SSMsOnPlane

This repository shares vectorised python scripts to calculate various surrogate safety measures (SSMs), or in another way called, surrogate measures of safety (SMoS) for pairs of road users on an abstracted plane of road, i.e., in a two-dimensional space.

Two branches of SSMs are considered:

• Longitudinal SSMs that are originally designed for one-dimensional (rear-end) conflicts and collisions, but can be extended to two-dimensional space by assuming constant velocities. These include Time-To-Collision (TTC) ¹, Deceleration Rate to Avoid Collision (DRAC) ², Modified Time-To-Collision (MTTC) ³, and Proportion of Stopping Distance (PSD) ⁴ in this repository. A previous repo Two-Dimensional-Time-To-Collision is referred to for more details on the vectorised extention.
• Two-Dimensional SSMs that are specifically designed for conflicts and collisions involving both longitudinal and lateral movements. These include Time Advantage (TAdv) ⁵, Anticipated Collision Time (ACT) ⁶, and Two-Dimensional Time-To-Collision (TTC2D) ⁷ in this repository. In addition to the above, a recently proposed indicator, Emergency Index (EI) ⁸, is open-sourced by its authors in the linked repo.

These metrics/indicators are designed to be used with trajectory data from road users, such as vehicles or cyclists, to assess their interaction safety in a given scenario. For references to these indicators, please scroll down to the bottom of this page.

Thanks to vectorisation, the implementations in this repository are very efficient in time for large-scale calculation. Helper functions to evaluate the efficiency are therefore also provided.

Overview

The repository is structured as follows:

• src/ contains the main Python modules implementing the functions:
  • geometry_utils.py provides geometric helper functions (e.g., intersect, getpoints, etc.) used to compute distances, intersections, and angles.
  • longitudinal_ssms.py implements longitudinal safety measures including TTC, DRAC, MTTC, and PSD.
  • two_dimensional_ssms.py provides functions for two-dimensional safety measures including TAdv, TTC2D, and ACT.
  • efficiency_utils.py contains helper functions to evaluate the computational efficiency of the indicators by timing their execution on sample data.
• assets/ contains supplementary files such as around 10,000 example data samples which are extrated from the lane-changes in the highD dataset, and a plot comparing the efficiency of indicators.

For more details on each function and its underlying logic, see the inline documentation in the source code.

Efficiency evaluation

The notebook example.ipynb provides a full demonstration of the efficiency evaluation functions. With a range of 1e4, 1e5, and 1e6 pairs of vehicles, below is a comparison plot showing the execution time of each indicator, tested over 20 runs.

Package requirements

Any versions of the following packages should work: NumPy, Pandas, Matplotlib (for plotting in the notebook), and tqdm (for progress visualization in the notebook).

Usage

To compute a safety measure, import the corresponding function and pass in a pandas dataframe with the required variables.

Variable :	Explanation
x_i :	x coordinate of the ego object (usually assumed to be centroid)
y_i :	y coordinate of the ego object (usually assumed to be centroid)
vx_i :	x coordinate of the velocity of the ego object
vy_i :	y coordinate of the velocity of the ego object
hx_i :	x coordinate of the heading direction of the ego object
hy_i :	y coordinate of the heading direction of the ego object
acc_i :	acceleration along the heading direction of the ego object (only required if computing MTTC)
length_i :	length of the ego object
width_i :	width of the ego object
x_j :	x coordinate of another object (usually assumed to be centroid)
y_j :	y coordinate of another object (usually assumed to be centroid)
vx_j :	x coordinate of the velocity of another object
vy_j :	y coordinate of the velocity of another object
hx_j :	x coordinate of the heading direction of another object
hy_j :	y coordinate of the heading direction of another object
acc_j :	acceleration along the heading direction of another object (optional)
length_j :	length of another object
width_j :	width of another object

For instance, to compute the Time-To-Collision (TTC):

import pandas as pd
from src.longitudinal_ssms import TTC

# Create or load your samples
df = pd.read_csv('your_data.csv')

results = TTC(df, toreturn='dataframe')
print(results[['TTC']].head())

Notes

• The two road users under evaluation are considered to never collide if they keep current speed when

  • indicator value is np.inf if the used indicator is TTC, MTTC, TTC2D, TAdv, or ACT;
  • indicator value is 0 if the used indicator is DRAC.

• When the indicator value is smaller than 0, the bounding boxes of the two road users are overlapping. This is due to approximating the space occupied by an object with a rectangular. In other words, negative indicator in this computation means a collision almost (or although seldom, already) occurred.

• The computation can return extreme small positive values (for TTC/MTTC) or extreme large values (for DRAC) even when the vehivles overlap a bit (so should be negative values). In order to improve the accuracy, please use the function geometry_utils.CurrentD(samples) to exclude overlapping objects.

License

This repository is licensed under the MIT License. See the LICENSE file for more details.

References

Footnotes

1. [TTC, 1972] Hayward, J., Near miss determination through use of a scale of danger. 51st Annual Meeting of the Highway Research Board, 384, 24–34. ↩

2. [DRAC, 1976] Cooper, D., Ferguson, N., Traffic studies at T-junctions – A conflict simulation record. Traffic Engineering and Control, 17 (7), 306–309. ↩

3. [MTTC, 2008] Ozbay, K., Yang, H., Bartin, B., Mudigonda, S., Derivation and Validation of New Simulation-Based Surrogate Safety Measure. Transportation Research Record, 2083(1), 105-113. ↩

4. [PSD, 1978] Allen, B., Shin, B., Cooper, P., Analysis of traffic conflicts and collisions. Transportation Research Record, 667, 67–74. ↩

5. [TAdv, 2010] Laureshyn, A., Svensson, Å., Hydén, C., Evaluation of traffic safety, based on micro-level behavioural data: Theoretical framework and first implementation. Accident Analysis & Prevention, 42(6), 1637-1646. ↩

6. [ACT, 2022] Venthuruthiyil, S. P., Chunchu, M., Anticipated Collision Time (ACT): A two-dimensional surrogate safety indicator for trajectory-based proactive safety assessment. Transportation research part C: emerging technologies, 139, 103655. ↩

7. [TTC2D, 2023] Guo, H., Xie, K., Keyvan-Ekbatani, M., Modeling driver’s evasive behavior during safety–critical lane changes: Two-dimensional time-to-collision and deep reinforcement learning. Accident Analysis & Prevention, 186, 107063. ↩

8. [EI, 2025] Cheng, H., Jiang, Y., Zhang, H., Chen, K., Huang, H., Xu, S., Zheng, S., Emergency Index (EI): A two-dimensional surrogate safety measure considering vehicles’ interaction depth. Transportation Research Part C: Emerging Technologies, 171, 104981. ↩