yhts of ca. 
wn values 
DTM was 
id has an 
00 m but 
Ihe 1225 
'S, has an 
1500 m. 
at can be 
nost parts 
| and 35 - 
also lakes 
? present. 
1ap sheet 
tential of 
ved from 
oints and 
First, an 
ie SPOT 
he points 
rthophoto 
nd 26064 
vely) and 
yes. After 
iometric 
hophotos 
92 points 
nts were 
otos) and 
he given 
  
DTMs. Using the object to image PMFs, pixel 
coordinates were derived and matching could be 
performed. 
For matching the following 5 different versions were run: 
Version 1: patch size 17 x 17, no geometric 
constraints, conformal transformation 
Version 2: patch size 17 x 17, constraints, conformal 
transformation 
Version 3: patch size 17 x 17, constraints, shifts only 
Version 4: patch size 17 x 17, constraints, conformal 
transformation, grey level image 
Version 5: patch size 9 x 9, constraints, shifts only 
All versions used gradient magnitude images with the 
exemption of version 4 that used grey level images. The 
choice of these versions was based on preliminary 
investigations that were performed with some of the 
worst out of the 136 points. The aim was to compare 
constraints vs. no constraints, grey level vs. gradient 
magnitude images, conformal vs. shift transformation, 
and shifts with different patch sizes. The case of affine 
transformation was excluded a priori because in many 
cases it is not stable since the selected points lie at edges 
and thus two scales and one shear are often not 
determinable. 
Some points were unsuccessfully matched either because 
they were transformed outside the search window or 
because they needed more than 20 iterations. Table 1 
shows these results. 
Table 1 Matching versions 
  
  
  
  
  
  
  
  
1224 1225 
8 Successfully Tizatiors Successfully herations 
> matched per point matched per point 
points points 
1 94.4% 5.6 97.1% 52 
2 97.7% 4.1 98.5% 4.2 
3 99.2% 3.4 99.2% 3.8 
4 94.4% 4.9 97.2% 4.3 
5 | 984% | 36 98.9% 36 
  
  
  
  
  
  
  
These results were analysed for automatic detection of 
blunders. The criteria that have been used for quality 
analysis are: standard deviation of unit weight from the 
least square matching, correlation coefficient between the 
template and the patch, number of iterations, x-shift (i.e. 
change from the approximate values), standard deviation 
of x-shift, y-shift, standard deviation of y-shift, and the 
size of the 4 shaping parameters (two scales, two shears). 
With the conformal transformation only two shaping 
parameters were used (one scale, one shear). After 
matching, the median (M) and the standard deviation of 
the mean absolute difference from the median (s(MAD)) 
were computed for each criterion. The median and the 
S(MAD) were used instead of the average and the 
standard deviation because they are robust against 
blunders. The threshold for the rejection of one criterion 
was defined as M + N - s(MAD). N was selected to be 3 
for all criteria with the exemption of the number of 
iterations, the two shifts and the two scales which should 
be left to vary more (N = 4). A point was rejected (i) 
when one of its criterion did not fulfil the aforementioned 
threshold (relative threshold derived from the image 
statistics), or (ii) one of its criteria did not fulfil a very 
loosely set threshold, e.g. for the correlation coefficient 
0.2 (absolute threshold, valid for all images). The same N 
and absolute thresholds were used for all versions. Table 
2 gives information on the amount of rejected points. 
Table 2 Points rejected by automatic blunder detection 
  
  
  
  
  
  
  
  
1224 1225 
§ | Percentage Percentage 
5 over Remaining over Remaining 
> | successful |good points| successful |good points 
points | points 
1 16.1% 15987 15.7% 18504 
2 11.4% 17485 12.7% 19417 
3 9.2% 18173 9.0% 20391 
4 18.1% 15606 17.2% 18183 
5 10.8% 17714 8.7% 20394 
  
  
  
  
  
  
  
As it can be seen from Table 1 and Table 2, the amount of 
successfully matched points decreases and the percentage 
of detected blunders increases when (i) no geometric 
constraints are used (version 1), and (ii) grey level 
images are used (version 4). From the remaining 
versions, the ones using shifts result in more successful 
points because they are more stable (robust) than the one 
using the conformal transformation. The conformal 
transformation includes a scale which is not always well- 
determinable. Constrained matching needs less iterations 
per point than unconstraint version, especially when only 
shifts are used. The differences between the two shift 
versions are minimal although their patch size differs 
considerably. The above results are valid and similar for 
both map sheets in spite of the different terrain form and 
land usage. 
For the accuracy analysis two comparisons were made: 
e The matched points are bilinearly interpolated in the 
reference DTM grid and the differences between the 
interpolated heights and the heights as estimated by 
matching are computed (Table 3). 
e Andanew DTM was derived from the matched points 
and compared to the reference DTM (Table 5). 
921