# Dynamic Mode Decomposition for Real-Time Background/Foreground Separation in Video

arXiv: https://arxiv.org/abs/1404.7592 · HTML: https://mlsanity.com/paper/1404.7592/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2014.

## Built on by (most cited first, 9 of 9)

- [Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification](https://mlsanity.com/paper/2107.10878/) (2021)
- [Unsupervised Learning of Equivariant Structure from Sequences](https://mlsanity.com/paper/2210.05972/) (2022)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)
- [Deep Learning Based Object Tracking in Walking Droplet and Granular Intruder Experiments](https://mlsanity.com/paper/2302.05425/) (2023)
- [StiefelGen: A Simple, Model Agnostic Approach for Time Series Data Augmentation over Riemannian Manifolds](https://mlsanity.com/paper/2402.19287/) (2024)
- [Real-Time Motion Detection Using Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05057/) (2024)
- [A Dynamic Mode Decomposition Approach to Morphological Component Analysis](https://mlsanity.com/paper/2510.05977/) (2025)
- [CollideNet: Hierarchical Multi-scale Video Representation Learning with Disentanglement for Time-To-Collision Forecasting](https://mlsanity.com/paper/2604.16240/) (2026)
- [A neural operator framework for data-driven discovery of stability and receptivity in physical systems](https://mlsanity.com/paper/2604.19465/) (2026)

## Abstract (arXiv)

This paper introduces the method of dynamic mode decomposition (DMD) for robustly separating video frames into background (low-rank) and foreground (sparse) components in real-time. The method is a novel application of a technique used for characterizing nonlinear dynamical systems in an equation-free manner by decomposing the state of the system into low-rank terms whose Fourier components in time are known. DMD terms with Fourier frequencies near the origin (zero-modes) are interpreted as background (low-rank) portions of the given video frames, and the terms with Fourier frequencies bounded away from the origin are their sparse counterparts. An approximate low-rank/sparse separation is achieved at the computational cost of just one singular value decomposition and one linear equation solve, thus producing results orders of magnitude faster than a leading separation method, namely robust principal component analysis (RPCA). The DMD method that is developed here is demonstrated to work robustly in real-time with personal laptop-class computing power and without any parameter tuning, which is a transformative improvement in performance that is ideal for video surveillance and recognition applications.