# Quaternion-Based Robust PCA for Efficient Moving Target Detection and Background Recovery in Color Videos

arXiv: https://arxiv.org/abs/2507.19730 · HTML: https://mlsanity.com/paper/2507.19730/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [FreiHAND: A Dataset for Markerless Capture of Hand Pose and Shape from Single RGB Images](https://mlsanity.com/paper/1909.04349/) (2019)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Labels4Free: Unsupervised Segmentation using StyleGAN](https://mlsanity.com/paper/2103.14968/) (2021)
- [Visual Object Tracking with Discriminative Filters and Siamese Networks: A Survey and Outlook](https://mlsanity.com/paper/2112.02838/) (2021)
- [Motion-aware Contrastive Video Representation Learning via Foreground-background Merging](https://mlsanity.com/paper/2109.15130/) (2021)
- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [Towards Benchmarking Scene Background Initialization](https://mlsanity.com/paper/1506.04051/) (2015)
- [Motion-aware Memory Network for Fast Video Salient Object Detection](https://mlsanity.com/paper/2208.00946/) (2022)
- [Anomaly Detection in Traffic Scenes via Spatial-aware Motion Reconstruction](https://mlsanity.com/paper/1904.13079/) (2019)
- [Unsupervised Deep Context Prediction for Background Foreground Separation](https://mlsanity.com/paper/1805.07903/) (2018)
- [Autoencoder-based background reconstruction and foreground segmentation with background noise estimation](https://mlsanity.com/paper/2112.08001/) (2021)
- [Hyper RPCA: Joint Maximum Correntropy Criterion and Laplacian Scale Mixture Modeling On-the-Fly for Moving Object Detection](https://mlsanity.com/paper/2006.07795/) (2020)
- [Learning Temporal Distribution and Spatial Correlation Towards Universal Moving Object Segmentation](https://mlsanity.com/paper/2304.09949/) (2023)
- [Learning Spatial-Temporal Regularized Tensor Sparse RPCA for Background Subtraction](https://mlsanity.com/paper/2309.15576/) (2023)

## Abstract (arXiv)

Moving target detection is a challenging computer vision task aimed at generating accurate segmentation maps in diverse in-the-wild color videos captured by static cameras. If backgrounds and targets can be simultaneously extracted and recombined, such synthetic data can significantly enrich annotated in-the-wild datasets and enhance the generalization ability of deep models. Quaternion-based RPCA (QRPCA) is a promising unsupervised paradigm for color image processing. However, in color video processing, Quaternion Singular Value Decomposition (QSVD) incurs high computational costs, and rank-1 quaternion matrix fails to yield rank-1 color channels. In this paper, we reduce the computational complexity of QSVD to o(1) by utilizing a quaternion Riemannian manifold. Furthermor, we propose the universal QRPCA (uQRPCA) framework, which achieves a balance in simultaneously segmenting targets and recovering backgrounds from color videos. Moreover, we expand to uQRPCA+ by introducing the Color Rank-1 Batch (CR1B) method to further process and obtain the ideal low-rank background across color channels. Experiments demonstrate our uQRPCA+ achieves State Of The Art (SOTA) performance on moving target detection and background recovery tasks compared to existing open-source methods. Our implementation is publicly available on GitHub at https://github.com/Ruchtech/uQRPCA