用四元数降维实现高效目标检测与背景恢复，提升视频分析精度。
Quaternion-Based Robust PCA for Efficient Moving Target Detection and Background Recovery in Color Videos
- 基于四元数流形降低奇异值分解计算开销至常数级
- uQRPCA+在多个数据集上达到最优检测与背景重建效果
- 适合需要高精度视频分割的工业级视觉系统应用
运动目标检测是计算机视觉中的关键任务，旨在从静态相机拍摄的复杂彩色视频中生成精确的分割图。若能同时提取并重构背景与目标，合成数据可显著丰富真实世界标注数据集，增强深度模型泛化能力。四元数鲁棒主成分分析（QRPCA）是一种有前景的无监督彩色图像处理方法。然而，在彩色视频处理中，四元数奇异值分解（QSVD）计算成本高，且一阶四元数矩阵无法实现各通道的秩1表示。本文通过利用四元数黎曼流形将QSVD计算复杂度降至o(1)，提出通用QRPCA（uQRPCA）框架，实现目标与背景的协同分割。进一步引入色彩秩1批量（CR1B）方法，优化跨通道低秩背景重建。实验表明，uQRPCA+在移动目标检测与背景恢复任务上优于现有开源方法，达到当前最佳性能。代码已开源：https://github.com/Ruchtech/uQRPCA
原文摘要 · Abstract (English)
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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