Temporal Margins and Behavioral Features for Early Risk Assessment in Left-Turn Vehicle and Bicycle Conflicts at Signalized Intersections

Abstract

Between 2019 and 2023, left-turn crashes accounted for 4.5% of traffic accidents in Japan, with 36% of injuries involving cyclists and 66% at signalized intersections. This study quantifies conflict situations between left-turning vehicles and straight-moving bicycles in real-world traffic environments and provides a foundation for determining appropriate timing of future in-vehicle early warning systems. Trajectories reconstructed from seven hours of camera footage yielded six spatio-temporal and behavioral indicators for 37 events with a post-encroachment time (PET) ≤ 3 s. Indicators—PET, time-to-crossing (TTC), right-of-way, urgent braking, deceleration to avoid a crash, and Kalman-based trajectory variance—were statistically related to a composite risk index, R. Approximately 80% of events fell within PETs of 2–3 s, while urgent braking occurred in 50% of cases with PETs of ≤2 s. Each 1 s reduction in PET increased R by 0.18 (R² = 0.55). PETs ≤ 2.5 s or TTCs ≤ 1.5 s flagged 95% of high-risk events 0.5 s in advance. Joint thresholds involving urgent braking and high variance raised coverage to 100%, with lead times of 0–1.4 s and a false alarm rate of 8%. These findings provide an innovative multi-indicator framework based on real-world trajectories, offering quantitative scenario-specific thresholds for effective in-vehicle warnings at urban intersections.

1. Introduction

Although the overall traffic accident rate in Japan has been decreasing, left-turn collisions have been increasing, accounting for more than 4.5% of all accidents during the five-year period leading up to 2023. In 2023, there were 307,991 traffic accidents, including 15,671 involving left turns, with 36% of these collisions involving bicycles and 66% of bicycle casualties occurring at intersections [1,2,3].

Previous research on the prevention of left-turn collisions has focused on accident rates involving vehicles and bicycles. This includes improvements to infrastructure employing passive safety measures, such as roadway and traffic signal design, as well as the behavioral characteristics of traffic participants under active safety measures for analysis and real-time risk assessment. The results of these assessments are utilized in human–machine interfaces (HMIs) to propose strategies for improving safety. Kojima et al. analyzed data and aerial photographs of traffic accidents in Saitama Prefecture, Japan, and emphasized the necessity of location-based safety design based on how bicycle travel patterns influence accident characteristics. However, their study focused solely on accident data to predict positions and did not examine actual traffic scenarios [4]. Yamanaka et al. investigated potential collisions between bicycles and left-turning vehicles at intersections using a coordinated simulator and emphasized the importance of risk assessment and intersection design, though their findings were limited by discrepancies between simulated and real-world conditions [5]. Islam et al. investigated the relationship between post-encroachment time (PET) and traffic signal timing using video data collected by unmanned aerial vehicles (UAVs) and demonstrated that collision risk can be reduced by adjusting signal timing to improve PET. However, their analysis focused on aggregate PET statistics and did not assess the risk associated with the distribution of PETs in specific interaction scenarios [6]. By contrast, the present study examines event-level PET in typical vehicle–bicycle encounters and integrates kinematic and behavioral indicators for fine-grained, real-time risk identification. Although previous studies have highlighted the risks associated with left-turn maneuvers, empirical analyses based on continuous trajectories that capture real-time interactions between left-turning vehicles and bicycles remain limited. Moreover, existing methods have not systematically incorporated the behavioral indicators or scenario-specific thresholds necessary for reliable real-world applications.

This critical gap limits the applicability of current safety measures in dynamic urban intersections, where detailed behavioral insights and scenario-specific thresholds are essential. This study addresses the limitation by integrating continuous real-world trajectories and comprehensive behavioral metrics, thereby enhancing the reliability and practical relevance of safety assessments.

To translate insights gained from risk assessment into practical traffic safety improvements, it is essential to design effective HMI-based alert systems that account for real-time interaction dynamics. In 2019, the Ministry of Land, Infrastructure, Transport and Tourism in Japan introduced a safety regulation requiring blind spot information systems on trucks weighing over 8 tons to prevent accidents by sending optical signals to warn approaching bicycles during left turns [7]. However, this measure has not been extended to passenger vehicles. Moreover, building effective HMIs between left-turning vehicles and bicycles at intersections remains challenging due to the complexity of dynamic scenarios. Therefore, solely relying on regulation-oriented HMI solutions is insufficient to meet the real-time interaction demands of dynamic urban intersections. To address these limitations, recent advances in connected and automated vehicle (CAV) technology—particularly vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication—are opening new avenues for real-time safety assessment and information sharing at intersections. By leveraging these capabilities, CAVs can proactively coordinate and respond to complex urban scenarios, laying the foundation for more robust risk assessment and intelligent alert systems [8]. Furthermore, recent integrated frameworks utilizing advanced deep reinforcement-learning methods, such as combining Bootstrapped DQN with inverse reinforcement learning (IRL), have significantly improved autonomous vehicles’ safety in high-speed cruising scenarios [9]. However, these approaches mainly target highway environments and vehicle-to-vehicle interactions, thus substantially differing from our study, which specifically addresses low-speed urban intersections involving vulnerable road users and emphasizes detailed behavioral indicators and fine-grained real-time analysis.

Researchers have conducted empirical analyses of left-turning vehicle–bicycle conflicts using UAVs or roadside cameras in real traffic scenarios. Hao et al. extracted PET indicators from UAV videos, revealing a significant relationship between PET and conflict risk; however, their study overlooked behavioral and uncertainty dimensions that are crucial for hierarchical warnings [10]. Using pre-crash trajectories from freeway rear-end crashes, Chen et al. integrated multiple indicators—including time-to-collision and deceleration rate to avoid a crash (DRAC)—and demonstrated that combined indicators yield higher predictive performance than single time-to-collision-based approaches. Nevertheless, their model was primarily tailored to freeway conditions, limiting its applicability to mixed urban intersection scenarios [11]. Guo et al. proposed quantifying prediction uncertainty using Kalman filter covariance and dynamically adjusting alarm thresholds in autonomous driving. However, their method was not combined with time domain safety metrics to evaluate imminent traffic conflict risks [12]. In this study, we combine filter-derived uncertainty with real-time PET and TTC metrics to enhance direct detection of collision risks in mixed-traffic environments. Regarding HMI design, Kraft et al. used a bicycle simulator to evaluate the impact of external HMIs on cyclist behavior, confirming that visual alerts improve reactions. However, they did not examine the optimal timing of warnings [13]. Nabi et al. demonstrated the potential of vehicle-to-everything (V2X)-based left-turn conflict warnings for road users without incorporating multisource fusion or hierarchical logic into the system design [14].

