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Safety-oriented pedestrian trajectory prediction at urban intersections using time-to-collision and crossing-zone context

Erel Avineri, Yftach Gil, Yehudit Aperstein

arXiv:2609.29706v1cs.LG

TL;DR

Predicting pedestrian motion at urban intersections is challenging because people adapt to vehicles and environmental cues. This study combines pedestrian trajectories with TTC and crossing-zone context and evaluates safety-oriented training and error measures. On the evaluated inD intersection, the pooled model reduced threshold-exceedance counts relative to a safety-oriented position-only LSTM.

  • Problem

    Pedestrian motion at urban intersections is difficult to infer from positions alone because pedestrians adapt to vehicles, traffic, and environmental cues.

    Source: §1 · p. 2

  • Method

    The framework combines pedestrian motion history with TTC interaction information and crossing-zone context, alongside safety-oriented error evaluation and weighted training.

    Source: §1 · p. 3, §7 · p. 20

  • Results

    The pooled configuration reduced ADE and FDE threshold-exceedance counts by approximately 33.5% and 6.3%, respectively, relative to the safety-oriented position-only LSTM.

    Source: §7 · p. 20

  • Takeaways & Limitations

    Mean displacement error alone can obscure meaningful differences in the occurrence of large prediction failures.

    Source: §7 · p. 20

    All experiments used one inD intersection, so external validity across other intersections remains to be established.

    Source: §6.4 · p. 19

Abstract

from arXiv · show

Accurate pedestrian trajectory prediction is important for proactive road-safety applications, particularly at urban intersections where pedestrian motion is shaped by both vehicle interactions and crossing context. This study presents a safety-oriented trajectory-prediction framework that combines pedestrian motion history with Time-to-Collision (TTC) information and crossing-zone indicators. Using naturalistic trajectories from one urban intersection in the inD (Intersection Drone) dataset, several neural architectures were evaluated with 1.6 s observation and 2.4 s prediction horizons. A pooled Long Short-Term Memory (LSTM) separately encodes TTC histories and crossing-zone context before integrating them with pedestrian positions. In addition to conventional Average Displacement Error (ADE) and Final Displacement Error (FDE), prediction performance was assessed using the frequency and magnitude of errors exceeding a study-defined 1 m tolerance. A weighted loss was also introduced to place greater training emphasis on large coordinate-wise errors. Applying this loss to the position-only LSTM reduced ADE from 0.210 to 0.190 m and FDE from 0.550 to 0.503 m, while reducing ADE and FDE exceedance counts by 34.8% and 19.8%, respectively. The final pooled configuration incorporating TTC and crossing-zone information achieved an ADE of 0.184 m and FDE of 0.491 m, with further reductions of 33.5% and 6.3% in ADE and FDE exceedance counts relative to the safety-oriented position-only LSTM. The results indicate that safety-oriented training and structured integration of interaction and contextual information can reduce large trajectory-prediction errors, although broader validation across pedestrians, sites, and datasets is required.

1. Introduction

Pedestrian prediction at urban intersections must account for adaptive responses to vehicles and environmental cues, not just past positions. This study brings interaction and crossing context together with safety-oriented training and evaluation that emphasize large errors.

1. Introduction

  • Position history alone can be insufficient because pedestrians adapt to approaching vehicles, surrounding traffic, and environmental cues.The paper motivates prediction for proactive interventions such as braking, warnings, or evasive maneuvers.Source: §1 · p. 2
  • The study investigates whether adding TTC-based interaction information and crossing-zone context improves prediction on naturalistic urban-intersection trajectories.The paper emphasizes reducing errors that exceed a defined tolerance rather than focusing only on average accuracy.Source: §1 · pp. 2–3
  • The study combines continuous TTC interaction histories and crossing-zone indicators with pedestrian trajectories, using a structured pooled recurrent architecture to integrate these inputs.TTC and crossing context are encoded separately before fusion with the pedestrian trajectory for recurrent prediction.Source: §1 · pp. 2–3
  • The framework complements ADE and FDE with threshold-exceedance measures that quantify the frequency and magnitude of large prediction errors.The study treats the tolerance as a practical evaluation criterion, not a formally established safety standard.Source: §1 · p. 3
  • A threshold-weighted loss increases training emphasis on large coordinate-wise errors while retaining standard quadratic treatment of smaller errors.The loss is designed to align optimization with the proposed safety-oriented evaluation objective.Source: §1 · p. 3

2. Background and Related Work

The background connects dynamic pedestrian–vehicle conflicts and surrogate safety measures to trajectory prediction, interaction modeling, context, and safety-relevant evaluation. It identifies limited joint integration of TTC, crossing context, and methods targeting large prediction errors as the research gap.

