Trajectory segmentation refers to dividing a trajectory into meaningful consecutive sub-trajectories. This paper focuses on trajectory segmentation for 3D rigid-body motions. Most segmentation approaches in the literature represent the body's trajectory as a point trajectory, considering only its translation and neglecting its rotation. We propose a novel trajectory representation for rigid-body motions that incorporates both translation and rotation, and additionally exhibits several invariant properties. This representation consists of a geometric progress rate and a third-order trajectory-shape descriptor. Concepts from screw theory were used to make this representation time-invariant and also invariant to the choice of body reference point. This new representation is validated for a self-supervised segmentation approach, both in simulation and using real recordings of human-demonstrated pouring motions. The results show a more robust detection of consecutive submotions with distinct features and a more consistent segmentation compared to conventional representations. We believe that other existing segmentation methods may benefit from using this trajectory representation to improve their invariance.

翻译：轨迹分割是指将一条轨迹划分为有意义的连续子轨迹。本文专注于三维刚体运动的轨迹分割。文献中的大多数分割方法将物体的轨迹视为点轨迹，仅考虑其平移而忽略其旋转。我们提出了一种新的刚体运动轨迹表示方法，该方法同时包含平移和旋转，并展现出多种不变特性。该表示由几何进展率和三阶轨迹形状描述子构成。通过运用旋量理论的概念，此表示实现了时间不变性以及物体参考点选择的不变性。这种新表示方法在自监督分割方法中得到了验证，包括在仿真环境及人演示倒水动作的真实记录中均进行了测试。结果表明，与传统表示相比，该方法能够更稳健地检测具有显著特征的连续子运动，并且分割结果更加一致。我们相信其他现有的分割方法也可能受益于采用这种轨迹表示以增强其不变性。