Fuse, Takashi 
  
However, it would be very costly to solve these equations simultaneously by one of the methods, such as Gauss-Jordan 
elimination. So, these equations should be solved by iterative method that is Gauss-Seidel method (Press et al, 1988). 
In the temporal optimization method, smoothness condition is expressed as 
Qu Y 9v Y 
- — |. 13 
The total error is minimized in the same way as spatial global optimization method. 
3. EXPERIMENTS 
3.1 Empirical Comparison among Gradient-Based Approaches 
In this chapter, various gradient-based approaches described in Chapter 2 are applied to real sequential images of traffic 
scene. The size of the frame in the sequential images is 720 by 480 pixels. And time interval is 1/30 second. 
Figure 1 shows the frame of sequential images used in the optical flow estimation. The vehicles in Figure 1 move 
from upper right to bottom left. Velocities of the vehicles in this image were measured, and the results were about (1) 
20 pixels/frame, (2) 3 pixels/frame and (3) 2 pixels/frame, respectively. These values were used as measurements for 
comparison among the several approaches. 
    
Figure 1: Image of Traffic Scene. ; 
Figure 2 through Figure 9 show optical flow estimated by each method at a frame. Estimated optical flow is depicted 
as segment at an interval of 20 pixels, and the length of segments is ten times as long as estimated value. 
Figure 2 shows the result which was solved by spatial local optimization method. The spatial neighborhood was 
defined as 5by 5 pixels. A constant optical flow over these neighborhoods was assumed. The magnitude of one of 
the estimated flow vectors in each vehicle was (1) 6.4 pixels/frame, (2) 2 .0 pixels/frame and (3) 1.5 pixels/frame, 
respectively. While there were precise flow vectors in the vehicles (2) and (3), even in the same vehicles flow vectors 
could not be obtained at many pixels. This problem will be described later. In the vehicle (1) though there were 
  
  
   
  
   
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à : s ; = + + = = F3 > $ T os 5B EM u d s * og s * idm a = 8 3 Pogosow ; ü Bog | 3 
N 10pixels/frame d. 3131.. 10pixels/frame 
Figure 2: Spatial Local Optimization Method. Figure 3: Temporal Local Optimization Method. 
  
272 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.