Out experimental environment is shown in Figure 4.1. We mounted two cameras at the Mackay Memorial Hospital and the overpass in front of National Tsing Hua University. In Figure 4.1, we can see that FOVs of these two cameras are non-overlapped and these two scenes are linked by Kuang Fu Road (indicated by the red line). Besides, there are three intersections and some bus stops along the road between these two FOVs. This makes the traffic situations more complicated.
The traffic videos were taken from about 9:45 in the morning till 19:00 in the afternoon. We divide the time–line into 34 overlapped time–windows. The length of each time–window is 60 minutes, with 45 minutes overlapped with the previous window, as shown in Figure 4.2
We first check the traffic videos and manually select frames that contain buses. All the entry/exit times of buses are recorded. Then we apply the proposed EM algorithm for each time–window. Here we use a Gaussian mixture model with 3 Gaussians to model the transition–time distribution. For the first time–
window, the parameters of the GMM are initialized with µ = {50, 150, 250}, σ2 = {200, 200, 200} and w = {0.33, 0.33, 0.33}. Then the initialization for EM in all the other time–windows follows the method we described in Section 3.4.
Figure 4.3, Figure 4.4, and Figure 4.5 show the computed transition–time distri-butions and the ground–truths in different time–windows. We can see that the distribution calculated by our algorithm is reasonably similar to the ground truth.
Here we also give some results by applying the method in [25] to our experi-mental data, as shown in Figure 4.6. We can see that the results are not as accurate
Figure 4.1: The experimental environment: monitor the traffic between two non–overlapping FOVs at Mackay Memorial Hospital and the NTHU overpass.
Figure 4.2: We divide the timeline into 34 overlapped time–windows. The length of each time–window is 60 minutes, with 45 minutes overlapped with the previous window.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
Figure 4.3: The transition–time distribution from time–window # 01 to time–window # 12.
(a) Time–window 09 : 45 ∼ 10 : 45. (b) Time–window 10 : 00 ∼ 11 : 00. (c) Time–window 10 : 15 ∼ 11 : 15.
(d) Time–window 10 : 30 ∼ 11 : 30. (e) Time–window 10 : 45 ∼ 11 : 45. (f) Time–window 11 : 00 ∼ 12 : 00.
(g) Time–window 11 : 15 ∼ 12 : 15. (h) Time–window 11 : 30 ∼ 12 : 30. (i) Time–window 11 : 45 ∼ 12 : 45.
(j) Time–window 12 : 00 ∼ 13 : 00. (k) Time–window 12 : 15 ∼ 13 : 15. (l) Time–window 12 : 30 ∼ 13 : 30.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
Figure 4.4: The transition–time distribution from time–window # 13 to time–window # 24.
(a) Time–window 12 : 45 ∼ 13 : 45. (b) Time–window 13 : 00 ∼ 14 : 00. (c) Time–window 13 : 15 ∼ 14 : 15.
(d) Time–window 13 : 30 ∼ 14 : 30. (e) Time–window 13 : 45 ∼ 14 : 45. (f) Time–window 14 : 00 ∼ 15 : 00.
(g) Time–window 14 : 15 ∼ 15 : 15. (h) Time–window 14 : 30 ∼ 15 : 30. (i) Time–window 14 : 45 ∼ 15 : 45.
(j) Time–window 15 : 00 ∼ 16 : 00. (k) Time–window 15 : 15 ∼ 16 : 15. (l) Time–window 15 : 30 ∼ 16 : 30.
(x–axis: transition time; y–axis: milli–probability).
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j)
Figure 4.5: The transition–time distribution from time–window # 25 to time–window # 34.
(a) Time–window 15 : 45 ∼ 16 : 45. (b) Time–window 16 : 00 ∼ 17 : 00. (c) Time–window 16 : 15 ∼ 17 : 15.
(d) Time–window 16 : 30 ∼ 17 : 30. (e) Time–window 16 : 45 ∼ 17 : 45. (f) Time–window 17 : 00 ∼ 18 : 00.
(g) Time–window 17 : 15 ∼ 18 : 15. (h) Time–window 17 : 30 ∼ 18 : 30. (i) Time–window 17 : 45 ∼ 18 : 45.
(j) Time–window 18 : 00 ∼ 19 : 00.
(a) (b) (c)
Figure 4.6: Some results from applying the method in [25] to our experimental data. (a) Time–window 12 : 00 ∼ 13 : 00. (b) Time–window 12 : 15 ∼ 13 : 15. (c) Time–window 17 : 00 ∼ 18 : 00.
characteristics of the real life traffic while the method in [25] only depends on the weaker minimum entropy assumption about the transition time distribution.