These empirical insights underscore the necessity of multidimensional indicators and have driven the development of integrated risk modeling approaches that more comprehensively incorporate such variables for assessing traffic conflict risks. These models aim to unify time domain indicators (e.g., PET and time-to-collision), dynamic characteristics (e.g., speed and acceleration), and behavioral responses into a cohesive framework for quantitatively analyzing conflict severity in complex interaction scenarios. A common approach is the composite risk index (R) model, which integrates multiple proxy indicators through linear weighting. Related studies have shown that, compared to single-indicator methods, multisource fusion models demonstrate higher sensitivity and robustness in identifying conflict risk [15]. Regarding integrated model development, Li et al. defined the hourly composite risk index (HCRI), which integrates time-to-collision-based severity and conflict-type weights applied to hourly lane-change and rear-end conflict counts into a unified score [16]. However, the HCRI primarily targets aggregated vehicle-to-vehicle scenarios. More broadly, existing studies still lack an objective framework that couples real-world continuous trajectories with multidimensional behavioral and temporal indicators for scenario-specific threshold determination—an essential need for interactions involving vulnerable road users like cyclists.

To address this gap, the present study focuses on urban intersections and systematically identifies and quantifies potential conflict scenarios between left-turning vehicles and straight-moving bicycles using continuous real-world trajectories captured through multi-camera observations. The goal is to establish a robust empirical foundation for determining appropriate timing and thresholds for future in-vehicle early warning systems.

In this study, we (1) reconstruct conflict trajectories; (2) extract multiple spatio-temporal and behavioral indicators; (3) integrate these indicators into a composite risk framework; (4) statistically analyze the relationships between the indicators and overall risk; and (5) establish a framework for determining early warning thresholds.

The methods include motion trajectory reconstruction, indicator extraction and integration, composite risk index construction, and statistical analyses such as regression and non-parametric tests to quantify each indicator’s contribution and determine optimal thresholds. Unlike previous studies, our primary innovation is explicitly integrating multiple key behavioral and spatio-temporal indicators—including PET, time-to-crossing (TTC), urgent braking, right-of-way dominance, and Kalman-based trajectory uncertainty—with continuous real-world trajectories into a composite risk assessment framework. This comprehensive approach addresses existing limitations in capturing dynamic interactions and behavioral nuances, enabling the determination of practical, scenario-specific thresholds and improving the reliability and effectiveness of early warning systems in complex urban environments.

To systematically achieve these objectives, we adopt a data-driven, multi-indicator methodology that leverages continuous footage captured by multiple synchronized cameras. We reconstruct real-world trajectories of left-turning vehicles and bicycles, derive key spatio-temporal and behavioral indicators, and integrate them into a composite risk index. This index enables robust quantification of interaction risk and supports the derivation of scenario-specific HMI thresholds. The following section outlines the procedures for data collection, trajectory processing, indicator integration, and composite risk modeling employed in this study.

2. Proposed Method

2.1. Data Collection and Processing

To ensure representativeness under real-world conditions, the experimental design accounted for factors such as traffic volume, lane configuration, frequency of left-turning vehicles, and observation angles. The Itabashi district in Tokyo was selected as the primary research site due to its high rate of traffic accidents. According to official data, the number of personal injury traffic accidents increased from 844 in 2021 to 1005 in 2022 and remained nearly constant at 1004 in 2023, indicating an overall upward trend [17,18,19]. A signalized intersection allowing both straight and left turns at the Itabashi Junction Overpass on Route 17, Japan, was selected for detailed observation because of its high traffic volume and complex layout. The intersection consists of three straight lanes (total width: 10.6 m) adjacent to a pedestrian crosswalk frequently used by cyclists (width approximately 4.6 m), as illustrated in Figure 1. The structural complexity of the intersection and its history of left-turn collisions make it an appropriate site for analyzing typical conflict scenarios between left-turning vehicles and crossing cyclists.

The intersection layout and experimental setup are illustrated in Figure 1 and Figure 2. As shown in Figure 1, yellow arrows indicate the trajectories of left-turning vehicles, while red arrows represent bicycle paths along the designated pedestrian–bicycle corridor. Three standard traffic signal heads (red, amber, and green) regulate vehicle and cyclist movements. Signal phases for bicycles and pedestrians are separated, implementing a protected crossing strategy to minimize conflicts during green phases. Under Japan’s traffic signal system, left-turning vehicles are generally permitted to proceed during the same green phase as crossing pedestrians and cyclists. Although drivers are legally required to yield, misjudgment, limited visibility, and underestimated cyclist speed often lead to conflict risk. The overlapping movement paths at this intersection represent the primary scenario analyzed in this study. Four GoPro cameras (30 fps, 4K resolution) were mounted on traffic lights 1 and 2, providing overlapping, multi-angle views of both the left-turn lanes and straight-through bicycle paths, as shown in Figure 2. The system continuously recorded 7 h of traffic footage (07:00–14:00) on 26 October 2023, under clear and sunny weather conditions, coinciding with peak traffic periods [18]. This experiment was approved by the Ethics Committee of the National Transportation Safety and Environmental Laboratory (NTSEL), Japan.

To identify valid conflict events for analysis, a rigorous manual annotation and screening process was applied to the collected video footage. Two independent annotators reviewed the full 7 h, multi-camera dataset frame by frame. All scenarios in which left-turning vehicles and through-moving bicycles demonstrated spatial proximity, potential interaction risk, or overlapping trajectories were preliminarily flagged. Events lacking actual interaction or exhibiting entirely separated movements were excluded. Using DIPP-Motion V (version 1.1.29) software, the exact timestamps at which the front wheel of each vehicle or bicycle crossed the conflict point were manually annotated, and PET values were calculated on a frame-by-frame basis. Only events with PETs ≤ 3 s were retained as valid conflicts, consistent with established definitions of high-risk interactions [20]. All candidate samples were cross-validated by both annotators, resulting in 37 confirmed high-risk conflict events selected for detailed analysis. No automated algorithms or heuristic filtering methods were used at any stage of this process.

Following the establishment of the high-risk conflict dataset, data processing and analysis were conducted using a structured pipeline, as shown in Figure 3. This workflow comprises three primary modules: preprocessing, feature extraction and refinement, and statistical analysis.

2.2. Data Processing

The recorded video footage underwent structured preprocessing, as outlined in Figure 3 (Steps 1–2)

• Step 1: Camera Synchronization and Time Alignment

Multi-camera footage was synchronized using an LED-based trigger system. Visual LED signals captured within each camera’s field of view enabled precise frame-level alignment, which was conducted using Adobe Premiere Pro 2024.

b.

Step 2: Distortion Correction

Lens distortion was corrected by calibrating intrinsic camera parameters—namely, focal length, principal point, and distortion coefficients—in MATLAB R2024a using the Zhang checkerboard method [21]. A total of 27 checkerboard images captured from multiple viewpoints were used to ensure high spatial calibration accuracy. Following calibration, all raw video data were standardized to a uniform resolution of 3840 × 2160 pixels at 30 frames per second to ensure consistency in subsequent trajectory analysis.

