Fuse, Takashi 
  
4. EXPERIMENTS 
4.1 Confirmation of Effectiveness of Proposed Method 
We applied the original probabilistic relaxation method and the proposed method to simulated data. We employed 
traffic micro simulator PARAMICS (PARAMICS TRAFIIC SIMULATION LTD.) for producing the simulated data. 
The data were on a one-way and two-lane road. The time interval of successive images was 1.5 seconds. Detected 
vehicles are 52 in Image 1 and 51 (one vehicle disappeared) in Image 2, respectively. 
We applied the following method: 
(a) Original probabilistic relaxation method (original method); 
The initial probabilities are specified equally, and only one direction label probabilities are considered. 
(b) Probabilistic relaxation method with color information (with color information); 
The initial probabilities are specified by taking account of color information, and only one direction label 
probabilities are considered. 
(c) Probabilistic relaxation method with opposite label (with opposite label); 
The initial probabilities are specified equally, and two direction label probabilities are considered. 
(d) Proposed method; 
The initial probabilities are specified by taking account of color information, and two direction label probabilities 
are considered. 
Parameter A4, B and C in (21) and (24) were specified based on results. 
We applied these methods to two types of images. In the first, all vehicles were detected ( (1) without appearance and 
disappearance: Without), in second, 1096 of vehicles were not detected intentionally ( (2) with appearance and 
disappearance: With). Table 1 shows the results. 
Table 1: Correct Rates to Simulated Data. 
  
  
  
  
  
(1) Without | (2) With 
(a) Original method 82.7% 80.1% 
(b) With color information 88.5% 91.5% 
(c) With opposite label 98.1% 97.8% 
(d) Proposed method 100.0% 100.0% 
  
  
  
  
  
The correct rate by the proposed method are 100.0% in the both cases, that are without appearance/disappearance, and 
with appearance/disappearance. These results verify the effectiveness of the proposed method and robustness to 
appearance/disappearance problem. 
4.2 Application to Sample Images 
4.2.1 Specification of Parameters with Simulated Data 
When the proposed method are applied to real image, some parameters must be specified. Parameters 7, R and D(T: 
threshold for consistency, R: threshold for neighborhood, D: maximum of vehicles movement) can be specified easily 
by considering the limit of vehicle velocity in the road of interest, and so on. 
Parameters 4, B and C in (21) and (24), however, cannot be specified easily. Because these parameters are affected by 
state of traffic flow, time interval of successive images, and so on. It is appropriate that these parameters are specified 
by applying to simulated data which assume the real traffic flow. To be specific, simulated data reproduce the real 
traffic flow of interest. The methods are applied to simulated data with the various value of parameters, and then the 
results are compared. Based on the comparison, the parameters will be specified. 
In this paper, we used following value of parameters. 
A= 0.5, B= 1, C= |, 7=20, R=200, D=150. 
Here, we varied value of A from 0 to 1 at an interval of 0.1, values of B and C from 0 to 10 at an interval 0.2. 
  
282 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.