# Real-Time Motion Detection Using Dynamic Mode Decomposition

arXiv: https://arxiv.org/abs/2405.05057 · HTML: https://mlsanity.com/paper/2405.05057/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 8 May 2024.

## Builds on (most cited first, 11 of 11)

- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Residual Dynamic Mode Decomposition: Robust and verified Koopmanism](https://mlsanity.com/paper/2205.09779/) (2022)
- [Compressed Dynamic Mode Decomposition for Background Modeling](https://mlsanity.com/paper/1512.04205/) (2015)
- [Sparse Identification of Slow Timescale Dynamics](https://mlsanity.com/paper/2006.00940/) (2020)
- [Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video](https://mlsanity.com/paper/1404.7592/) (2014)
- [Port-Hamiltonian Dynamic Mode Decomposition](https://mlsanity.com/paper/2204.13474/) (2022)
- [Quaternion-based dynamic mode decomposition for background modeling in color videos](https://mlsanity.com/paper/2112.13982/) (2021)
- [Dynamic Mode Decomposition based feature for Image Classification](https://mlsanity.com/paper/1910.03188/) (2019)
- [An Optimized Dynamic Mode Decomposition Model Robust to Multiplicative Noise](https://mlsanity.com/paper/2109.11850/) (2021)

## Abstract (arXiv)

Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coherent modes that evolve in time according to exponential growth/decay or with a fixed frequency of oscillation. A prolific application of DMD has been to video, where one interprets the high-dimensional pixel space evolving through time as the video plays. In this work, we propose a simple and interpretable motion detection algorithm for streaming video data rooted in DMD. Our method leverages the fact that there exists a correspondence between the evolution of important video features, such as foreground motion, and the eigenvalues of the matrix which results from applying DMD to segments of video. We apply the method to a database of test videos which emulate security footage under varying realistic conditions. Effectiveness is analyzed using receiver operating characteristic curves, while we use cross-validation to optimize the threshold parameter that identifies movement.