International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
Dempster-Shafer theory allows the combination of the 
probability masses from several sensors to compute a combined 
Hr > 9 
probability mass for each class 4 e 2^: 
[1m (8, ) 
  
BOB m. MB„= A] Isisp 
m(A)= — (2) 
1- I; (8) 
BOB MB =0] ISisp 
As soon as the combined probability masses m(A) have been 
determined from the original ones, both Sup(A) and Sup( A ) 
can be computed. The accepted hypothesis C, e 0 is the class 
obtaining maximum support. 
2.2 Initial Land Cover Classification 
In this process, we want to achieve a per-pixel classification of 
the input data into one of four classes: buildings (B), trees (7), 
grass land (G), and bare soil (S). Five cues are used for this 
purpose, two of them being surface roughness parameters 
derived by applying polymorphic feature extraction (Fórstner, 
1994) to the first derivatives of the DSM. They are as follows: 
1.The height differences AH between the DSM and the DTM 
distinguish elevated objects (trees and buildings) from others. 
We assign a probability mass Pj — P; (AH) ascending with 
AH to the combined class B CT, and (7 - P4) to G CS. 
2.The height differences AH;, between the first and the last 
pulse DSMs are large in areas covered by trees. We assign a 
probability mass Py; — Py, (AHpj;) ascending with AH, to 
class T, and (/ - Pr) to B (GG CS. By doing so we neglect 
that large values of A77; might also occur at the borders of 
buildings and at power lines. 
3.The NDVI is an indicator for vegetation, thus for classes 7 
and G. We assign a probability mass Py = Py(NDVI) 
ascending with NDVI to the combined class 7 « G, and 
(1- Py) to B US. 
4. The strength R of surface roughness, i.e. the texture strength 
of polymorphic feature extraction, is large in areas of great 
variations of the surface normal vectors, which is typical for 
trees. We assign a probability mass Pr = Pg(R) ascending 
with A to class 7, and (/- Pj) to B UG US. By doing so we 
neglect that large values of A might also occur at the borders 
of buildings and at step edges of the terrain. 
5.The directedness D of surface roughness, i.e. the texture 
directedness of polymorphic feature extraction, is also an 
indicator for trees, but only if R differs from 0 significantly; 
otherwise, D is dominated by noise. We assign a probability 
mass Pp = Pp(R, D) ascending with D to class T7, and (1- Pp) 
to B UG CS. 
The probability masses Py, Pri, Py, Pr, and Pp, are assumed to 
be equal to a constant P; for input parameters x « x;. For input 
parameters x ^ x; they are assumed to be equal to another 
constant P», with 0 € P, « P; x I. Between x, and x», the 
probability mass is assumed to be a cubic parabola: 
I: 
In equation 3, i € /AH, R, FL, N, D}. P, and P; are chosen to be 
5% and 95%, respectively. Further, we choose (x, xj) = 
P(x)» P, « (P, - A): (n x- 
X» T X 
X 
Ny =X 
514 
(1.5 m, 3.0 m) for AH and AH; and (x;, x) = (30%, 65%) for 
the NDVI. With respect to Ps, (x;. x;) are linked to the median 
of R to make the definition of P, adaptive to the slope 
variations in a scene: (x, x») = [2-median(R), 15-median(R)]. 
Pj is modelled in the same way with (x, x) = (0.1, 0.9) if 
R € R,,;,, and by Py = 0.5 otherwise: if the slope variations are 
not significant, D thus cannot be used to distinguish any of the 
classes. We choose Rai 5-median(R). The combined 
probability masses are computed for each pixel using equation 
2, and the pixel is assigned to the class of maximum support. It 
is an important property of this method that no sharp thresholds 
are required, but the probability mass functions have a smooth 
transition between two levels P; and P;. 
2.3 Final Classification of Building Regions 
After the initial classification, we obtain a binary image of 
building pixels. Only a small local neighbourhood contributed 
to the classification of each pixel (via R and D), which causes 
classification errors, e.g. singular "building" pixels, or "tree" 
pixels inside buildings. We use a morphological opening filter 
to eliminate singular building pixels. After that, we create a 
building label image by a connected component analysis. A 
second classification based on the Dempster-Shafer theory is 
applied to the initial building regions thus detected, using four 
cues representing average values for each building region. The 
average height differences AH, between the DSM and the DTM 
and the average NDVI (NDVI,) are used in the same way as AH 
and NDVI in the initial classification. We use different 
parameters related to surface roughness. The percentage 77 of 
pixels classified as "homogeneous" in polymorphic feature 
extraction is an indicator for an object consisting of smooth 
surface patches. Thus, we assign a probability mass Py ^ Pj(H) 
to class B (G C S, and (1 - Pjj) to T. The percentage P of 
pixels classified as “point-like” in polymorphic feature 
extraction is an indicator for trees. We assign a probability mass 
Pp = Pp(P) to class T, and (7 - Py) to B (G CS. 
The mathematical model described in section 2.2 is also used 
for computing the probability masses for AH, H, P, and NDVT,. 
Again, we choose P; = 5% and P, = 95%, further (x; x;) = 
(1.5 m, 3.0 m) for AH, (Xi, x) = (30%, 65%) for NDVI, 
(x5, x3) = (0%, 60%) for H, and (x, x») = (30%, 75%) for P. 
The combined probability masses are evaluated for each initial 
building region, and if such a region is assigned to another class 
than “building”, it is eliminated. Finally, the building regions 
are slightly grown to correct for building boundaries 
erroneously classified as trees. 
2.4 Results of Building Detection 
Figure 1 shows the results of the initial Dempster-Shafer 
classification on the left and the final building label image on 
the right. After morphological opening of the binary image of 
the building pixels and after eliminating candidate regions 
smaller than 10 m? the second Dempster-Shafer classification 
is carried out for altogether 2291 building candidate regions. 
344 of these regions are found to belong to a class other than 
“building”, so that we finally obtain 1947 building regions. 
In the initial classification, class “bare soil” mainly corresponds 
to streets and parking lots. Trees are situated near the river 
crossing the scene, along the streets in the residential areas, and 
in backyards. Step edges at the building boundaries are often 
classified as trees. Given the resolution of the LIDAR data, it