2.1 Pedestrian-Vehicle Conflicts and Safety-Oriented Analysis

  • Conflict-based safety analysis focuses on dynamic interactions and behavioral adaptation that precede crashes, motivating prediction before hazardous interactions escalate.Conflicts provide information about risk mechanisms without relying exclusively on crash records.Source: §2.1 · p. 3

2.2 Surrogate Safety Measures and Time-To-Collision

  • TTC estimates remaining time until collision under constant-motion assumptions and is widely used to characterize pedestrian–vehicle interaction severity.Prior trajectory-prediction approaches have incorporated TTC through risk-based agent selection or interaction energy.Source: §2.2 · p. 4

2.3 Predictive Modeling of Pedestrian Motion

  • Trajectory-prediction research spans recurrent, convolutional, generative, graph-based, transformer, and language-model-inspired approaches, while ADE and FDE may obscure rare large failures.Crowded or interaction-rich settings can make motion less predictable from past positions alone.Source: §2.3 · p. 4

2.4 Interaction Modeling and Environmental Context

  • Interaction models capture dependencies among nearby agents, while crossing infrastructure and individual characteristics shape pedestrian behavior.Empirical work reports behavioral differences at marked and unmarked crossings, including changes in speed, hesitation, and gap acceptance (Ni et al., 2016). The present study uses explicit crossing-zone indicators.Source: §2.4 · pp. 4–5

2.5 Datasets, Evaluation, and Safety-Relevant Limitations

  • Evaluation research highlights limits of displacement metrics alone, including missed distribution quality and application criteria beyond single-trajectory accuracy.Rasouli (2020), Dendorfer (2023), and Uhlemann et al. (2024) motivate evaluation beyond mean displacement accuracy.Source: §2.5 · p. 5

2.6 Summary and Research Gap

  • Prior work has developed TTC-based interaction modeling and environmental context largely separately, with limited joint integration alongside training and evaluation targeting large errors.This study brings together continuous TTC histories, explicit crossing-zone context, and safety-oriented training and evaluation on naturalistic urban-intersection data.Source: §2.6 · p. 5

3. Data and Study Site

The study uses naturalistic inD trajectories but restricts its analysis to one Aachen intersection with pedestrian–vehicle interactions and both marked and informal crossings. The tracks were downsampled to support the experiments’ temporal resolution.

3.1 Naturalistic Trajectory Data for Safety Analysis

  • The inD dataset was selected for its naturalistic urban-intersection trajectories and mixed road-user composition, which provide pedestrian–vehicle interaction data.The dataset uses unobtrusive bird’s-eye-view recordings from camera-equipped drones (Bock et al., 2020).Source: §3.1 · p. 6, §3.2 · p. 6

3.2 The inD Dataset

  • The inD dataset includes about 10 hours of recordings from four unsignalized Aachen intersections and 13,599 road users across several road-user classes.Tracks were extracted from 4K video at 25 Hz, with reported positional accuracy of approximately 10 cm.Source: §3.2 · p. 6

3.3 Study Site Selection

  • The analysis focuses on Location 2, a four-arm unsignalized intersection with frequent pedestrian–vehicle interactions and both a marked zebra crossing and informal crossing areas.Restricting the study to one site offers a controlled setting but limits generalization across road geometries and traffic environments.Source: §3.3 · pp. 6–7, Figure 1 · p. 7

3.4 Trajectory Representation and Temporal Resolution

  • The original 25 Hz tracks were downsampled to 5 Hz, yielding one observation every 0.2 seconds for both observation and prediction sequences.Pedestrians are prediction targets; vehicle trajectories support interaction-feature computation.Source: §3.4 · p. 7

4. Methodology

The method forecasts future pedestrian positions from observed motion, vehicle-derived TTC histories, and crossing-zone context. It generates fixed-length sequence samples with an 1.6-second observation window and a 2.4-second prediction horizon.

