Roland Geibel 
  
equation (7) and (8) are fulfilled, the T-segment is denoted as over-segmented. In Fig. 5d M1 is intersected by T only to 
a little part, such that equation (8) does not hold and only M2 is assigned to T as correct. T is not over-segmented. 
Under-segmentation. If one M-segment intersects with more than one T- 
segment, we can expand our definition of the measures St and Sy to: 
Stu = As / Aqiur2 and Suv = As/ AM (9) 
Like in the case of over-segmentation a segment could already be classified as 
correct, now one of the T-segments can already be classified as correct or as 
over-segmented. If no classification is assigned and if 
  
  
Fig. 6: Two T-segments and 
Sq; » Sa. and Suv » S4, (10) one Megaman under- 
holds, then the M-segment is classified as under-segmented. If however one of 
the T-segments was already classified as correct or over-segmented, then in 
addition to equation (10) the average of the measures for the under-segmentation 
must be bigger than the average of the measures for the former classification (cp. 
equation (8)). In Fig. 6 M is first assigned to T1 as a correct classification, then to 
T1u T2 as under-segmentation. 
  
  
  
  
  
Missed and Noise. T-Segments, which then are neither classified as ‘correct’, nor 
as over-segmented' nor as under-segmented' are classified as missed (Fig. 7a). M- 
segments, which then are neither classified as ‘correct’, nor as ‘over-segmented’ 
nor as 'under-segmented' are classified as noise (Fig. 7b). 
  
  
  
  
  
  
  
  
  
3.3 Segmentation of multiple areas 
The above classification is carried out for all T-segments and all M-segments of 
an object (e.g.: a building). Thereon one T-segment can be related to many M- 
segments and one M-segment can be related to many T-segments. For instance the 
classification of the segmentation result shown in Fig. 2d (43 segments) based on 
the ground truth with 27 segments (Fig. 3) results in 10 correct T- and M- 
segments, 5 over-segmented T-segments, 4 under-segmented M-segments, 4 
missed T-segments and 8 noise M-segments. In investigating multiple objects of a 
scene for a valuation of different procedures, such a classification is obtained for 
each object. 
  
3.4 Valuation of the segmentation 
Fig. 7 a) T-segment (missed), 
In order to receive a quality measure for single objects (e.g.: buildings) or a b) M-segment (noise) 
complete scene (e.g.: city model), the measurements and classifications of single 
object parts (roof parts) must be evaluated. A simple measure of quality can be 
derived from the number of correctly found segments ITk| or from its ratio to all T-segments IT Al : 
i-re] /Iral um 
However since the intersection with the T-segments can differ even if they have been classified as found correctly the 
measure St should be taken into account as a weight factor for each of the T-segments. 
q= > Sr /|TA| (12) 
TeTK 
Since the segments which were classified as over-segmented or even those which were classified as under-segmented 
can be used for further processing and make a contribution to the segmentation quality as compared to missed or noise 
segments they should be recognised in calculating the quality measure. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 331