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many flow vectors, inaccurate flow vectors were included. 
Figure 3 shows the result which was solved by temporal local optimization method. The temporal neighborhood was 
defined as 3 frames. Optical flow estimated in the vehicle were much inaccurate, more over in the background, which 
are not moved naturally, were estimated as large magnitude. It is said that temporal local optimization method 
performed well, only when the velocity of object is less than 1 pixel/frame. Hence, when the time interval is about 
1/30 seconds, it is not appropriate that a constant optical flow over temporal neighborhood is assumed. 
The results which was solved by multispectral constrains method (Figure 4) was also worse. Because brightness of 
channels (RGB) in images taken in the air are similar, the solution is unstable (Figure 5). 
  
  
  
  
  
  
  
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Figure 6: Second Order Derivative Method. Figure 7: Spatial Global Optimization Method. 
The results which was solved by second order derivative method (Figure 6) were also worse. In the second order 
derivative method, degree of freedom of overdetermined linear equation system is 1 as well as multispectral constraints 
method. Accordingly, the solution is also unstable and influence of noise become larger. 
Table 1 shows averages of standard deviations of optical flow @, v) estimated by the approaches, which solve the 
constraints equation by increasing in the number of observation equations. Comparing the orders of those averages, 
(a) spatial local optimization method gives the best estimated value in all over the image. 
In global optimization method, iterative number was 100, and coefficient was defined as 100. In the result which was 
solved by spatial global optimization method, the optical flow tended to be small (Figure 7). The magnitude of one of 
the estimated flow vectors in each vehicle was (1) 5.3 pixels/frame, (2) 2.0 pixels/frame and (3) 0.9 pixels/frame, 
respectively. The smoothness constraint smoothes variety of direction of flow vectors, so the magnitudes of flow 
vectors are under estimated. 
In addition to above-mentioned methods, which were applied to the real sequential images, the results by other method 
were worse. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 273