1 Introduction
2 Related Work
2.1 Modeling of Vehicle Turning Trajectory
2.2 Automatic Trajectory Extraction
3 CNNs and R-CNNs
3.1 Convolutional Neural Networks (CNNs)
3.2 Regions with CNNs (R-CNNs)
3.3 Data Collection and CNN Training
4 Trajectory Extraction Using R-CNN
4.1 Transformation from Image to Real-World Coordinates
4.2 Verification of the Proposed CNN Tool
5 Trajectory Analyses
5.1 Minimum-Jerk Method
5.2 Identification of the Starting and Ending Points of the Turning Maneuver
5.3 Statistical Analysis
\( x_{0} \) (m) | \( x_{f} \) (m) | \( v_{x,0} \) (m/s) | \( v_{x,f} \) (m/s) | \( a_{x,0} \) (m/s2) | \( a_{x,0} \) (m/s2) | \( x_{0} \) (m) | \( x_{f} \) (m) | \( v_{x,0} \) (m/s) | \( v_{x,f} \) (m/s) | \( a_{x,0} \) (m/s2) | \( a_{x,0} \) (m/s2) | \( t_{f} \) (s) | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\( \varvec{\mu} \) | 35.7 | − 29.4 | − 9.68 | − 6.57 | 1.03 | − 0.971 | − 49.3 | − 45.06 | 8.98 | − 7.45 | − 1.44 | − 0.708 | 7.72 |
\( \varvec{\sigma} \) | 3.27 | 4.29 | 1.22 | 0.77 | 1.46 | 1.17 | 2.74 | 3.33 | 1.16 | 1.04 | 1.22 | 1.36 | 0.74 |
5.4 Comparison Between Simulated and Observed Trajectories
6 Conclusions and Future Recommendations
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The R-CNN used in this work was trained using images taken from a single intersection with specific geometric characteristics and surrounding conditions. Therefore, the proposed R-CNN can only be used to accurately track vehicles at this particular intersection. Training the network using a larger set of images that are collected from multiple intersections is required to generate a more versatile R-CNN.
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The trajectory models developed in this study are based on a limited number of trajectories (N = 44) extracted from a single intersection. A larger number of trajectories obtained from several intersections are essential to achieve a deeper insight into the behavior of drivers at signalized intersections. Furthermore, the proposed trajectory model assumes that the start and end points of the turning trajectory are known; accordingly, it is required to develop probabilistic models to estimate the distribution of these points (i.e., start and end of turning path) as functions of the vehicle entry speed and intersection geometry.