Video background subtraction is one of the fundamental problems in computer vision that aims to segment all moving objects. Robust principal component analysis has been identified as a promising unsupervised paradigm for background subtraction tasks in the last decade thanks to its competitive performance in a number of benchmark datasets. Tensor robust principal component analysis variations have improved background subtraction performance further. However, because moving object pixels in the sparse component are treated independently and do not have to adhere to spatial-temporal structured-sparsity constraints, performance is reduced for sequences with dynamic backgrounds, camouflaged, and camera jitter problems. In this work, we present a spatial-temporal regularized tensor sparse RPCA algorithm for precise background subtraction. Within the sparse component, we impose spatial-temporal regularizations in the form of normalized graph-Laplacian matrices. To do this, we build two graphs, one across the input tensor spatial locations and the other across its frontal slices in the time domain. While maximizing the objective function, we compel the tensor sparse component to serve as the spatiotemporal eigenvectors of the graph-Laplacian matrices. The disconnected moving object pixels in the sparse component are preserved by the proposed graph-based regularizations since they both comprise of spatiotemporal subspace-based structure. Additionally, we propose a unique objective function that employs batch and online-based optimization methods to jointly maximize the background-foreground and spatial-temporal regularization components. Experiments are performed on six publicly available background subtraction datasets that demonstrate the superior performance of the proposed algorithm compared to several existing methods. Our source code will be available very soon.

翻译：视频背景减除是计算机视觉中的基本问题之一，旨在分割所有运动物体。近十年来，鲁棒主成分分析因其在多个基准数据集上的优异表现，被认定为背景减除任务中一种有前景的无监督方法。张量鲁棒主成分分析的变体进一步提升了背景减除性能。然而，由于稀疏分量中的运动目标像素被独立处理且无需遵循时空结构化稀疏约束，对于具有动态背景、伪装目标及相机抖动问题的序列，其性能会下降。本文提出一种时空正则化张量稀疏RPCA算法以实现精确背景减除。我们在稀疏分量中以归一化图拉普拉斯矩阵的形式施加时空正则化。为此，我们构建两个图：一个覆盖输入张量的空间位置，另一个覆盖其时域中的前向切片。在最大化目标函数时，我们强制张量稀疏分量充当图拉普拉斯矩阵的时空特征向量。由于所提出的基于图的正则化共同包含基于时空子空间的结构，稀疏分量中的离散运动目标像素得以保留。此外，我们提出一种独特的目标函数，采用批处理和在线优化方法联合最大化背景-前景分量与时空正则化分量。我们在六个公开背景减除数据集上进行实验，结果表明所提算法相较于现有多种方法具有更优性能。我们的源代码将很快公开。