2.3. Feature Extraction and Refinement

Following preprocessing, feature extraction was performed as shown in Figure 3 (Steps 3–5).

c.

Step 3: Perspective Projection Transformation (2D)

To convert pixel coordinates into real-world metric coordinates, a homography transformation was applied using a 3 × 3 matrix. Four precisely surveyed reference points within a 2.4 m × 7.4 m pedestrian area, as illustrated in Figure 4, served as calibration targets. These reference points enabled robust and accurate metric conversion across all camera views.

d.

Step 4: Manual Pointing

Stable wheel–ground contact points—specifically the front wheels for bicycles and the left front wheels for vehicles—were manually annotated every 10 frames using DIPP-Motion V (version 1.1.29) software to ensure accurate initial trajectory points.

e.

Step 5: Trajectory Interpolation and Smoothing

Cubic spline interpolation was employed to generate continuous trajectories at 30 frames per second, and a moving average filter was applied to reduce noise and enhance trajectory continuity. Figure 5 illustrates this process, displaying both the manually annotated and smoothed trajectories for selected keyframes (frames 0–90). These refined trajectories served as essential inputs for subsequent risk metric analyses, including PET, TTC, and DRAC.

2.4. Statistical Analysis (Trajectory and Risk Indicators)

As shown in Step 6 of Figure 3, the refined trajectories were processed in custom MATLAB (R2024a) to compute key risk indicators, including PET, TTC, DRAC, speed, acceleration, and urgent braking, and to obtain frame-wise uncertainty from the Kalman filter covariance. The resulting dataset was then analyzed in Python 3.10 using pandas, NumPy, SciPy, and statsmodels. Welch’s t-tests, Spearman rank correlations (a non-parametric test), and ordinary least squares (OLS) regressions were used to quantify each indicator’s contribution to conflict risk. Meanwhile, Durbin–Watson and Shapiro–Wilk tests were applied to check residual autocorrelation and normality, respectively. These statistical procedures provided the empirical basis for the early warning thresholds proposed in this study.

2.5. Motion Feature Optimization and Uncertainty Reduction

To ensure accurate conversion from pixel to physical coordinates, a high-resolution camera (3840 × 2160 pixels) was mounted at a height of approximately 4.5 m with a downward tilt angle of ~35°. The camera’s intrinsic and extrinsic parameters were calibrated using an 8 × 8 checkerboard pattern, yielding a root mean square reprojection error $\Delta u_M$ of 0.11 px.

The DIPP-Motion V (version 1.1.29) software reported a maximum localization error $\Delta u_H=$0.10 px during homography transformation and sub-pixel tracking, resulting in a combined pixel error of ${\mathsf{\sigma }}_{px}=$ 0.15 pixels and an average positional uncertainty $\sigma X\approx$ of approximately 0.86 mm. At the 30-frame-per-second rate used in this study, these values corresponded to velocity and acceleration errors of roughly 0.026 m/s and 1.11 m/s², respectively. While the velocity error was minimal, the acceleration error was notably amplified due to the second-order differencing, which is highly sensitive to high-frequency noise. Additionally, tracking points were manually annotated every 10 frames using DIPP-Motion V (version 1.1.29), while the intermediate 20 frames were interpolated using the software’s built-in cubic spline algorithm. This interpolation step contributed further to trajectory uncertainty.

To effectively reduce uncertainty caused by noise and interpolation, a second-order constant-acceleration Kalman filter (CA-KF) was applied. This optimal recursive algorithm is based on a linear Gaussian state-space model comprising prediction and correction steps [22,23,24]. In this study, the state vector was defined as ${\left[\begin{array}{c}{v}_k,a_k\end{array}\right]}^{\mathrm{\top }}$, where $v_k$ and $a_k$ represent the velocity and acceleration at frame k, respectively. A sampling interval of $\Delta \mathrm{t}=$ 0.033 s (corresponding to 30 frames per second) was used. The measurement vector included velocity and acceleration values directly obtained from DIPP-Motion V (version 1.1.29). The measurement noise covariance matrix $R$ was derived from the empirically estimated RMS pixel error of 0.15 px, while the process noise covariance $Q$ was calibrated to 2% of the acceleration variance computed from a representative urgent-braking sample.

The results demonstrate that the CA-KF effectively reduces uncertainty in velocity and acceleration estimates. After filtering, the velocity error was reduced to below 0.02 m/s, and the acceleration error decreased to approximately 0.25 m/s²—substantially outperforming traditional differencing and median filtering techniques. Moreover, the posterior covariance generated by the CA-KF serves as a reliable indicator of uncertainty, supporting more robust PET-based risk evaluation and the optimization of HMI alert systems. These improvements enhance the reliability and practical applicability of the proposed analytical framework.

2.6. Definition of Risk Scenarios and Behavioral Feature Extraction

Each potential conflict event was quantified using PET, defined as the absolute temporal difference between the moment the first road user (vehicle or bicycle) exited the potential collision point (T1) and the moment the second road user arrived at that same location (T2), as expressed in Equation (1). A shorter PET value indicates a smaller temporal buffer between the two parties, thereby reflecting a higher level of collision risk [25].

$$PET=\left|T2-T1\right|$$

(1)

For each event, the object trajectories were analyzed to extract speed, acceleration, Kalman filter-based uncertainty, and behavioral indicators such as sudden braking and DRAC. To account for interaction sequence effects, the scenarios were categorized based on which road user—vehicle or bicycle—passed the potential collision point first. Figure 6 illustrates the definition of these scenarios, distinguishing whether the bicycle or the vehicle led the crossing. As shown, the severity of a potential collision varies depending on the leading object, underscoring the importance of differentiating interaction order in risk assessment [26].

2.7. Composite Risk Index and Indicator Fusion

To address the limitations of relying on a single metric, such as PET, in traffic conflict risk assessment [27,28], this study developed a composite risk index (R) by integrating multiple agent-based safety indicators. Although PET intuitively reflects the time gap between road users reaching a potential collision point and holds some value for risk indication, it often fails to identify high-risk scenarios in complex settings—such as intersections with substantial speed differentials or irregular driving behavior [29]. For example, even when PET values appear high (e.g., 2.0–3.0 s), collisions may still occur if a rear vehicle approaches at high speed or undergoes sudden deceleration. Previous research has emphasized that a single PET value is insufficient to capture critical aspects like instantaneous time margins or dynamic interactions during real-world traffic encounters [30,31]. Therefore, the composite index R incorporates multiple dimensions: time margins (PET, TTC), dynamic responses (combined velocity $v_{Sum}$, DRAC), right-of-way dominance (Dom), and emergency behaviors (urgent braking flag, BrakeFlag). This multi-indicator fusion enhances the precision and reliability of risk detection in urban intersection scenarios.

