4.2 Probabilistic Relaxation method 
Probabilistic relaxation method (Takagi, 1991) was developed 
as an algorithm for numerical calculation, and the method has 
been widely applied for image matching techniques. The image 
matching is performed by the following procedures: firstly, 
candidate ranges for matching points are estimated in stereo 
image. Secondly, matching probabilities of each point are 
calculated respectively. Finally, these candidate points are 
iteratively improved, and image matching is achieved. 
Generally, the matching probability is called labelling 
probability. The search range is a, the label of each point is 4, 
and the similarity of each point is S. Consequently, labelling 
probability Pi is calculated by the following equation. 
S(A, d, 
P e Ua =P ny )} @) 
S(A,.,a,) 
k'-l 
where, 
i-12,---,n 
k -12,---,m-1 
Ay, : constant value set by a user (usually 0.05 — 0.3) 
  
Figure 6. Extracted Lines in the Last Image 
(Result of Epipolar Matching) 
4.3 Results of Epipolar Matching 
The epipolar lines were estimated along the both ends of 
unmatched lines, and point matching for the both ends were 
performed for 14 neighbouring row around the epipolar lines by 
probabilistic relaxation method. As a result, 54 lines were 
newly matched between the first image and the last image. 
Consequently, the line matching was achieved for total of 182 
out of 268 lines. Figure 6 shows results of the epipolar 
matching. 
S. OBJECT RECOGNITION BY 3D DATA 
5.1 3D Data Acquisition 
In order to acquire 3D data efficiently, camera calibration only 
for X and Y out of orientation parameters was performed in this 
paper under assumption that the image are vertical and Z is 
given by the altitude. Then, orientation for the first and last 
image were performed using only one random GCP which is 
one of the end of matched line. Consequently, 3D data of the 
both ends of all matched lines were calculated respectively. 
5.2 Object Recognition 
Recognition of each object in the image needed to be performed 
3D city modelling. Therefore, object recognition was performed 
using the above 3D data in this paper. AB and CD in Figure 7 
shows the matched lines in the last image. In order to recognize 
these 2 lines which constitute the same object, following 3 
conditions needed to be satisfied. 
* A and C should be placed closer in the image. 
+ The height of the A and C should be almost the same value. 
+ The intersection angle of the AB and CD should be almost 
equal to right angle. 
   
Figure 7. Object Recognition (a) 
On the other hand, EF and GH in Figure 8 shows also matched 
lines in the last image. Similarly, in order to recognize these 2 
lines, following 2 conditions needed to be satisfied. 
+ The height of the E and G should be almost the same value. 
+ The line EG should be corresponded with any line in the first 
image. 
  
Figure 8. Object Recognition (b) 
In Figure 8, line matching for the line EG can be achieved by 
the above procedure. Therefore, additional matched lines are 
added to 182, then, the line matching was achieved for total of 
210 out of 268 lines. Figure 9 shows the final result of line 
matching. In addition, 143 out of 210 lines were recognized for 
each object correctly. On the other hand, the lines which were 
recognized as the same object are expected to have almost the 
same height value; therefore, these values were averaged for 
each object respectively. 
—502- 
  
  
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