains candidates for 
removal. 
The resulting image is thresholded again, in order to mark only those points that show a minimum difference 
determined beforehand. This step is necessary to avoid a misclassification of points having only small height- 
differences, originating among others from ground unevenness. The threshold value to be determined is a function of 
the characteristics of the area of examination. A value smaller than approximately 0,5 m doesn't appear meaningful for a 
terrain with a spacing of 1m per pixel, since an unambiguous classification can hardly be guaranteed below this value. 
The objects classified by this method can now be removed from the original height image. A method for filling the 
resulting gaps is to interpolate in two directions from the border points of the gaps. This simple type of interpolation fits 
to the surroundings quite well in a smooth terrain. At bigger gaps, however, the interpolation can generate an artificial 
crosswise pattern, which is produced by border points of varying heights. In order to smooth this effect, finally a mean 
value-filter is applied to the interpolation area in consideration of the border. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 543