Fast computation of the TGOSPA metric for multiple target tracking via unbalanced optimal transport

2025-03-12

AI Summary

In multi-object tracking, the trajectory generalized optimal subpattern assignment (TGOSPA) metric offers theoretical advantages but suffers from poor scalability due to its reliance on computationally expensive linear programming for exact computation. This work reformulates TGOSPA as an unbalanced multi-marginal optimal transport problem, introduces entropic regularization, and derives an efficient iterative algorithm based on Lagrangian duality. The proposed method circumvents traditional optimization bottlenecks while preserving assessment accuracy sufficient for practical applications. Experimental results demonstrate that the algorithm achieves over an order-of-magnitude speedup compared to exact linear programming solvers, enabling scalable, robust, and theoretically grounded approximate evaluation of large-scale tracking performance.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

In multiple target tracking, it is important to be able to evaluate the performance of different tracking algorithms. The trajectory generalized optimal sub-pattern assignment metric (TGOSPA) is a recently proposed metric for such evaluations. The TGOSPA metric is computed as the solution to an optimization problem, but for large tracking scenarios, solving this problem becomes computationally demanding. In this paper, we present an approximation algorithm for evaluating the TGOSPA metric, based on casting the TGOSPA problem as an unbalanced multimarginal optimal transport problem. Following recent advances in computational optimal transport, we introduce an entropy regularization and derive an iterative scheme for solving the Lagrangian dual of the regularized problem. Numerical results suggest that our proposed algorithm is more computationally efficient than the alternative of computing the exact metric using a linear programming solver, while still providing an adequate approximation of the metric.

Problem

• Efficient computation of TGOSPA metric for tracking evaluation.
• Approximation algorithm for large-scale tracking scenarios.
• Entropy regularization improves computational efficiency in optimal transport.

Innovation

• Approximates TGOSPA via unbalanced optimal transport
• Uses entropy regularization for computational efficiency
• Iterative scheme for solving Lagrangian dual