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

2025-07-25

AI Summary

This work addresses the joint modeling challenge of moving object detection and background recovery from color video sequences captured by static cameras. To this end, we propose the uQRPCA framework and the CR1B method. uQRPCA employs quaternion-based robust principal component analysis (RPCA) to model the background as a low-rank structure on the Riemannian manifold, reducing quaternion SVD complexity to constant time. CR1B introduces a Color Rank-1 Batch mechanism to enforce inter-channel consistency across RGB channels, thereby enhancing synergy between foreground segmentation and background reconstruction. Evaluated on multiple standard benchmarks, our approach achieves state-of-the-art performance among open-source methods, with significant improvements in both processing efficiency and segmentation accuracy. The source code is publicly available.

Technology Category

• Computer Vision: Motion & Tracking
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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

Problem

• Efficient moving target detection in color videos
• Background recovery for synthetic data generation
• Reducing computational complexity of Quaternion SVD

Innovation

• Quaternion Riemannian manifold reduces QSVD complexity
• Universal QRPCA balances target segmentation and background recovery
• Color Rank-1 Batch method ensures ideal low-rank background