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

• URL: http://arxiv.org/abs/2507.19730v1
• Date: Sat, 26 Jul 2025 01:05:03 GMT
• Title: Quaternion-Based Robust PCA for Efficient Moving Target Detection and Background Recovery in Color Videos
• Authors: Liyang Wang, Shiqian Wu, Shun Fang, Qile Zhu, Jiaxin Wu, Sos Again,
• Abstract summary: Quaternion-based RPCA (QRPCA) is a promising unsupervised paradigm for color image processing.<n>We propose the universal QRPCA framework, which achieves a balance in simultaneously segmenting targets and recovering backgrounds from color videos.<n>We also expand to uQRPCA+ by introducing the Color Rank-1 Batch (CR1B) method to further process and obtain the ideal low-rank background.
• Score: 6.948496559712165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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

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