Table 1. Definition of the Composite Risk Index (R).

Indicator	Symbol	Definition	Risk Direction	$\mathbf{Weight} {\mathit{w}}_{\mathit{i}}$
Post-encroachment time	PET	$\left|T2-T1\right|$	↓(smaller = higher risk)	$w_{PET}$ (0.30)
Time-to-crossing	TTC	$s_f\left(i_{\mathrm{lead} }\right)/v_f\left(i_{\mathrm{lead} }\right)$	↓(smaller = higher risk)	$w_{TTC}$ (0.30)
Combined speed	$v_{\mathit{Sum}}$	$v_{\mathit{lead}}\left(i^{*}\right)+v_{\mathit{follow}}\left(i^{*}\right)$	↑(larger = higher risk)	$w_{v_{\mathit{Sum}}}$ (0.20)
Deceleration rate to avoid a crash	DRAC	$v_{\mathit{follow}}{\left(i^{*}\right)}^2/$2$\cdot s_f\left(i^{*}\right)$	↑(larger = higher risk)	$w_{DRAC}$ (0.10)
Right-of-way dominance	Dom	Binary (lead/follow)	Context-dependent	$w_{Dom}$ (0.05)
Urgent-brake flag	BrakeFlag	1 if |a| > $a_{thr};\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e} 0$	1 = higher risk	$w_{Brake}$ (0.05)

Note: All continuous indicators are min–max normalized to [0, 1] before weighting; binary variables take values of {0, 1}. T1 and T2 are times when leader/follower crosses the potential conflict point; $i^{*}$ is the frame where TTC is at its minimum.

summarizes the definitions of each indicator, including calculation formulas, risk direction, assigned weights, and related notes.

For indicator fusion, the six normalized metrics are linearly weighted as $w=$ [$w_{PET}, w_{TTC}, w_{v_{Sum}}, w_{DRAC}, w_{Dom}, w_{Brake}$] = [0.30, 0.30, 0.20, 0.10, 0.05, 0.05]. This allocates 60% of the emphasis to time margins (PET and TTC), 30% to collision energy and dynamic clearance ($v_{Sum}$ and DRAC), and the remaining 10% to the right-of-way context and emergency response (Dom and BrakeFlag). The mathematical formulation of R is given as follows:

$$R=\sum _{i=1}^6 w_i\cdot z_i+w_{\mathrm{Brake} }\cdot \mathrm{BrakeFlag}$$

(2)

Here, $z_i$ represents the six standardized proxy risk indicators (PET, TTC, $v_{\mathrm{Sum} }$, $\mathrm{D}\mathrm{R}\mathrm{A}\mathrm{C}$, $\mathrm{Dom}$, and $\mathrm{BrakeFlag}$) each normalized to a [0, 1] range using min–max scaling. $w_i$ denotes the corresponding non-negative weight assigned to each indicator, while BrakeFlag is a binary variable indicating the occurrence of urgent braking. The definitions of these metrics are as follows.

(1) PET: A time margin indicator; smaller values correspond to higher risk due to reduced reaction times and limited margins for error.

(2) TTC: The minimum time remaining between the rear vehicle and the potential conflict point, calculated as $\mathrm{TTC} =s_f\left(i_{\mathrm{lead}}\right)/v_f\left(i_{\mathrm{lead}}\right)$, where a lower TTC implies greater collision risk.

(3) $v_{\mathrm{Sum} }$: The combined instantaneous speeds of the leading and following objects at the frame where TTC reaches its minimum. This metric captures how joint speed contributes to the potential severity of the conflict. The calculation is defined in Equation (3), where $i^{*}$ denotes the frame at which TTC is minimized.

$$v_{\mathit{Sum}}=v_{\mathit{lead}}\left(i^{*}\right)+v_{\mathit{follow}}\left(i^{*}\right)$$

(3)

(4) DRAC (m/s²): The minimum deceleration required by the following vehicle to avoid a collision, based on its current speed and distance from the lead vehicle. A higher DRAC value signifies a more urgent braking demand and corresponds to an elevated risk level. This value is computed at frame $i^{*}$, where TTC reaches its minimum, as defined in Equation (4).

$$\mathrm{DRAC} ={\displaystyle \frac{v_{\mathit{follow}}{\left(i^{*}\right)}^2}{2\cdot s_f\left(i^{*}\right)}}$$

(4)

(5) Dom: The entity that dominates the passage through the potential conflict point, representing the influence of right-of-way dynamics on collision risk. This indicator reflects whether the vehicle or bicycle holds precedence in the interaction based on leading-order behavior.

(6) BrakeFlag: A binary indicator that captures whether the following vehicle exhibits sudden braking behavior, thereby compensating for the limitations of purely spatio-temporal metrics by incorporating real-time driver responses. The flag is set using frame-by-frame acceleration data. If the instantaneous acceleration $a_f\left(j\right)$ falls below −3.0 m/s² for motor vehicles or −2.5 m/s² for non-motorized vehicles at any frame $j$, the event is marked as a hard brake (BrakeFlag = 1); otherwise, BrakeFlag = 0. These thresholds are grounded in the SAE J2944 standard, which identifies −3.0 m/s² as the onset of hard braking for motor vehicles [32]. For non-motorized vehicles, the −2.5 m/s² threshold is based on empirical studies that represent the upper bound of typical bicycle deceleration during emergency stops [33,34]. Acceleration is computed as described in Equation (5).

$$a_f(j)={\displaystyle \frac{v_f\left(j\right)-v_f(j-1)}{\Delta t}}$$

(5)

By integrating the six indicators described above, the composite risk index R more effectively captures dynamic interaction behaviors and risk levels during traffic conflicts. This integration enables the accurate identification of complex, high-risk scenarios that would likely be missed using PET-based methods alone.

3. Results

3.1. Sample Distribution

From the 7 h video data, 37 potential conflict events with PET ≤ 3.0 s were extracted.

Table 2. Counts in each PET range.

PET Bin (s)	(0, 1.0]	(1.0, 1.5]	(1.5, 2.0]	(2.0, 2.5]	(2.5, 3.0]	Total
Case Count	1	1	6	14	15	37
Share (%)	2.7	2.7	16.2	37.8	40.5	100

summarizes the distribution across different PET ranges, demonstrating that 78.4% of events occurred in the (2.0, 3.0] s range, whereas eight cases (21.6%) occurred within the high-risk zone (PET ≤ 2.0 s). This suggests that the 2–3 s PET range represents a common yet often overlooked risk zone in urban intersections.

3.2. Primary Risk Causes

Table 3. Overall distribution of primary risk causes.

