# Enhancing motion trajectory segmentation of rigid bodies using a novel screw-based trajectory-shape representation

arXiv: https://arxiv.org/abs/2309.11413 · HTML: https://mlsanity.com/paper/2309.11413/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 20 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Enhancing Hand Palm Motion Gesture Recognition by Eliminating Reference Frame Bias via Frame-Invariant Similarity Measures](https://mlsanity.com/paper/2503.11352/) (2025)

## Abstract (arXiv)

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.