4.1 Problem Formulation: Predicting Pedestrian Motion under Conflict Risk

  • The task predicts future two-dimensional pedestrian trajectories from observed motion while conditioning on vehicle-interaction information and crossing-infrastructure context.The formulation represents the future trajectory as a learned function of pedestrian positions, TTC features, and crossing-zone indicators.Source: §4.1 · pp. 7–8
  • The processing pipeline derives TTC features from surrounding-vehicle trajectories and combines them with pedestrian motion history and crossing-zone indicators to estimate future motion.The crossing-zone sequence encodes whether the pedestrian is within each of four predefined zones.Source: §4.1 · p. 8, Figure 2 · p. 8

4.2 Sample Generation and Prediction Protocol

  • Each sequence sample contains observed pedestrian motion, corresponding interaction and context histories, and the subsequent future trajectory.The common sequence-to-sequence setting supports training and evaluation across the models.Source: §4.2 · p. 8
  • The protocol uses 8 observed steps (1.6 seconds) and predicts 12 future steps (2.4 seconds) at 5 Hz, generating overlapping samples with a one-step sliding window.Tracks must contain at least 20 consecutive downsampled observations to provide complete input and prediction segments.Source: §4.2 · pp. 8–9

4.3 Time-to-Collision Computation and Interpretation

The study treats Time-to-Collision (TTC) as a continuous measure of pedestrian–vehicle interaction urgency under an unchanged-motion assumption. It computes TTC from road-user bounding-box geometry and retains multiple vehicle interactions as time-varying inputs.

4.3 Time-to-Collision Computation and Interpretation

  • TTC represents the remaining time until collision if pedestrian and vehicle motion and heading remain unchanged.It is used as a measure of interaction urgency.Source: §4.3 · p. 9
  • The two-dimensional computation uses positions, headings, velocities, and physical dimensions to determine whether moving bounding boxes would intersect and when.The figure illustrates the geometry-based calculation between a pedestrian and an approaching vehicle.Source: §4.3 · p. 9, Figure 3 · p. 10
  • TTC is retained as a continuous predictive input rather than converted into discrete risk categories.The passage notes that conflict-severity thresholds vary across studies and applications.Source: §4.3 · p. 9
  • At each time step, the interaction representation retains TTC values for up to nine surrounding vehicles per pedestrian.The nine-slot choice reflects that observations with more than nine surrounding vehicles were rare in the study data.Source: §4.3 · p. 9

4.4 Crossing Zones as Environmental Context

The study represents crossing infrastructure with manually defined spatial zones and uses their indicators as compact environmental context. These indicators join pedestrian positions and TTC features in the enriched model input.

4.4 Crossing Zones as Environmental Context

  • Four study-site crossing regions comprise the marked zebra crossing and three informal areas, each represented by a binary indicator.The zones were manually defined from the intersection layout and observed pedestrian flow patterns; Figure 4 shows their locations and colors.Source: §4.4 · p. 10, Figure 4 · p. 11
  • Because the zones are mutually exclusive, the context vector is all zeros outside them or one-hot within a zone.This representation conditions predictions on crossing location without dense semantic maps or image-based inputs.Source: §4.4 · p. 10

4.5 Input Representation

  • The enriched input combines two position coordinates, nine TTC entries, and four zone indicators per step, forming an eight-step 8 × 15 sequence.The target is the future trajectory over 12 steps, represented as 12 × 2.Source: §4.5 · p. 11
  • The position-only baseline uses an 8 × 2 input, while unused TTC slots are zero-padded and non-collision cases receive a large finite sentinel value.The reduced baseline enables comparison with models incorporating TTC and crossing-zone information.Source: §4.5 · p. 11

4.6 Compared Predictive Models

The study compares feed-forward and recurrent trajectory predictors, including a pooled LSTM that separately encodes interaction and crossing context before recurrent prediction. The pooled architecture integrates those encodings with pedestrian motion history.

4.6 Compared Predictive Models

  • The compared models are a two-layer MLP, an encoder-decoder with latent noise, a standard LSTM, and an LSTM with pooling.The MLP directly maps fixed-length inputs without explicit temporal memory; the encoder-decoder encodes, perturbs, and decodes a latent representation, while the standard LSTM processes inputs recurrently.Source: §4.6 · pp. 11–12