Main Cause	Count	Share (%)	$\mathbf{Avg}. \overline{\mathit{R}} \pm$ SD	Typical Trigger Conditions
Bicycle urgent braking	16	43.2	0.50 ± 0.10	$\left|a_{bicycle}\right|$ > 2.5 m/s2 and TTClead ≤ 2 s
Bicycle fast approach	10	27.0	0.38 ± 0.05	TTClead ≤ 1.5 s, no deceleration
Vehicle fast approach	9	24.3	0.40 ± 0.15	TTClead ≤ 1.5 s, no deceleration
Vehicle urgent braking	1	2.7	0.31	${|a}_{vehicle}|$ > 3 m/s2
High kinetic energy	1	2.7	0.17	$v_{\mathrm{Sum} }$ > 6 m/s and DRAC > 1.3 m/s2

presents a statistical breakdown of the primary behavioral causes of risk, including the number and proportion of events attributed to each behavior category, along with the corresponding mean and sample standard deviation (SD) of the composite risk index. The SD captures within-group variability and provides variance estimates necessary for conducting Welch’s t-test, which evaluates the statistical significance of differences in risk levels across behavioral groups.

Table 3 shows that 70.3% of events were attributed to bicycles (due to urgent braking or fast approach), 27.0% to vehicles, and the remaining 2.7% to high-kinetic-energy scenarios. To evaluate differences in composite risk levels between urgent braking (n = 16, $\overline{R}$ = 0.50, s = 0.10) and fast approach events (bicycles + vehicles, n = 19, $\overline{R}$ ≈ 0.39, s ≈ 0.12), a Welch’s t-test was conducted. The difference in means (0.109, 95% CI: 0.040–0.177) was statistically significant (t = 3.12, df = 32.74, p = 0.0038), which indicates a statistically significant difference in risk levels, underscoring the importance of incorporating dynamic behavioral indicators such as urgent braking and DRAC in identifying high-risk conflict scenarios.

Further analysis of PET segmentation shows the proportion of urgent braking within each PET band:

• PET ≤ 2.0 s: 4/8 = 50% (95% CI: 22–78%);
• 2.0 s < PET ≤ 2.5 s: 7/14 = 50% (95% CI: 26–74%);
• PET > 2.5 s: 6/15 = 40% (95% CI: 20–64%).

These findings indicate that urgent braking was triggered in 40% of events despite relatively high PET values, highlighting a persistent safety risk that PET alone may underestimate.

In addition, TTC-based analysis further revealed that, among the 16 urgent braking events involving bicycles, 68.8% occurred under conditions of a TTC ≤2.0 s without prior deceleration, representing 29.7% of all cases. For TTCs ≤ 1.5 s and when no prior deceleration was observed, fast-approach events accounted for 24.3% (vehicles) and 27.0% (bicycles) of all cases. Applying a union threshold of a PET ≤2.5 s or TTC ≤1.5 s identified 29/37 events = 78% (Wilson 95% CI: 63–89%) and successfully captured 21/22 high-risk cases (R > 0.40) = 95% (95% CI: 78–99%). In contrast, the stricter intersection threshold—PETs ≤ 2.5 s and TTCs ≤ 1.5 s captured only ~45% (10/22) of high-risk events, making it more appropriate as a secondary trigger condition for urgent-level warnings. In summary:

• High speed and urgent braking by cyclists are the primary contributors to risk.
• When the time margin decreases to a PET ≤ 2 s, the urgent braking rate rises to 57%, indicating increased reliance on sudden braking to avoid conflict.
• A two-stage warning strategy—consisting of early alerts triggered by PETs ≤ 2.5 s or TTCs ≤ 1.5 s, followed by urgent intervention when both thresholds are crossed offers high sensitivity while minimizing false alarms.

3.3. Right-of-Way (Leading-Order) Effects

To further assess the impact of leading order on conflict risk, all 37 events were categorized into two groups based on the leading road user: vehicle-led (26 cases, 70%) and bicycle-led (11 cases, 30%).

Table 4. Distribution of leading-order scenarios and triggering mechanisms.

Leading Object	Trigger Type	Count	Share (%)
Vehicle-led (n = 26)	Bicycle urgent braking	16	61.5
	Bicycle fast approach	10	38.5
	Vehicle urgent braking	0	0.0
	High kinetic energy	0	0.0
Bicycle-led (n = 11)	Vehicle fast approach	9	81.8
	Vehicle urgent braking	1	9.1
	High kinetic energy	1	9.1

Note: Vehicle-led: ${\overline{R}}_V$ = 0.45 ± 0.10, speed = 3.35 m/s; Bicycle-led: ${\overline{R}}_B$ = 0.37 ± 0.15, speed = 2.42 m/s.

summarizes the mutually exclusive triggering mechanisms observed in each group.

As Table 3 shows, 16 of 26 cases (61.5%) in the vehicle-led group involved urgent braking, with an average rear vehicle speed of 3.35 m/s, highlighting behavioral differences and relative risk. In contrast, only 1 of 11 cases (9.1%) in the bicycle-led group involved urgent braking, and the average rear vehicle speed was 2.42 m/s. A two-sided Fisher exact test confirmed a statistically significant difference in urgent braking occurrence between these groups (p = 0.004, odds ratio = 16.0, 95% CI: 2.0–129), indicating a strong association between leading order and the likelihood of urgent braking. In terms of composite risk index, the vehicle-led group (${\overline{R}}_V=$ 0.45 ± 0.10) had a slightly higher average risk compared to the bicycle-led group (${\overline{R}}_B=$ 0.37 ± 0.15), with a mean difference of 0.08 (95% CI: −0.01 to 0.18). Welch’s t-test indicated a tendency toward a difference in mean risk between the two groups ($t$ = 1.56, $\mathrm{d}\mathrm{f}$ ≈ 14, $p$ = 0.14), although this difference was not statistically significant.

Furthermore, in the high-risk subset with PET ≤ 2 s, Spearman’s correlation between leading order (vehicle = 0, bicycle = 1) and composite risk index R increased from $\rho$ = 0.27 (full dataset) to $\rho$ = 0.42 (p = 0.029, 95% CI: 0.04–0.70), suggesting that the influence of right-of-way on conflict risk becomes more pronounced under low time margin conditions. Suggesting that the influence of right-of-way becomes particularly pronounced at low time margins.

From a scenario-coupling perspective, the combination of “vehicle-led + PET ≈ 2–3 s” accounts for approximately 62% of high-risk events ($R$ > 0.45), representing the most frequent and unstable conflict pattern. In contrast, the “bicycle-led + PET < 2 s”, though less frequent, was typically triggered by vehicles rapidly approaching with TTC < 1.5 s. These findings underscore the need for HMI system to apply differentiated warning strategies: stronger cyclist-side alerts in vehicle-leads scenarios at PETs ≈ 2.5 s, and enhanced driver-side distance warnings in bicycle leads scenario when the TTC falls below 1.5 s.

