Measuring the similarity between motions and established motion models is crucial for motion analysis, recognition, generation, and adaptation. To enhance similarity measurement across diverse contexts, invariant motion descriptors have been proposed. However, for rigid-body motion, few invariant descriptors exist that are bi-invariant, meaning invariant to both the body and world reference frames used to describe the motion. Moreover, their robustness to singularities is limited. This paper introduces a novel Bi-Invariant Local Trajectory-Shape descriptor (BILTS) and a corresponding dissimilarity measure. Mathematical relationships between BILTS and existing descriptors are derived, providing new insights into their properties. The paper also includes an algorithm to reproduce the motion from the BILTS descriptor, demonstrating its bidirectionality and usefulness for trajectory generation. Experimental validation using datasets of daily-life activities shows the higher robustness of the BILTS descriptor compared to the bi-invariant ISA descriptor. This higher robustness supports the further application of bi-invariant descriptors for motion recognition and generalization.

翻译：测量运动与已构建运动模型之间的相似性对于运动分析、识别、生成与适配至关重要。为增强跨不同场景的相似性度量，研究者提出了不变运动描述符。然而，针对刚体运动，目前存在极少数的双不变描述符（即同时不受描述运动时使用的物体参考系和世界参考系影响），且其对奇异点的鲁棒性有限。本文提出一种新型双不变局部轨迹形状描述符（BILTS）及其相应的相异度量。推导出BILTS与现有描述符之间的数学关系，揭示了其属性的新见解。文中还包含从BILTS描述符重建运动的算法，证明了其双向性及在轨迹生成中的实用性。利用日常活动数据集的实验验证表明，与双不变ISA描述符相比，BILTS描述符具有更高的鲁棒性，这进一步支持了双不变描述符在运动识别与泛化中的应用。