Fuse, Takashi 
  
2. VEHICLE TRACKING PROBLEM 
The vehicle tracking problem basically consists of two components. The first is how to detect vehicles automatically 
in each image. The next is how to estimate displacement vectors of vehicles in successive images. Though sensors 
on the stratospheric platforms are not decided yet, taking account of altitude of about 20km, it is expected to result in 
high spatial resolution images. We can fairly expect the spatial resolution to be in the range of 20cm-50cm. Figure 1 
compares between a high resolution image (a), which expected to be produced by stratospheric platforms, and a usual 
satellite’s image (b). High resolution image (a) has resolution of 30cm and usual satellite’s image (b) has resolution of 
30m. It is obvious that vehicles can be recognized easily in the high resolution image. Using such high resolution 
images, it is expected to be comparatively easier to detect vehicles accurately. In this paper, we were concerned with 
the second component of the problem, that is estimation of displacement vectors. 
   
(a) High Resolution Image (Aerial HDTV Image, 30cm) (b) Usual Satellite’s Image (LANDSAT TM, 30m) 
Figure 1: Comparison of High Resolution Image with Ordinary Satellite's Image. 
The estimation of displacement vector specifies the origins and destinations of all vehicles in successive images. 
When the vehicles are detected as in Figure 2, the vehicle A in the image 1 can move to C, D or E in the image 2 or 
disappear. The most characteristic problem for the vehicle tracking is that appearance/disappearance of vehicles occur, 
when they are under overhead bridges or shadows of buildings, or going outside the image, or so on. The existence of 
the appearance/disappearance make the task of vehicle tracking challenging. 
  
Image 1 
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Image 2 
Figure 2: Vehicle Tracking Problem. 
  
3. PROBABILISTIC RELAXATION METHOD AND IMPROVEMENT OF THE METHOD 
The relaxation method was originally developed as an algorithm for numerical calculation (Takagi and Shimoda, 1991). 
The relaxation method has been widely employed for image matching techniques (Zucker, Hummel and Rosenfeld, 
1977, Barnard and Thompson, 1980, Peleg, 1980, Ohmi and Yu, 1998, Sakamoto, Uchida and Wang, 1998). In the 
image matching, sets of candidate matching points are first selected independently in each image. An initial network 
of possible matches between the two sets of candidates is then constructed. An initial estimate of the probability of 
each possible match is made equally. Finally, these estimates are iteratively improved by a relaxation labeling 
technique making use of the local consistency property of displacement vectors, that is similarity between the 
displacement vectors of near candidate points. 
We employed the probabilistic relaxation method for tracking vehicles, because the similarity between the displacement 
vectors is appropriate to a characteristic of movement of vehicles. The probabilistic relaxation method is summarized 
  
278 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.