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43 GPS Utilization 
As above-mentioned, the method is difficult to estimate real 
scale in world coordinates. To deal with the problem, GPS as 
auxiliary information is utilized. For easy application, single 
point positioning of GPS is used here. Since low-end device 
cannot be expected to enough accurate positioning, relative 
position between the measurements is applied for scale 
correction. Specifically, relative orientation is applied based on 
the feature points matching result in the previous section, and 
then the baseline b. is modified to B by using GPS data. 
  
5 JX. iis -AY; 0 
b 
  
Where (X, Y, Zj) is a GPS measurement at time # For the 
sequential frames, above process is applied. With the frames, 
whose position is modified by GPS, the bundle adjustment is 
applied for improving the accuracy. In the sense of 
computation, the local bundle adjustment is more preferable at 
the expense of accuracy. The local bundle adjustment can be 
applied recursively (Mclauchlan, 2000). 
ESTEE, (8) 
1:7+1 
E,; expresses the objective function by using from Ist key 
frame to jth key frame. According to the recursive form, bundle 
adjustment can be conducted effectively. It is important to 
point out here that the accuracy depends on the number of key 
frames with the recursive form. We examined the relationships 
between number of key frames and computation time / sum of 
squared error (Figure 7). In this case, the sum of squared error 
does not decrease more than four key frames. On the other 
hand, the computation time monotonically increase. Figure 8 
depicts the comparison between the trajectories of before and 
after adjustment. After bundle adjustment, perturbation of the 
trajectory is affected. 
(pixel) (s) 
700 4 r 140 
600 | C : 120 wes sum of squared error 
800. 1 e ms asi i 100 (pixels) 
400 Í C r 80 computation time 
300 A. i 60 (seconds) 
200 s - 40 
0 ; - 0 
2 3 4 5  #key frames 
Figure 7. Relationships between number of key frames and 
computation time / sum of squared error 
  
  
0 
before adjustment after adjustment trajectory of camera 
Figure 8. Trajectory with bundle adjustment 
     
  
  
  
  
4.4 Application of the proposed method 
The proposed method was applied to images taken in urban area. 
The images were taken around a building with the resolution of 
1280 x 720. The frame rate is 30 frames per second. In this 
application, we attempted to superimpose flooded height of a 
hazard map (Figure 9) onto the sequential image. The colour 
grids of the hazard map correspond to the flooded height (e.g. 
green represents 0.5-1.0m of flooded height). 
  
    
  
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4l ous SREB 
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Figure 9. Flood hazard map 
    
  
  
  
Figure 10 shows an original image, a result of superimposition, 
and transition of the result (after one to three seconds). 
Compared with hazard map, it is realize that impression is 
improved with the real scene. Scale in world coordinate system 
can be kept in this application. The absolute position, however, 
decreases along with time. 
5. CONCLUSIONS 
This study verified the applicability of a popular method of 
SLAM to wide outdoor space. The method strongly depended 
on the feature points tracking. According to the verification, 
modification of feature points tracking and auxiliary 
information were introduced. We selected marker-based 
approach and GPS as the auxiliary information, and improved 
the stability of the method. In the application of GPS, we also 
studied effect of number of key frames for the local bundle 
adjustment. Through the application, the significance and 
limitation of the method were confirmed. Potential to various 
application of AR was implied. 
As a further work, combination of model based method (Lepetit 
et al, 2003) will be investigated. When three dimensional 
models of large-scale structure are employed, parts of the 
models will be expected to contribute improvement of feature 
points tracking and reconstruction. Additionally, combination 
of sensor based method using IMU and so on, will become 
important issues. Finally, framework building of data fusion 
and sensor fusion will be required. As a result, more impressive 
visualization will be accomplished. 
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