For example, in Figure 4.6(c), the distribution of the ground truth has a wider range and thus has a larger entropy value than that of the distribution found by the algorithm in [25].
To infer the traffic flow state, we can first use the average transition time of the last 15–minute observation within each time–window as a statistic to represent the state. As shown in Figure 4.7, the chart of the traffic–flow state may give us the direct message about how the traffic dynamically changes over time. For in-stance, we may probably guess that the increase of the average transition time at about 12:00 is due to the lunch–time traffic, which is always a rush hour. More-over, we could also express the traffic flow state by classifying the traffic changes as “stable”, “increasing”, and “decreasing,” as shown in Figure 4.8. This figure indicates how the traffic changes with respect to the previous stage. This kind of description is much more user–friendly.
In addition to the aforementioned setting of the time–line division and the ini-tialization method, here we provide some examples of different settings to support
that our setting is reasonable. In the first example of different settings, we divide the time–line into 60–minute time–windows with 30 minutes overlapped with the previous window. For the EM initialization of the following time–windows, we propagate the parameters of GMM from the previous window. Figure 4.9 shows the transition–time distributions of some time–windows. We can see that the com-puted transition–time distributions cannot adapt quickly enough to the changes of the ground truth. One reason for this phenomenon is due to the problem of initial-ization we presented in Figure 3.11. Moreover, since the information propagated from the previous window only dominates 50% of the data in the processing win-dow, the degree of change for the transition–time distribution might be too big to be tracked by the algorithm. Then, in the second example of different setting, we use the same time–windows as in the first example; and for the EM initialization of the following time–windows, we follows the method described in Section 3.4.
Figure 4.10 shows the transition–time distributions of the time–windows which are the same as those in Figure 4.9. We can see that even there are some im-provement in Figures 4.9(b), 4.9(d), and 4.9(e), the problem of miss–tracking still exists, as shown in Figure 4.9(c). Hence, in our experiment, we choose to di-vide the timeline into time–windows with much more overlaps with the previous time-window.
Figure 4.7: Traffic flow state expressed by the average transition time of the last 15–minute observation within each time–window. The red line is computed by our proposed method; The blue line is from the ground truth.
Figure 4.8: Express the traffic flow state by classifying the traffic changes as “stable”, “increasing”, and “decreas-ing.” (Green color: stable traffic; Red color: increasing traffic flow; Blue color: decreasing traffic flow).
(a) (b) (c)
(d) (e) (f)
Figure 4.9: Some transition–time distributions from the first example of different setting. Each time–windows is 60 minutes long including 30 minutes overlapped with the previous window. The EM initialization of the following time–windows is with the parameters of GMM propagated from the previous window.
(a) Time–window 10 : 45 ∼ 11 : 45. (b) Time–window 11 : 15 ∼ 12 : 15. (c) Time–window 11 : 45 ∼ 12 : 45.
(d) Time–window 12 : 15 ∼ 13 : 15. (e) Time–window 12 : 45 ∼ 13 : 45. (f) Time–window 13 : 15 ∼ 14 : 15.
(x–axis: transition time; y–axis: milli–probability).
(a) (b) (c)
(d) (e) (f)
Figure 4.10: Some transition–time distributions from the second example of different setting. Each time–windows is 60 minutes long including 30 minutes overlapped with the previous window. The EM initialization of the following time–windows follows the method described in Section 3.4.
(a) Time–window 10 : 45 ∼ 11 : 45. (b) Time–window 11 : 15 ∼ 12 : 15. (c) Time–window 11 : 45 ∼ 12 : 45.
(d) Time–window 12 : 15 ∼ 13 : 15. (e) Time–window 12 : 45 ∼ 13 : 45. (f) Time–window 13 : 15 ∼ 14 : 15.
(x–axis: transition time; y–axis: milli–probability).
5 Conclusion
We propose an efficient method to probabilistically model the dynamic traffic flow between non–overlapping FOVs. Unlike previous works, our approach does not attempt to directly build the object correspondence across non–overlapping cam-eras. Instead, we model object correspondence and the parameters estimation of the transition time model as a unified problem. By building the physical con-nection between the transition time model and the object correspondence, the proposed EM–based framework can iteratively determine the optimal object cor-respondence and the model parameters. In addition, by dividing the time–line into many overlapped time–windows, our method can sequentially infer the time–
varying traffic flow and recognize the dynamic changes of the traffic status over time. Moreover, our system is efficient and may provide a new thinking to well utilize the existing surveillance cameras for wide–area traffic monitoring. The ex-periments have shown that our approach performs well in a complicated traffic environment in real life.
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