4.7 Proposed Pooled LSTM Architecture

  • The pooled model encodes the complete observation-window histories of TTC and crossing zones into low-dimensional representations that are combined with pedestrian positions.The two encoders each produce a two-dimensional latent representation.Source: §4.7 · p. 12
  • It generates future positions autoregressively for 12 steps, keeping the observation-derived TTC and zone representations fixed while using each generated position as the next positional input.The experimental pooled model has three LSTM layers with hidden-state dimension 128.Source: §4.7 · p. 12
  • The proposed pooled LSTM encodes TTC interaction features and crossing-zone context separately before fusing them with pedestrian motion history for recurrent prediction.Unlike direct feature concatenation in the standard LSTM, the pooled architecture uses dedicated latent representations; Figure 5 depicts this integration.Source: §4.7 · p. 12, §4.6 · p. 12, Figure 5 · p. 12

4.8 Safety-Oriented Loss Function

The loss formulation gives greater training emphasis to large coordinate-wise prediction errors. It uses thresholded weights on squared errors and averages them across predicted steps and spatial coordinates.

4.8 Safety-Oriented Loss Function

  • The safety-oriented objective threshold-reweights standard mean squared error because the study treats large coordinate-wise errors as more consequential than small deviations.The stated motivation is that large errors can undermine timely intervention in high-risk situations.Source: §4.8 · p. 13
  • The training loss averages weighted squared errors over all predicted time steps and both spatial coordinates.Source: §4.8 · p. 13
  • Errors below P_t retain their standard quadratic weight, while errors exceeding P_t are upweighted by P_f.P_f is the penalty factor and is greater than 1.Source: §4.8 · p. 13

4.9 Evaluation Metrics

The evaluation combines conventional displacement metrics with sample-level threshold-exceedance measures to characterize both typical accuracy and large prediction errors. A 1 m threshold is used as a study-defined practical tolerance, not a standardized safety boundary.

4.9 Evaluation Metrics

  • ADE measures mean displacement error across the prediction horizon, while FDE measures displacement error at the final predicted time step.Dataset-level ADE and FDE average these measures across evaluated samples.Source: §4.9 · p. 13
  • Threshold-exceedance counts and rates summarize how often sample-level ADE or FDE exceeds its evaluation threshold.Exceedance rates enable comparisons across evaluation subsets.Source: §4.9 · p. 13
  • For threshold-exceeding samples, mean and median exceedance values characterize error magnitude; the experiments use a 1 m practical tolerance, not a standardized safety boundary.The study sets both ADE and FDE thresholds to 1 m.Source: §4.9 · p. 14

5. Experiments and Results

The experiments compare position-only and enriched-feature models, then assess safety-oriented training and pooled integration of TTC and crossing-zone context. The final pooled configuration reduces both displacement errors and threshold-exceedance counts relative to the standard-loss position-only baseline.

5.1 Experimental Setup

  • Tracks were downsampled to 5 Hz, split 80%/20% by track, and converted into 8 observed steps and 12 prediction steps; the test set contained 59,095 samples.The observation and prediction windows correspond to 1.6 s and 2.4 s, respectively.Source: §5.1 · p. 14

5.2 Position-Only Baseline Comparison Under Standard Loss

  • The position-only LSTM achieved substantially lower displacement errors than the MLP and encoder-decoder baselines, so it was selected as the reference model.Table 2 reports the preliminary position-only architecture comparison under standard loss.Source: §5.2 · p. 15, Table 2 · p. 15

5.3 Enriched-Feature Comparison Under Standard Loss

  • Enriched inputs did not improve performance automatically: direct concatenation degraded standard-LSTM performance, while the pooled LSTM achieved the best overall results in that setting.The pooled LSTM separately encodes TTC and crossing-zone features before recurrent prediction; these results compare configurations, not pooling alone as an isolated causal factor.Source: §5.3 · pp. 15–16, Table 3 · p. 15