3.4. Velocity–Acceleration–PET Dynamic Coupling Analysis

To quantitatively assess the relationship among time margin, kinematic behavior, and composite risk, an ordinary least squares (OLS) regression was conducted using 37 (PET, R) pairs. Before modeling, the validity of regression assumptions was confirmed using the Durbin–Watson test ($DW$ = 1.81, indicating no significant autocorrelation in residuals) and the Shapiro–Wilk test for residual normality ($p$ = 0.802, confirming approximate normality of residuals).

Urgent braking events were identified using thresholds of ${|a}_{vehicle}|$ > 3 m/s² or $\left|a_{bicycle}\right|$ > 2.5 m/s². The regression result was $\widehat{R}=$ 0.85–0.18 PET, with an $R^2$ of 0.55, indicating that approximately 55% of the variability in the composite risk index is explained by PET alone. The intercept was 0.85 (95% CI: 0.714–0.980), and the slope was −0.18 (95% CI: −0.237 to −0.124); both are statistically significant (p < 0.001). This negative slope implies that a 1 s reduction in PET corresponds, on average, to an increase in the composite risk index of 0.18, highlighting the importance of time margin in risk assessment. Figure 7 illustrates the PET–R scatter plot overlaid with an OLS regression line. Circular markers denote cases without urgent braking, while crosses indicate events that included urgent braking. With the PET ≤2.0 s interval, all eight cases were categorized as high-risk (R > 0.40), and four of them (50%, 95% CI: 22–78%) involved urgent braking. Notably, even among the 15 cases in the PET >2.5 s interval, 6 cases (40%, 95% CI: 20–64%) involved urgent braking. This result demonstrates that a generous PET alone does not ensure safety, and emphasizes the necessity of including dynamic indicators such as high deceleration or DRAC to supplement PET-based thresholds.

3.5. Velocity and Acceleration Patterns Across PET Bands

Figure 8a illustrates the average speeds of vehicles and bicycles across different PET intervals at the individual level. Here, the average refers to the arithmetic mean of the Kalman-filtered velocity and acceleration calculated over a ±30-frame window (60 frames total) centered on the PET frame. The results indicate that although overall speed tends to decrease as PET increases, notable variability exists within each PET range. The mean bicycle speed was 3.16 m/s, approximately 1.1 m/s higher than that of vehicles (2.01 m/s), suggesting that bicycles typically travel faster during conflict scenarios and thus contribute more substantially to collision kinetic energy.

As shown in Figure 8b, acceleration patterns reveal an average deceleration of −1.86 m/s² for bicycles and −0.50 m/s² for vehicles. Notably, bicycles exhibited more frequent and pronounced deceleration at lower PET levels, underscoring the critical role of cyclist-side urgent braking in elevating conflict risk.

To further analyze dynamic patterns,

Table 5. PET average velocity/acceleration under segmentation.

PET Bin (s)	n	${\mathit{v}}_{\mathit{v}\mathit{e}\mathit{h}\mathit{i}\mathit{c}\mathit{l}\mathit{e}}$ (m/s) ↑	${\mathit{v}}_{\mathit{b}\mathit{i}\mathit{c}\mathit{y}\mathit{c}\mathit{l}\mathit{e}}$ (m/s) ↑	${\mathit{a}}_{\mathit{v}\mathit{e}\mathit{h}\mathit{i}\mathit{c}\mathit{l}\mathit{e}}$ (m/s2) ↓	${\mathit{a}}_{\mathit{b}\mathit{i}\mathit{c}\mathit{y}\mathit{c}\mathit{l}\mathit{e}}$ (m/s2) ↓
(0, 1.5]	2	2.48	3.57	+0.22	+0.45
(1.5, 2.0]	5	2.65	3.36	–0.77	−4.43
(2.0, 2.5]	14	2.00	3.33	+0.13	−1.56
(2.5, 3.0]	16	1.71	2.88	–1.07	−1.60

Note: The arrows indicate the direction of greater risk: ↑ for higher velocities; ↓ for stronger deceleration (more negative values). Boldface indicates the peak value in each PET interval (by absolute magnitude).

summarizes the Kalman-filtered speeds and accelerations across four PET intervals. Bicycles consistently maintained speeds that were 1.1–1.4 m/s higher than those of vehicles. In the PET 1.5–2.0 s range, both vehicles and bicycles exhibited the highest deceleration values (−0.77 m/s² and −4.43 m/s², respectively), with urgent braking observed in two of the five events (40%, 95% CI: 12–77%). These characteristics help define a representative conflict-resolution window for this PET range.

Further analysis using metric coupling revealed that the risk gap G, defined as the difference between TTC and PET, is significantly negatively correlated with the composite risk index (Spearman’s $\rho$ = −0.33, $p$ = 0.049, 95% CI: −0.58 to −0.01), whereas the relative margin M showed no significant association. A negative value of G (G < 0) indicates that the follower is predicted to reach the potential conflict point before the leader has cleared it, effectively representing a complete loss of safety margin. This finding suggests that G < 0 can serve as a practical distance–speed hard threshold for real-time risk alerts. When combined with PET, TTC thresholds, and real-time urgent braking detection, this multi-criterion approach improves the sensitivity and specificity in identifying high-risk scenarios.

Additionally, Figure 9 provides a side-by-side comparison across four PET intervals, illustrating the average speed difference ($\Delta v$) and acceleration difference ($\Delta a$) between the follower and the leader. The right vertical axis shows the proportion of emergency braking events. The $\Delta v$ remains consistently positive (0.7–1.3 m/s), indicating that the following bicycle generally carries more kinetic energy. In the PET range of 1.5–2.0 s, Δa reaches its minimum (−3.66 m/s²), while the emergency braking rate for bicycles peaks at 60% (95% CI: 23–88%), suggesting that strong deceleration is the primary conflict resolution strategy. Even in the relatively safe PET range of 2.5–3.0 s, approximately 44% (95% CI: 23–67%) of events still involve emergency braking—primarily by vehicles—highlighting that a large PET alone does not fully mitigate risk.

These motion–behavior couplings underscore the need for a dual-indicator warning strategy: time margin thresholds should be complemented by real-time monitoring of extreme deceleration (e.g., DRAC) to enable timely and accurate warnings through the HMI.

3.6. Comprehensive Summary of Warning Threshold Performance and Key Indicators

This section provides a comprehensive evaluation of various proposed warning thresholds, summarizing their effectiveness in terms of early lead time, coverage of high-risk conflicts, and rates of false alarms.

Table 6. Performance of warning threshold (high-risk: R > 0.40, low-risk: R ≤ 0.40).

