Table 3 Differences of estimated heights (cleaned 
data) to heights bilinearly interpolated in 
  
  
  
  
  
  
  
  
  
  
  
  
  
the reference DTM 
= 1224 1225 
€ [absolute absolute 
S Max. RMSE max RMSE 
1 31.7 7.2 42.9 8.9 
2 33.8 8.4 44.8 9.4 
3 38.7 9.5 47.6 112 
4 40.9 9.6 48.0 10.0 
5 41.7 10.2 52.7 10.7 
  
  
Table 4 Differences of estimated heights (raw 
data) to heights bilinearly interpolated in 
  
  
  
  
  
  
  
  
  
  
  
  
  
the reference DTM 
= 1224 1225 
= | Notus] sr. [tole | parer 
1 203.3 11.5 158.8 12.6 
2 175.1 12.6 157.5 13.3 
3 251.2 14.0 236.8 15.9 
4 198.8 19.5 224.1 17.1 
5 248.7 19.0 298.3 18.3 
  
  
Table 5 Differences between new and reference 
  
  
  
  
  
  
  
  
  
  
  
  
  
DTM 
= 1224 1225 
1 94.3 8.9 271.5 19.9 
2 93.6 9.5 235.6 18.6 
3 94.7 10.4 191.6 18.5 
4 107.8 10.9 233.0 19.3 
S 98.6 10.4 52.7 17.0 
  
  
  
Table 3 represents the accuracy of our matching 
approach. The accuracy is in the subpixel level! The 
figures of Table 5 are worse due to interpolation errors 
(330,000 points were interpolated from 16,000 - 20,000 
points). Still the results for map sheet 1224 are close or 
less than 10 m. The results for map sheet 1225 are worse 
due to the mountainous terrain, many forests and the lake. 
With denser measurement points they should be close to 
the results of map sheet 1224 as Table 3 also indicates. 
Version 1 (without constraints) is surprisingly good. The 
reason is that the approximations were very good. 
Additionally the points were chosen along nearly vertical 
edges. Thus, the precision in x-direction is good and 
errors in y (gliding along the edge) influence minimally 
the estimated heights due to the horizontal base. 
Additionally, the results of version 1 are based on fewer 
points due to many detected blunders (Table 2). This 
922 
reduced density, however, influence the accuracy as it 
can be seen for map sheet 1225 (Table 5). The 
advantages of the use of the constraints will become more 
apparent in a realistic case when the approximate values 
are poorer. 
Version 4 is worse than the similar version with gradient 
magnitude images (version 2). The difference is not so 
big again due to good approximations and many reduced 
points for version 4. The shift versions (3 and 5) perform 
quite well. Version 5 gives the best results of Table 5 for 
map sheet 1225 due to the small patch size which models 
better the irregular terrain surface, and the large number 
of correct points which reduces the interpolation errors. 
The improvement of the results due to blunder detection 
is remarkable. Table 4 shows the same results as Table 3 
but for the raw data (including blunders). The results are 
as the average 37% worse than those of Table 3. 
For visualisation the absolute differences d between the 
two DTMs which are higher than the threshold value t are 
combined with the orthophoto and marked as white areas 
(Figure 7 and Figure 8). The new DTM was derived from 
the points of version 2 and the threshold is defined by: 
t = d+ RMS) (2) 
with d mean of absolute differences. 
Differences higher than the threshold can be found 
especially in three types of areas (Figure 7 and Figure 8 at 
a, b and c): 
(a) At the mountain-ridges and cliffs. At these regions 
there are surface discontinuities and forests. 
Additionally interpolation errors occur because the 
density of the selected points was low at these regions 
and thus the terrain surface could not be modelled 
correctly (see Figure 9 with the triangles used for 
DTM interpolation). 
(b) At forest areas, because the matched points are on 
the tree tops and the reference DTM refers to the earth 
surface. 
(c) On the lake surface. The selected points lied on 
either sides of the lake, and at certain places much 
higher than the lake surface. Thus, the large triangle 
that were used for the DTM interpolation (Figure 9) 
were lying much higher than the lake surface.