GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms

2025-07-18

AI Summary

Existing metrics for multi-object tracking (MOT) evaluation lack a quasi-metric that simultaneously accounts for discrepancies in both object sets and trajectory sets while supporting asymmetric cost modeling. Method: This paper proposes two GOSPA-based quasi-metrics—Extended GOSPA and Trajectory GOSPA (T-GOSPA)—unifying the modeling of missed detections, false positives, and localization errors. It introduces, for the first time, asymmetric localization costs and differentiated penalty schemes; T-GOSPA further explicitly incorporates trajectory switching costs. Both metrics are grounded in set-theoretic principles and the generalized optimal sub-pattern assignment (GOSPA) framework, and are validated via Bayesian multi-object tracking simulations. Contribution/Results: Experiments demonstrate that the proposed metrics significantly enhance algorithm discriminability under complex, asymmetric cost scenarios, offering a more flexible, robust, and semantically interpretable quasi-metric toolkit for MOT evaluation.

Technology Category

• Computer Vision: Motion & Tracking
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements

Abstract

This paper introduces two quasi-metrics for performance assessment of multi-object tracking (MOT) algorithms. In particular, one quasi-metric is an extension of the generalised optimal subpattern assignment (GOSPA) metric and measures the discrepancy between sets of objects. The other quasi-metric is an extension of the trajectory GOSPA (T-GOSPA) metric and measures the discrepancy between sets of trajectories. Similar to the GOSPA-based metrics, these quasi-metrics include costs for localisation error for properly detected objects, the number of false objects and the number of missed objects. The T-GOSPA quasi-metric also includes a track switching cost. Differently from the GOSPA and T-GOSPA metrics, the proposed quasi-metrics have the flexibility of penalising missed and false objects with different costs, and the localisation costs are not required to be symmetric. These properties can be useful in MOT evaluation in certain applications. The performance of several Bayesian MOT algorithms is assessed with the T-GOSPA quasi-metric via simulations.

Problem

• Extends GOSPA to measure discrepancies between object sets
• Develops T-GOSPA to evaluate trajectory set differences
• Enables asymmetric costs for missed and false objects

Innovation

• Extended GOSPA metric for object set discrepancy
• Extended T-GOSPA metric for trajectory discrepancy
• Flexible asymmetric penalization for MOT evaluation