Fuse, Takashi 
  
According to experimental results, when the velocity of a vehicle is large, the estimated value tends to be incorrect. It 
is said that gradient-based approaches perform well, when the velocity of object is small. In this case, resolution of the 
image is important. To avoid this problem, hierarchical estimation of flow vectors has been proposed (Sato and Sasaki, 
1986, Tominaga et al, 1989). At first, multi-resolution images (4, Z!, — 1,4, Z3, (4), 12, — 1,47, 1?) are prepared. 
The image 7,' and I? is composed 2* by 2* pixels. From low resolution image to high resolution image, optical flow is 
estimated step by step. Let f, be optical flow in image /,. When f, is estimated, the 7? is shifted following f,. At the 
time, the flow vector is 
f7f,*2x f... (14) 
This process is carried outrepeatedly. Finally, estimated optical flow is 
ff HANS te 42 A. (15) 
In addition, flow vectors were extracted near edges, and no flow vectors inside the vehicles. According to this result, 
the edges were defined as spatial neighborhood, and then spatial local optimization method were applied (Davis, Wu 
and Sun, 1983). 
  
  
20pixels/frame 
Figure 10: Hierarchical Estimation and Spatial Local Optimization Method with Neighborhood of Edge. 
  
  
  
Figure 10 shows the result which was solved by hierarchical estimation and spatial local optimization method with 
neighborhood of edge. Estimated optical flow is depicted as segment at an interval of 5 pixels, and the length of 
segments is three times as long as estimated value. The magnitude of flow vector was improved. However, the 
results were not precise and dense sufficiently to be employed for 3D reconstruction and structure from motion. 
4. CONCLUSION 
The conclusions of this paper are as follows: 
(1) Theoretical review of gradient-based approaches from the viewpoint of regularization; 
(2) Empirical comparison among basic method of gradient-based approach from the viewpoint of application to vehicle 
motion analysis. 
In this paper, the sequential image was taken at an interval about 1/30, and such a sequential image can be acquired 
easily. According to the empirical comparison, it is difficult to estimate precise and dense optical flow by the basic 
methods of gradient-based approach and their combination, when sequential images are taken at an interval about 1/30 
seconds. And then, it is difficult to analyze details of vehicle motions such as 3D reconstruction by the flow vectors 
which are solved by the basic methods of gradient-based approach and their combination in this case. Hence, other 
approaches, which are different with gradient-based approach fundamentally, are required. 
The future works are as follows: 
(1) Application to sequential images which are taken at an shorter interval; 
(2) Empirical comparison with methods of pattern matching such as Least Squares Matching. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 275