5.4 Final Comparison and Threshold-Exceedance Analysis

  • Applying safety-oriented loss to the position-only LSTM reduced ADE/FDE by 9.5%/8.5% and ADE/FDE exceedance counts by 34.8%/19.8% versus its standard-loss baseline.The pooled-LSTM sensitivity analysis selected Pt = 1 m and Pf = 1.2; that setting was used for the final runs.Source: §5.1 · p. 14, Figure 6 · p. 14, §5.4 · p. 16
  • The final pooled model reduced ADE/FDE by 12.4%/10.7% and ADE/FDE exceedance counts by 56.7%/24.8% versus the standard-loss position-only baseline.Tables 4 and 5 report ADE- and FDE-related comparisons, respectively.Source: Table 4 · p. 16, Table 5 · p. 16, §5.4 · p. 16
  • With safety-oriented loss, pooling further reduced ADE/FDE by 3.2%/2.4% and ADE/FDE exceedance counts by 33.5%/6.3% versus the position-only LSTM.For exceedance magnitudes, the pooled model reduced mean ADE and FDE values, improved median FDE, and slightly increased median ADE; occasional large errors remained.Source: §5.4 · pp. 16–17
  • ADE exceedances cluster relatively near 1 m, whereas FDE has a longer right tail; pooling mainly reduces exceedance frequency rather than eliminating occasional large errors.Figure 7 shows distributions for the safety-oriented position-only and pooled LSTM configurations.Source: Figure 7 · p. 17, §5.4 · p. 17

6. Discussion

The discussion reports improved average and threshold-based errors with safety-oriented training, with further exceedance reductions from the pooled TTC and crossing-zone configuration. It also qualifies these results by noting distribution-specific trade-offs, limited validation scope, and that prediction-error reductions do not establish crash-risk reduction.

6.1 Main Findings and Safety-Oriented Interpretation

  • ADE fell from 0.210 m to 0.190 m and FDE from 0.550 m to 0.503 m; 1 m exceedance counts fell from 247 to 161 for ADE and from 7,521 to 6,033 for FDE.These comparisons are for the position-only LSTM with safety-oriented loss versus the same LSTM with standard loss.Source: §6.1 · p. 18
  • Approximately 3.2% lower ADE and 2.4% lower FDE, with ADE and FDE exceedance counts reduced by approximately 33.5% and 6.3%, respectively, for the final pooled configuration versus the safety-oriented position-only LSTM.The pooled model's clearest advantage was fewer threshold-exceeding predictions, rather than uniform improvement across error-distribution measures.Source: §6.1 · p. 18
  • The pooled model reduced mean ADE and FDE among exceedances and median FDE exceedance, but median ADE exceedance rose slightly, so its error-distribution gains were not uniform.Its clearest advantage was reducing the number of threshold-exceeding predictions.Source: §6.1 · p. 18

6.2 Role of TTC, Crossing Context, and Structured Feature Integration

  • TTC encodes dynamic interaction while crossing zones encode spatial context; separate encoding outperformed direct concatenation in evaluated configurations, though model capacity also differed.The experiments therefore do not isolate pooling as the cause of the observed difference.Source: §6.2 · pp. 18–19
  • Because TTC and crossing-zone features were introduced jointly, the results characterize their combined representation and do not isolate either feature family's independent contribution.Feature-specific analysis is left for future work.Source: §6.2 · p. 19

6.3 Implications for Safety-Oriented Pedestrian Prediction

  • Fewer large forecast errors could be useful for downstream risk assessment, warning, planning, or braking, but these results do not demonstrate crash-risk reduction.The 1 m threshold is a study-defined tolerance for characterizing large errors, not a validated safe-versus-unsafe boundary.Source: §6.3 · p. 19

6.4 Limitations and Future Work

  • Validation is limited to one inD intersection; manually defined crossing zones need adaptation across layouts, and pedestrian characteristics were outside the study's scope.Site geometry, traffic composition and volume, and pedestrian behavior may affect external validity.Source: §6.4 · p. 19
  • TTC assumes constant motion and offers only an instantaneous interaction approximation, while the model simplifies the mutual adaptation of pedestrians and drivers.Future work could examine bidirectional and multi-agent interaction mechanisms.Source: §6.4 · p. 19

7. Conclusion

The study combines motion history with TTC and crossing-zone context and evaluates large prediction errors through a safety-oriented framework. In the evaluated inD intersection, pooled inputs improved the position-only safety-oriented model’s displacement errors and threshold-exceedance counts, while broader generalization remains to be tested.

7. Conclusion

  • The framework combines motion history, TTC-based vehicle-interaction information, and crossing-zone context, while weighting coordinate-wise errors above a predefined threshold more heavily.Source: §7 · p. 20
  • ADE 0.184 m and FDE 0.491 m; against the safety-oriented position-only LSTM, the pooled model lowered ADE/FDE by 3.2%/2.4% and exceedance counts by 33.5%/6.3%.These findings are within the evaluated inD intersection.Source: §7 · p. 20
  • The authors call for pedestrian- and site-disjoint evaluation and additional intersections and datasets to test whether the reductions generalize.Source: §7 · p. 20
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