# Robust Online Matrix Factorization for Dynamic Background Subtraction

arXiv: https://arxiv.org/abs/1705.10000 · HTML: https://mlsanity.com/paper/1705.10000/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2017.

## Built on by (most cited first, 10 of 10)

- [From Sky to the Ground: A Large-scale Benchmark and Simple Baseline Towards Real Rain Removal](https://mlsanity.com/paper/2308.03867/) (2023)
- [Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices](https://mlsanity.com/paper/2201.12592/) (2022)
- [Universal Background Subtraction based on Arithmetic Distribution Neural Network](https://mlsanity.com/paper/2104.08390/) (2021)
- [Bayesian Inference Forgetting](https://mlsanity.com/paper/2101.06417/) (2021)
- [Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtraction](https://mlsanity.com/paper/2309.15576/) (2023)
- [It's Not the Target, It's the Background: Rethinking Infrared Small Target Detection via Deep Patch-Free Low-Rank Representations](https://mlsanity.com/paper/2506.10425/) (2025)
- [Working memory inspired hierarchical video decomposition with transformative representations](https://mlsanity.com/paper/2204.10105/) (2022)
- [A Bioinspired Retinal Neural Network for Accurately Extracting Small-Target Motion Information in Cluttered Backgrounds](https://mlsanity.com/paper/2103.00848/) (2021)
- [Auto robust relative radiometric normalization via latent change noise modelling](https://mlsanity.com/paper/2111.12406/) (2021)
- [Generalized Low-Rank Matrix Completion Model with Overlapping Group Error Representation](https://mlsanity.com/paper/2407.08517/) (2024)

## Abstract (arXiv)

We propose an effective online background subtraction method, which can be robustly applied to practical videos that have variations in both foreground and background. Different from previous methods which often model the foreground as Gaussian or Laplacian distributions, we model the foreground for each frame with a specific mixture of Gaussians (MoG) distribution, which is updated online frame by frame. Particularly, our MoG model in each frame is regularized by the learned foreground/background knowledge in previous frames. This makes our online MoG model highly robust, stable and adaptive to practical foreground and background variations. The proposed model can be formulated as a concise probabilistic MAP model, which can be readily solved by EM algorithm. We further embed an affine transformation operator into the proposed model, which can be automatically adjusted to fit a wide range of video background transformations and make the method more robust to camera movements. With using the sub-sampling technique, the proposed method can be accelerated to execute more than 250 frames per second on average, meeting the requirement of real-time background subtraction for practical video processing tasks. The superiority of the proposed method is substantiated by extensive experiments implemented on synthetic and real videos, as compared with state-of-the-art online and offline background subtraction methods.