vectors in each vehicle was (1) 5.3 pixels/frame, (2) 2.0 
pixels/frame and (3) 0.9 pixels/frame, respectvely. The 
smoothness constraint smoothes variety of direction of 
flow vectors, so the magnitudes of flow vectors are under 
estimated. 
Data at a pixel 
and Sun, 1983). Figure 13 shows the result which was 
solved by spatial local optimization method with 
neighborhood of edge. However, the result were not 
precise and dense sufficiently to be employed for 3D 
reconstruction and structure from motion. 
Figure 10: Unstability of the Solution by Multispectral 
Constraints Method. 
The result which was solved by spatial local optimization 
method (Figure 2) was better than by 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 11 
illustrates the aperture problem. It shows a moving plane 
of constant brightness. When we see the plane through 
the aperture, we cannot recognize the moving of the plane. 
Figure 12: Vehicle Tracking Employing Spatial Local 
Optimization Method. 
-m -m 
- ***** ■ ' ■ ■ 
lOpixels/frame 
Figure 11: Aperture Problem. 
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 
the shape of the vehicles account by the flow vectors which 
are solved by basic methods of gradient-based approach. 
On the other hand, only vehicle tracking on the 2D screen 
can be achieved. Figure 12 shows a frame of vehicle 
tracking. Defining the black regions as the clusters, 
vehicles were tracked. 
By the way, 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 
Figure 13: Spatial Local Optimization Method with 
Neighborhood of Edge. 
CONCLUSION 
The conclusions of this paper are as follows: 
(1) 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 took at 
an interval about 1/30 seconds.