Rule	Trigger Condition	Lead Time (s)	High-Risk Captured	Low-Risk FP	Coverage	FAR
Time margin (early)	PET ≤ 2.5 s ∨ TTC ≤ 1.5 s	0.3–0.5	21/22 (95%)	8/15 (53%)	29/37 (78%)	8/29 (28%)
Intersection (urgent)	PET ≤ 2.5 s ∧ TTC ≤ 1.5 s	0.3–0.5	10/22 (45%)	0/15 (0%)	10/37 (27%)	0/10 (0%)
Urgent-brake flag	$\left|\mathrm{a}\right| > a_{thr}$	≤0.1	12/22 (55%)	5/15 (33%)	17/37 (46%)	5/17 (29%)
Urgent-brake ∧ PET ≤ 2 s	$\left|\mathrm{a}\right| > a_{thr}$ ∧ PET ≤ 2 s	≤0.2	4/22 (18%)	2/15 (13%)	6/37 (16%)	2/6 (33%)
Multi-source	margin ∨ brake ∨ σ	0–1.4	22/22 (100%)	2/15 (13%)	24/37 (65%)	2/24 (8%)

Note: Lead time represents the time between the first triggered threshold and the conflict frame, with positive values indicating an early warning. FP = false positives among low-risk events; FAR = false alarms/total alerts; margin = Union rule (PET or TTC); brake = Urgent-brake flag (|a| > $a_{thr}$); σ = high-variance cue (KF speed variance > 1 m/s²).

summarizes the performance metrics of different threshold conditions defined in this study. The false alarm rate (FAR) is calculated as the ratio of false alarms (i.e., low-risk events incorrectly flagged) to the total number of alerts triggered by each threshold.

The time margin (early) threshold alone captured 95% of high-risk events (21 out of 22), providing about 0.3–0.5 s of lead time, but it had a relatively high false alarm rate (28%). The stricter intersection (urgent) threshold showed perfect precision (0% FAR), yet only captured 45% of severe events, indicating its suitability as a secondary, critical-level warning condition. Using urgent-brake flags alone identified approximately half (55%) of the high-risk cases but offered minimal lead time (≤0.1 s). By combining multiple conditions (time margin, urgent braking, and high-variance indicators), coverage increased to 100% of high-risk events, extending the available lead-time window (0–1.4 s), and significantly reducing the false alarm rate to just 8%.

Furthermore,

Table 7. Key quantitative findings for major indicators.

Indicator	Value (95% CI)	Interpretation
PET ≤ 2 s → high-risk precision	8/8 = 100%	Short margin alone flags all severe cases
Bicycle–vehicle mean speed gap	+1.1 m/s	Cyclists carry higher kinetic energy
Mean ΔR (brake vs. approach)	+0.11 (0.040–0.177)	Sudden deceleration raises risk
Risk gap G vs. R (Spearman)	$\rho$$= -0.33, p$ = 0.049	Negative G indicates lost safety margin and higher risk

summarizes the key quantitative findings from the indicators, reinforcing the validity and practical value of the selected metrics.

These results clearly demonstrate the robustness of using combined multi-indicator thresholds to achieve accurate real-time conflict detection and warning, thus supporting effective design strategies for intelligent HMI-based safety systems.

4. Discussion

4.1. Main Finding

An analysis of 37 vehicle–bicycle conflicts (with PETs ≤ 3 s) at a signalized intersection revealed three consistent patterns. First, time margin emerged as the most effective early warning indicator. A union threshold (PET ≤ 2.5 s or TTC ≤ 1.5 s) successfully identified 29 conflict cases (78%, 95% CI: 63–89%), including 21 of the 22 high-risk events (R > 0.40), offering approximately a 0.3–0.5 s lead time. In contrast, the stricter intersection threshold (PET ≤ 2.5 s and TTC ≤ 1.5 s) identified only 45% of high-risk events, making it suitable as a secondary, urgent-level trigger condition.

Second, extreme deceleration—either urgent braking or a high DRAC value—marked the onset of elevated risk. Every high-risk conflict (R > 0.40) contained at least one such event. In the vehicle-lead subset, bicycle-side urgent braking alone accounted for 61.5% of cases (16/26, 95% CI: 41–78%), underscoring cyclists’ dominant role in last-moment collision avoidance.

Third, the leading-order role influenced conflict dynamics. When vehicles led, the most severe conflicts were triggered by following bicycles. In contrast, when bicycles led, risk typically arose from a rapidly approaching vehicle with a TTC of approximately ∼1.5 s. A two-sided Fisher exact test confirms a strong association between leading order and the likelihood of urgent braking ($p$ = 0.004; odds ratio = 16.0, 95% CI: 2.0–129). These findings suggest that a compact combination of time margin, deceleration pattern, and leading-role context can inform a real-time alert logic for intelligent HMI-based warning systems. Notably, integrating time margin, urgent-brake, and high-variance cues (multi-source rule) enabled the system to capture 100% of high-risk conflicts (22/22) with a false alarm rate of 8%, and a lead time of 0–1.4 s.

Compared with previous research, the present findings highlight several potential extensions. While Islam et al. [6] demonstrated that optimizing signal timing to increase overall PET can help reduce intersection risk, their analysis did not address the risks posed by short-PET events or atypical kinematic scenarios. Our findings suggest that PET-based thresholds alone may be insufficient for identifying all high-risk conflicts, especially those involving rapid approaches or urgent braking. Similarly, studies such as Chen et al. [11] have highlighted the value of composite risk indices, but their focus has been on controlled or freeway settings rather than the complex, mixed-traffic conditions at urban intersections. By integrating behavioral and uncertainty indicators—including PET, TTC, urgent-brake, and variance-based cues—our approach enhances the sensitivity and specificity of real-time conflict detection. In addition, while Guo et al. [12] introduced filter-derived variance for adaptive warnings, coupling such uncertainty metrics with time domain safety indicators appears particularly important for real-world urban applications. Overall, the proposed multi-indicator fusion strategy may support more effective and robust early risk detection in complex traffic environments.

4.2. Implications for a Tiered HMI

The three signals identified in Section 4.1—time margin, extreme deceleration, and leading role—can be used to construct a concise, two-stage warning logic that integrates seamlessly into existing driver and cyclist information systems without requiring significant interface modifications.

The first stage (early warning) is activated when either PET ≤ 2.5 s or TTC ≤ 1.5 s is met. This rule predicted 78% of conflicts approximately 0.5 s before reaching the conflict point. In this stage, the system issues only a suggestive cue, such as a steady icon compliant with ISO 2575 or mild haptic feedback, prompting drivers to reassess the situation without causing a startled reaction. This approach is consistent with previous studies that employed PET thresholds for proactive driver alerts in vehicle–bicycle interactions [35] and TTC-based first-level alerts in unsignalized environments [36].

The second stage (emergency warning) is activated when both PET ≤ 2.5 s and TTC ≤ 1.5 s are met, when an urgent braking or DRAC surge is detected, or when the Kalman speed variance exceeds 1 m/s². These conditions captured all high-risk events in the dataset and triggered alerts 0–1.4 s before the conflict point, with the shortest lead times (<0.1 s) arising from urgent-brake events. At this stage, alert salience should be elevated—for instance, by adding a brief auditory cue or intensifying the warning icon—while remaining within recommended limits for driver distraction. The warning message can be tailored according to right-of-way: when the vehicle has priority, a stronger warning is delivered to the cyclist; when the bicycle has priority, the warning targets the driver. This role-specific messaging aligns with dual-party HMI designs proposed in recent cooperative driving studies [37].

