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Jochen Schiewe
32 DSM Normalization
[n order to obtain heights relative to the terrain, a normalized Digital Surface Model (nDSM), i.e. the difference be-
tween the DSM and the Digital Terrain Model (DTM), has to be generated. In practise, neither the DTM nor any addi-
tional information (e.g., landuse data) are available, or these data are too expensive for an economic use, or they are not
accurate or reliable enough, so that an approximated DTM has to be computed automatically.
321 Discussion of previous work. Apart from other methods for the normalization task (e.g., Shi and Shibasaki,
1996) the most widely cited and used procedure is the one which is proposed by Weidner and Fôrstner (1995): Based on
mathematical greyscale morphology an opening consisting of an erosion, i.e. a minimum filtering on the original height
values, and a dilation, i.e. a maximum filtering on this result, is performed on the DSM. The size of the moving window
- also called the structural element W - has to be chosen in such a way that it is not entirely contained in the elements
above the terrain which shall be cut off (i.e., buildings and wooded areas).
Obviously, the problem with this method is the proper choice of the size of W: If it is set too small, the DTM becomes
too high and the normalized DSM too low (see figure 2, left hand side). If this nDSM shall be used for object extraction
(see section 3.3) valuable height information is lost (i.e., the number of omission errors is increasing). If on the other
hand W is too large, the approximated DTM becomes too low and the nDSM too high, so that the "false alarm rate"
(Le., the number of commission errors) is increasing.
Classical opening Compressing opening
(too small)
W, D ror; >
Level j
(Wrop still too small)
Wor; 11
ty
actual terrain
Level j+1
(Wrop larger than
object)
Local DTM approximation:
IR . .
coming from top
JITPTTT coming from bottom » »
Wsorja
Figure 2. Principles of classical and compressing opening methods.
322 Our approach. In order to find a (sub-)optimal compromise between the mentioned extremes we propose the
following method called compressing opening. This algorithm performs one opening from the top, i.e. starting with the
DSM itself (resp. a structural element size W-op of 1), and one from the bottom, i.e. starting with the global minimum
(resp. Wyorrom equals the image size). These openings are constantly repeated with a reduced W-op resp. an increased
Wsorroy until both element sizes are equal. This proceeding leads to a monotonous decrease of the local minimum
heights hzop resp. an increase of hgorrow (i.e., the compression effect). If hop equals hgorrow — which has to be checked
4 every level, this is an indication that the terrain surface has been reached from both directions and hence the desired
DTM approximation is obtained.
Figure 2 (right hand side) outlines the principle of the proposed method which in contrast to the classical opening in-
deed needs more computational time but delivers more reliable results. Figure 3 demonstrates a successful example
showing deviations of the approximated DTM from the actual one of less than 1 m.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 809
