# Quaternion-based dynamic mode decomposition for background modeling in color videos

arXiv: https://arxiv.org/abs/2112.13982 · HTML: https://mlsanity.com/paper/2112.13982/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 54 references that are in the map.
- First posted on arXiv 28 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [Deep Neural Network Concepts for Background Subtraction: A Systematic Review and Comparative Evaluation](https://mlsanity.com/paper/1811.05255/) (2018)
- [Deep Learning Enhanced Dynamic Mode Decomposition](https://mlsanity.com/paper/2108.04433/) (2021)
- [Compressed Dynamic Mode Decomposition for Background Modeling](https://mlsanity.com/paper/1512.04205/) (2015)
- [Color image recovery using low-rank quaternion matrix completion algorithm](https://mlsanity.com/paper/1909.06567/) (2019)
- [Towards Benchmarking Scene Background Initialization](https://mlsanity.com/paper/1506.04051/) (2015)
- [Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset](https://mlsanity.com/paper/1511.01245/) (2015)
- [Quaternion-based bilinear factor matrix norm minimization for color image inpainting](https://mlsanity.com/paper/2005.02886/) (2020)
- [Unsupervised Deep Context Prediction for Background Foreground Separation](https://mlsanity.com/paper/1805.07903/) (2018)

## Built on by (most cited first, 3 of 3)

- [Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition](https://mlsanity.com/paper/2408.05582/) (2024)
- [L2,1-Norm Regularized Quaternion Matrix Completion Using Sparse Representation and Quaternion QR Decomposition](https://mlsanity.com/paper/2309.03764/) (2023)
- [Real-Time Motion Detection Using Dynamic Mode Decomposition](https://mlsanity.com/paper/2405.05057/) (2024)

## Abstract (arXiv)

Scene Background Initialization (SBI) is one of the challenging problems in computer vision. Dynamic mode decomposition (DMD) is a recently proposed method to robustly decompose a video sequence into the background model and the corresponding foreground part. However, this method needs to convert the color image into the grayscale image for processing, which leads to the neglect of the coupling information between the three channels of the color image. In this study, we propose a quaternion-based DMD (Q-DMD), which extends the DMD by quaternion matrix analysis, so as to completely preserve the inherent color structure of the color image and the color video. We exploit the standard eigenvalues of the quaternion matrix to compute its spectral decomposition and calculate the corresponding Q-DMD modes and eigenvalues. The results on the publicly available benchmark datasets prove that our Q-DMD outperforms the exact DMD method, and experiment results also demonstrate that the performance of our approach is comparable to that of the state-of-the-art ones.