This study does not offer recommendations on color schemes or display locations, as such design elements are platform-specific and fall beyond the scope of this research. The primary contribution lies in mapping quantified risk thresholds to two distinct warning stages, achieving 95% coverage of high-risk conflicts with the time margin rule, and up to 100% coverage with multi-source fusion at the cost of an 8% false alarm rate.

4.3. Limitations and Future Works

In this study, all kinematic parameters were reconstructed from video-based multi-camera observations. The accuracy and reliability of trajectory reconstruction were inherently constrained by camera quality, video resolution, and potential manual tracking errors. Although Kalman filtering helped reduce inter-frame jitter, manual annotation bias, and projection distortion, the residual range error (±0.12 m at 20 m) still influenced the accuracy and stability of velocity, acceleration, and DRAC estimation, as well as the reliability of emergency braking detection. Moreover, PET and TTC were calculated using only the front wheel point, which does not capture the full geometric profile of vehicles and bicycles. When a vehicle leads and a bicycle follows, this simplification has a limited impact on risk estimation, as collisions typically occur at the front of the vehicle. However, when a bicycle leads, relying solely on the front wheel can substantially overestimate the safety margin, since the rear of the bicycle may still occupy the conflict zone and remain at risk. Given typical Japanese bicycle dimensions and observed speeds, this could lead to PET overestimation by up to 0.39 s. While this limitation does not affect the overall PET distribution trend, it may result in an underestimation of risk in high-conflict scenarios.

To address these limitations and reduce measurement uncertainties, future studies will incorporate higher-resolution cameras and automated detection and tracking algorithms. Additionally, all recordings in this study were obtained under clear daytime conditions; therefore, adverse weather (e.g., rain, snow, or low visibility) and nighttime scenarios—which typically reduce the accuracy and reliability of camera-based measurements—were not considered. Integrating LiDAR and millimeter-wave radar into the existing multi-sensor trajectory reconstruction system may mitigate these effects due to their lower sensitivity to weather and lighting conditions. By utilizing LiDAR’s sub-decimeter ranging accuracy (typically ±0.03–0.05 m), we expect to reduce the residual errors inherent in video-only measurements, thereby providing a more stable basis for estimating PET, TTC, and DRAC. Additionally, inspired by a recent integrated reinforcement learning control framework [9], future research could explore combining the composite risk assessment framework developed in this study with advanced decision-making and planning modules. Such integration would facilitate adaptive, scenario-specific threshold adjustments, human-like behavior modeling, and real-time responsiveness across diverse traffic contexts.

Furthermore, in point cloud-based processing, methods such as Oriented Bounding Box (OBB) can be leveraged to delineate the full spatial boundaries and movement trajectories of traffic participants [38]. Rather than relying solely on the front wheel, the improved framework will use the passing time of the vehicle or bicycle’s rear end—or alternatively, a broader dynamic conflict region—as the primary reference in PET and related calculations. This approach, combined with image and point cloud fusion, will offer a more accurate and robust foundation for risk assessment and threshold setting. Building on this enhanced data foundation will enable the construction of a real-time three-dimensional (3D) digital twin that stores precise lane geometry and continuously updates 3D meshes of all traffic participants. PET and DRAC are then computed based on actual object volumes and movement trajectories, further improving the practical relevance and reliability of traffic safety assessments. In addition, controlled simulation experiments based on this digital-twin environment could be used to systematically examine diverse conflict scenarios and validate the robustness of the proposed risk assessment models and thresholds under repeatable conditions.

The thresholds used in this study (such as PET ≤ 2.5 s and TTC ≤ 1.5 s) were calibrated using data from a single intersection and a relatively small sample size (37 high-risk events). This limited sample size reduces statistical robustness and may affect the stability and generalizability of the results to broader traffic environments. Moreover, threshold values are often site-specific and can be influenced by intersection geometry, signal phasing, and local traffic behavior. To address this limitation, future work will systematically collect multi-sensor data from a diverse range of intersections, including both signalized and unsignalized sites, high- and low-traffic locations, and varied geometric layouts. The dataset will cover PET >3 s safety intervals as well as extreme-risk scenarios to ensure broad representation of real-world traffic conditions. Thresholds will be re-optimized at each new site and cross-validated across locations to identify both generalizable and context-dependent parameters. Additionally, normalization strategies such as percentile-based risk stratification, adaptive threshold-setting, and the integration of signal phase data, real-time traffic counts, and V2X messages will be applied to enhance the robustness and practical deployment of the framework.

Furthermore, this study did not explicitly consider human factors such as variations in driver reaction time, cyclist behavioral uncertainty, or situational awareness, all of which may influence real-world risk dynamics. As a result, the current model may underestimate or misclassify atypical or extreme risk events. Future work will incorporate human factor modeling, including data collection on driver response time and cyclist trajectory variability, and will employ driving simulators, structured questionnaires, and real-world field experiments to enhance the realism and robustness of the proposed framework.

5. Conclusions

This study systematically analyzed 37 potential conflict events between left-turning vehicles and through-going bicycles with PETs ≤ 3.0 s at urban intersections using a multi-camera system. Based on these analyses, a multi-indicator framework was established that integrates behavioral indicators, uncertainty analysis, and real-world trajectories to improve the precision of scenario-specific early warning systems. The results indicate that the majority (78%) occurred within a PET of 2–3 s, while 22% fell within the high-risk range (PET ≤ 2.0 s). Bicycles, predominantly due to urgent braking, were identified as the primary contributors to risk, exhibiting significantly higher composite risk compared to fast-approach scenarios (p < 0.01).

The multi-indicator fusion model developed here demonstrated superior capability for reliably identifying high-risk scenarios compared to single-indicator methods. Specifically, a primary warning logic using PET ≤ 2.5 s or TTC ≤ 1.5 s captured 95% of severe events with an average lead time of about 0.5 s, albeit with a relatively high false alarm rate (28%). Combining this rule with additional thresholds involving urgent braking or high variance increased high-risk event coverage to 100%, provided a practical lead time window of 0–1.4 s, and significantly reduced the false alarm rate to 8%.

These results have clear policy and regulatory implications. Traffic authorities can adopt these validated thresholds and behavioral indicators into intersection safety standards and real-time HMI warning systems. Additionally, differentiated warning strategies based on leading-order contexts—intensified alerts targeting cyclists in vehicle-led scenarios, and enhanced driver alerts in bicycle-led cases—are recommended.

Future studies will expand validation to diverse intersections and incorporate advanced multimodal sensing (cameras, LiDAR, and V2X) to further refine real-time risk assessment models and facilitate robust digital twin intersection implementations.