# ReynoldsFlow: Physics-Inspired Spatiotemporal Flow Representation for Video Understanding

arXiv: https://arxiv.org/abs/2503.04500 · HTML: https://mlsanity.com/paper/2503.04500/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 69 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 23 of 23)

- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [RAFT: Recurrent All-Pairs Field Transforms for Optical Flow](https://mlsanity.com/paper/2003.12039/) (2020)
- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Optical Flow Estimation using a Spatial Pyramid Network](https://mlsanity.com/paper/1611.00850/) (2016)
- [3D human pose estimation in video with temporal convolutions and semi-supervised training](https://mlsanity.com/paper/1811.11742/) (2018)
- [Flow-Guided Feature Aggregation for Video Object Detection](https://mlsanity.com/paper/1703.10025/) (2017)
- [SEA-RAFT: Simple, Efficient, Accurate RAFT for Optical Flow](https://mlsanity.com/paper/2405.14793/) (2024)
- [Video Summarization with Long Short-term Memory](https://mlsanity.com/paper/1605.08110/) (2016)
- [Deep Learning in Video Multi-Object Tracking: A Survey](https://mlsanity.com/paper/1907.12740/) (2019)
- [Video Representation Learning by Recognizing Temporal Transformations](https://mlsanity.com/paper/2007.10730/) (2020)
- [EpicFlow: Edge-Preserving Interpolation of Correspondences for Optical Flow](https://mlsanity.com/paper/1501.02565/) (2015)
- [Fast Optical Flow using Dense Inverse Search](https://mlsanity.com/paper/1603.03590/) (2016)
- [Towards High Performance Video Object Detection](https://mlsanity.com/paper/1711.11577/) (2017)
- [Detect-and-Track: Efficient Pose Estimation in Videos](https://mlsanity.com/paper/1712.09184/) (2017)
- [Hierarchical Recurrent Neural Network for Video Summarization](https://mlsanity.com/paper/1904.12251/) (2019)
- [VideoMamba: Spatio-Temporal Selective State Space Model](https://mlsanity.com/paper/2407.08476/) (2024)
- [GolfDB: A Video Database for Golf Swing Sequencing](https://mlsanity.com/paper/1903.06528/) (2019)
- [Personalizing Human Video Pose Estimation](https://mlsanity.com/paper/1511.06676/) (2015)
- [TransVisDrone: Spatio-Temporal Transformer for Vision-based Drone-to-Drone Detection in Aerial Videos](https://mlsanity.com/paper/2210.08423/) (2022)
- [STNMamba: Mamba-based Spatial-Temporal Normality Learning for Video Anomaly Detection](https://mlsanity.com/paper/2412.20084/) (2024)
- [HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition](https://mlsanity.com/paper/2406.08570/) (2024)

## Abstract (arXiv)

Video understanding has largely relied on deep spatiotemporal architectures, including 3D convolutional networks and optical flow (OF) based models. While effective, these methods are often computationally expensive and depend on heuristic motion representations that are sensitive to illumination, scale, and structural changes. To address these limitations, we propose ReynoldsFlow, a physics-inspired representation grounded in the Reynolds transport theorem (RTT) and Helmholtz-Hodge decomposition (HHD). ReynoldsFlow decomposes motion into curl-free (CF) and divergence-free (DF) components, providing a principled and interpretable characterization of scene dynamics. By coupling intensity information with decomposed motion cues, it produces dynamics-aware, texture-preserving features that boost downstream tasks such as pose estimation, action recognition, and tiny object detection. Lightweight and modular, ReynoldsFlow can be readily integrated into existing architectures. Experiments across diverse benchmarks show that ReynoldsFlow consistently matches or surpasses existing approaches, offering improved generalizability and computational efficiency.