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.

翻译：当相似的物体运动在不同情境下执行，却需归入单一类别进行识别时，这些情境变化会成为干扰因素，对准确的运动识别产生负面影响。本文重点关注由参考系变化引起的情境差异。为鲁棒地处理这些变化，研究者引入了以情境不变方式比较物体运动轨迹的相似性度量方法。然而，现有方法大多对奇异点附近的噪声高度敏感（该处度量值无法唯一定义），且缺乏双不变性（即对世界坐标系和物体坐标系变化同时保持不变）。为解决这些问题，我们提出了新颖的\textit{双不变局部轨迹形状相似性度量}（BILTS）。相较于其他度量方法，BILTS度量独特地具备双不变性、有界性和三阶形状恒等性。面向实际应用需求，我们设计了离散化与正则化版本的BILTS度量，该版本展现出对奇异点异常优异的鲁棒性。通过使用多个数据集进行的严格识别实验验证了这一点。与其他不变物体运动相似性度量相比，BILTS平均取得了最高的识别率，且对情境变化最不敏感。我们相信BILTS度量是识别多样化情境下执行运动的有力工具，并在运动/力轨迹的识别、分割与适配等其他应用领域具有潜力。