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