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

TL;DR

This paper introduces BILTS, a novel bi-invariant similarity measure for object trajectory recognition that is robust to reference frame variations and noise, outperforming existing measures in recognition accuracy.

Contribution

The paper presents BILTS, a new bi-invariant, shape-preserving similarity measure for trajectories, with a discretized version that handles singularities and improves robustness.

Findings

BILTS achieves the highest recognition ratios among tested measures.

The discretized BILTS is highly robust to singularities and noise.

Experimental results validate BILTS's effectiveness across multiple datasets.

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 \textit{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.