# A Tube-and-Droplet-based Approach for Representing and Analyzing Motion Trajectories

arXiv: https://arxiv.org/abs/1609.03058 · HTML: https://mlsanity.com/paper/1609.03058/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2016.

## Built on by (most cited first, 5 of 5)

- [TrajGen: Generating Realistic and Diverse Trajectories with Reactive and Feasible Agent Behaviors for Autonomous Driving](https://mlsanity.com/paper/2203.16792/) (2022)
- [Spatio-Temporal Point Process for Multiple Object Tracking](https://mlsanity.com/paper/2302.02444/) (2023)
- [A Novel Deep Neural Network for Trajectory Prediction in Automated Vehicles Using Velocity Vector Field](https://mlsanity.com/paper/2309.10948/) (2023)
- [A principled distributional approach to trajectory similarity measurement](https://mlsanity.com/paper/2301.00393/) (2023)
- [GeoPTH: A Lightweight Approach to Category-Based Trajectory Retrieval via Geometric Prototype Trajectory Hashing](https://mlsanity.com/paper/2511.16258/) (2025)

## Abstract (arXiv)

Trajectory analysis is essential in many applications. In this paper, we address the problem of representing motion trajectories in a highly informative way, and consequently utilize it for analyzing trajectories. Our approach first leverages the complete information from given trajectories to construct a thermal transfer field which provides a context-rich way to describe the global motion pattern in a scene. Then, a 3D tube is derived which depicts an input trajectory by integrating its surrounding motion patterns contained in the thermal transfer field. The 3D tube effectively: 1) maintains the movement information of a trajectory, 2) embeds the complete contextual motion pattern around a trajectory, 3) visualizes information about a trajectory in a clear and unified way. We further introduce a droplet-based process. It derives a droplet vector from a 3D tube, so as to characterize the high-dimensional 3D tube information in a simple but effective way. Finally, we apply our tube-and-droplet representation to trajectory analysis applications including trajectory clustering, trajectory classification & abnormality detection, and 3D action recognition. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our approach.