Fuse, Takashi 
  
Table 1: Averages of Standard Deviations of Estimated Values by Each Method 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Std. Dev. of u (pixels) |Std. Dev. ofv (pixels) 
(a)Spatial Local Optimization Method 0.13 0.15 
(b)Temporal Local Optimization Method 1036 1014 
(c)Multispectral Constraints Method 720 636 
(d)Second Order Derivative Method 697 677 
(a)+(b) 67 65 
(a)+(c) 49 48 
(a)+(d) 45 44 
(b)*(c) 202 203 
(b)+(d) 190 188 
(c)*(d) 140 139 
(a)+(b)+(c) 28 27 
(a)+(b)+(d) 26 25 
(a)+(c)+(d) 19 19 
(b)+(c)+(d) 85 39 
(a)+(b)+(c)+(d) 12 5 
  
  
  
  
  
3.2 Improvement of Spatial Local Optimization Method 
The result, which was solved by spatial local optimization method (Figure 2), was better than other gradient-based 
approaches. In the spatial local optimization method, there were pixels at which flow vectors could not be estimated. 
It is called as aperture problem (Figure 8). It shows a moving plane of constant brightness. When we see the plane 
through the aperture, we cannot recognize the moving of the plane. 
Consequently, flow vectors at all feature points cannot be obtained by 
employing the basic methods of gradient-based approach and their combined 
methods. Hence, it is difficult to analyze details of vehicle motions taking 
into account the shape of the vehicles by the flow vectors which are solved by 
basic methods of gradient-based approach. 
  
Figure 9 shows the distribution of t-value of estimated optical flow only in the 
region of vehicles. In these figures, color at the pixel whose t-value is more 
than 2.0 is black. Particularly in the (a) t-value of estimated # , estimations 
of optical flow are significant at the pixels which locate near edges or have 
optical flow of small magnitudes. 
  
  
  
     
  
  
  
  
  
  
(a) T-Value of Estimated u (b) T-Value of Estimated v 
Figure 9: T-Value of Estimated Optical Flow in the Region of Vehicles 
  
274 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.