problem is as follow. Even if there is only one vehicle, the two 
clusters are formed. Especially the discontinuity of the cluster 
in time direction occurs, when vehicles are under overhead 
bridges or shadows of buildings, or so on. To deal with this 
problem, we merge the clusters after clustering. For merging 
clusters the history of locations and colour information are used. 
Let the location in x-y domain from the terminate frame of a 
cluster to two previous frame be denoted as (x, ,), Gb Vb 0 
2, X2), respectively. The location at time #+1 is estimated by 
making use of the history of location according to following 
equation. 
XH17 3x = 3x,,t X1-25 V1 3y, = yt Yı-2 (6) 
If a region, which is similar to one of the cluster of interest in 
the terminate frame in the sense of color, is encountered near 
the estimated location at time #+1, the two clusters are merged. 
Otherwise, we interpret the cluster as the disappearance of 
vehicle at the time. In the case of vehicle appearance, we can 
deal with it in the same fashion. Thus, this method can be 
applied to the appearance/disappearance of vehicles. 
3.6 Vehicle Recognition 
Finally, each cluster is labeled as a vehicle or not. For labeling, 
the continuity of velocities, shape and size in x-y domain are 
employed. Here, let a center of mass in x-y domain at time £ be 
denoted as (X. y.) in a cluster of interest. The velocity is 
defined as 
Ui = XciA7Xct, Vi — Yet-17Yet- (7) 
When the continuity of velocity is less than the threshold 7, the 
cluster is labeled as a vehicle. 
dr =a) or (8) 
where N is the number of frames of the spatio-temporal image. 
Figure 3. Aerial 
In order to distinguish vehicles, we make use of not only 
continuity of velocity but also the shape and size in x-y domain. 
The shape is defined as a ratio of two sides (a, b) of 
circumscribed rectangle for a section of cluster at time t. When 
the shape is less than the threshold 7, and size is between the 
threshold 7; and 7, the cluster is labeled as a vehicle. 
bla « T, (9) 
T;< ab «T, (10) 
Imposing these three conditions, the vehicle clusters are 
discriminated from others. 
4. EXPERIMENTS 
4.1 Confirmation of Effectiveness 
We applied the spatio-temporal clustering method to aerial 
HDTV image (Figure 3). The data of this image are as follows: 
Platform: Helicopter; 
Altitude of platform: 300m; 
Spatial resolution: 10cm; 
Time interval of successive image: 1/30 seconds; 
Number of frames: 600 frames; 
Number of channels: 3 (R, G and B, 8bit); 
Size of image: 1920 by 1080 pixels. 
In the spatio-temporal clustering method, 50 frames was used to 
construct the initial background image, and the parameters in 
equation (2), (4), (8), (9) and (10) must be specified. 
Parameters 7), 75, T, and T4 (T; threshold for velocity 
continuity, 75: threshold for vehicle shape, 75, 74: threshold for 
vehicle size) can be specified easily by physical characteristics. 
On the other hand, the parameters ey, eu, es ( *y, e, es: 
threshold for shadow detection) and weight parameters w in 
equation (2) and (4) are specified by trial and error, since an 
efficient method simply does not exit. In this paper, we used 
following values of parameters. 
*,—0.8, *471.0, *5—0.06, w—0.5, 
T,=50, T,=5.0, T5=200, 74-5000. 
  
HDTV image 
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