# A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms

arXiv: https://arxiv.org/abs/2110.13444 · HTML: https://mlsanity.com/paper/2110.13444/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 26 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [Performance Measures and a Data Set for Multi-Target, Multi-Camera Tracking](https://mlsanity.com/paper/1609.01775/) (2016)
- [HOTA: A Higher Order Metric for Evaluating Multi-Object Tracking](https://mlsanity.com/paper/2009.07736/) (2020)
- [MOT16: A Benchmark for Multi-Object Tracking](https://mlsanity.com/paper/1603.00831/) (2016)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms](https://mlsanity.com/paper/1605.01177/) (2016)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Poisson multi-Bernoulli mixture trackers: continuity through random finite sets of trajectories](https://mlsanity.com/paper/1812.05131/) (2018)
- [A metric for sets of trajectories that is practical and mathematically consistent](https://mlsanity.com/paper/1601.03094/) (2016)
- [Poisson Multi-Bernoulli Mixtures for Sets of Trajectories](https://mlsanity.com/paper/1912.08718/) (2019)
- [Spooky effect in optimal OSPA estimation and how GOSPA solves it](https://mlsanity.com/paper/1908.08815/) (2019)

## Built on by (most cited first, 6 of 6)

- [TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking](https://mlsanity.com/paper/2412.08321/) (2024)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Detection-aware multi-object tracking evaluation](https://mlsanity.com/paper/2212.08536/) (2022)
- [Fast computation of the TGOSPA metric for multiple target tracking via unbalanced optimal transport](https://mlsanity.com/paper/2503.09449/) (2025)
- [GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms](https://mlsanity.com/paper/2507.13706/) (2025)
- [Model-based Multi-object Visual Tracking: Identification and Standard Model Limitations](https://mlsanity.com/paper/2508.13647/) (2025)

## Abstract (arXiv)

This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches. The proposed metric extends the metric in [1] by including weights to the costs associated to different time steps. The time-weighted costs increase the flexibility of the metric [1] to fit more applications and user preferences. We first introduce a metric based on multi-dimensional assignments, and then its linear programming relaxation, which is computable in polynomial time and is also a metric. The metrics can also be extended to metrics on random finite sets of trajectories to evaluate and rank algorithms across different scenarios, each with a ground truth set of trajectories.