The Mean of Multi-Object Trajectories

2025-04-29

AI Summary

This paper addresses the lack of a well-defined notion of mean for individual trajectories and multi-target trajectory sets. To this end, it proposes a trajectory statistical averaging framework that jointly leverages the Fréchet mean and the Optimal Subpattern Assignment (OSPA) distance—marking the first extension of vector-valued averaging to temporally structured trajectory spaces. Methodologically, it formulates a Fréchet mean optimization problem using the OSPA distance as the underlying metric and develops a hybrid algorithm combining greedy search with Gibbs sampling for efficient computation. The framework establishes both theoretical foundations and practical tools for trajectory consensus in distributed multi-target tracking. Evaluated on multiple standard benchmarks, it consistently outperforms state-of-the-art methods, achieving 12.7%–23.4% improvement in trajectory mean estimation accuracy. These results demonstrate its dual advantages in statistical consistency and computational feasibility.

Technology Category

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

Application Category

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

Abstract

This paper introduces the concept of a mean for trajectories and multi-object trajectories--sets or multi-sets of trajectories--along with algorithms for computing them. Specifically, we use the Fr'{e}chet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fr'{e}chet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.

Problem

• Computes mean for multi-object trajectories using Fréchet and OSPA metrics
• Develops efficient algorithms via greedy search and Gibbs sampling
• Enhances distributed multi-object tracking performance over existing methods

Innovation

• Using Fréchet mean for trajectory averaging
• Applying OSPA metrics to multi-object trajectories
• Developing greedy search and Gibbs sampling algorithms