# Background Subtraction via Generalized Fused Lasso Foreground Modeling

arXiv: https://arxiv.org/abs/1504.03707 · HTML: https://mlsanity.com/paper/1504.03707/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2015.

## Built on by (most cited first, 4 of 4)

- [A Guide to Image and Video based Small Object Detection using Deep Learning : Case Study of Maritime Surveillance](https://mlsanity.com/paper/2207.12926/) (2022)
- [Autoencoder-based background reconstruction and foreground segmentation with background noise estimation](https://mlsanity.com/paper/2112.08001/) (2021)
- [A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations](https://mlsanity.com/paper/2311.12319/) (2023)
- [Quasi-SVD: Learning a Lie-constrained matrix factorisation for real-time imaging](https://mlsanity.com/paper/2607.25967/) (2026)

## Abstract (arXiv)

Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts.