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GPS measured viewpoints —— other viewpoints “+. Conflict to the result of pair-wise registration in 
sequential registration 
  
(a) Residuals between viewpoints obtained in 
multiple registration and GFS data (b) Conceptual structure of sequential alignment 
       
  
      
    
(c) Result of sequential alignment (d) After minimizing violations (overlapped with a 1/500 digital map!) 
Figure 10: Multiple registration using two GPS points which are located near to each other. 
Figure 11(c) and Figure 12(c). Results after minimizing violations are shown in Figure 11(d) and Figure 12(d). 
Obvious violations can still be found in Figure 12(d), while the model in Figure 11(d) has a better consistency. 
Both of the models are overlapped with a 1:500 digital map to show the matching between them. Registration 
accuracy is examined by evaluating the residuals from registered locations to the ground truth of GPS data as 
shown in Figure 11(a) and Figure 12(a). Mean of residuals in Figure 11(a) is 0.712m, and 1.525m in Figure 
12(a). In both of the cases, mean of residuals is larger than the registration error without using GPS data, 
because a least square transformation is conducted in accuracy examination in later one. Conclusion drawn 
from this examination is balancing the distance between GPS points will help in reducing registration error. 
Figure 13 and Figure 14 compares the results of registration accuracy when using two, four, six and nine GPS 
points. Locations of GPS points are shown in Figure 13, as well as the models of range images after minimizing 
violation. In the case of registration using two GPS measured viewpoints, the points are located the same 
with those shown in Figure 11, and so does the model generated. From Figure 13, we can not nd obvious 
di erences between the models generated, since the registration errors of most of the viewpoints are lower than 
Im, which is the pixel size of the Z-images. Registration error of each viewpoint is shown in Figure 14. Mean 
of residuals is 0.712m when using two GPS points, 0.612m when using four GPS points, 0.436m when using six 
GPS points and 0.283m when using nine GPS points. Since the measurement of GPS points has an error of 
20cm, registration using nine GPS points has almost the same order with GPS measurement. In most of the 
cases. as the number of GPS points used in multiple registration increased, higher accuracy in registration can 
be obtained. However, exceptions can be found when GPS data on the other hand upset the local consistency 
among the range images nearby, hence cause larger residuals. Reason for this might be inaccurate GPS data or 
extremely low overlapping between neighboring range image pairs. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 1039