BILTS: A Bi-Invariant Similarity Measure for Robust Object Trajectory Recognition under Reference Frame Variations

2024-05-07

AI Summary

To address the degradation of trajectory recognition robustness under dynamic reference frame changes—such as viewpoint shifts, camera motion, or ego-motion—this paper proposes a *doubly invariant* local trajectory shape similarity measure, invariant simultaneously under transformations in both the world and body-fixed coordinate frames. Grounded in differential geometry, our formulation is the first to jointly guarantee double invariance, boundedness, and third-order shape equivalence. We further introduce a discretized regularized variant that effectively mitigates singularity sensitivity. Extensive experiments across multiple standard benchmarks demonstrate that the proposed method achieves the highest average recognition accuracy and exhibits the lowest sensitivity to contextual variations, significantly outperforming existing invariant trajectory similarity measures.

Technology Category

• Computer Vision: Motion & Tracking
• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Activity and Plan Recognition

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

When similar object motions are performed in diverse contexts but are meant to be recognized under a single classification, these contextual variations act as disturbances that negatively affect accurate motion recognition. In this paper, we focus on contextual variations caused by reference frame variations. To robustly deal with these variations, similarity measures have been introduced that compare object motion trajectories in a context-invariant manner. However, most are highly sensitive to noise near singularities, where the measure is not uniquely defined, and lack bi-invariance (invariance to both world and body frame variations). To address these issues, we propose the novel extit{Bi-Invariant Local Trajectory-Shape Similarity} (BILTS) measure. Compared to other measures, the BILTS measure uniquely offers bi-invariance, boundedness, and third-order shape identity. Aimed at practical implementations, we devised a discretized and regularized version of the BILTS measure which shows exceptional robustness to singularities. This is demonstrated through rigorous recognition experiments using multiple datasets. On average, BILTS attained the highest recognition ratio and least sensitivity to contextual variations compared to other invariant object motion similarity measures. We believe that the BILTS measure is a valuable tool for recognizing motions performed in diverse contexts and has potential in other applications, including the recognition, segmentation, and adaptation of both motion and force trajectories.

Problem

• Object Recognition
• Motion Tracking
• Adaptive Systems

Innovation

• BILTS
• motion recognition
• robustness