Principal component analysis (PCA) is one of the most widely used dimension reduction techniques. A related easier problem is termed subspace learning or subspace estimation. Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning (RSL) or robust PCA (RPCA). For long data sequences, if one tries to use a single lower-dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of RSL and tracking. In particular, solutions for three problems are discussed in detail: RPCA via sparse+low-rank (S+LR) matrix decomposition; RST via S+LR; robust subspace recovery (RSR). RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and, hence, are well modeled as sparse corruptions.

Robust principal component analysis (RPCA) via decomposition into low-rank plus sparse matrices offers a powerful framework for a large variety of applications such as image processing, video processing, and 3-D computer vision. Indeed, most of the time these applications require to detect sparse outliers from the observed imagery data that can be approximated by a low-rank matrix. Moreover, most of the time experiments show that RPCA with additional spatial and/or temporal constraints often outperforms the state-of-the-art algorithms in these applications. Thus, the aim of this paper is to survey the applications of RPCA in computer vision. In the first part of this paper, we review representative image processing applications as follows: 1) low-level imaging such as image recovery and denoising, image composition, image colorization, image alignment and rectification, multifocus image, and face recognition; 2) medical imaging such as dynamic magnetic resonance imaging (MRI) for acceleration of data acquisition, background suppression, and learning of interframe motion fields; and 3) imaging for 3-D computer vision with additional depth information such as in structure from motion (SfM) and 3-D motion recovery. In the second part, we present the applications of RPCA in video processing which utilize additional spatial and temporal information compared to image processing. Specifically, we investigate video denoising and restoration, hyperspectral video, and background/foreground separation. Finally, we provide perspectives on possible future research directions and algorithmic frameworks that are suitable for these applications.

Accurate and robust visual object tracking is one of the most challenging and fundamental computer vision problems. It entails estimating the trajectory of the target in an image sequence, given only its initial location, and segmentation, or its rough approximation in the form of a bounding box. Discriminative Correlation Filters (DCFs) and deep Siamese Networks (SNs) have emerged as dominating tracking paradigms, which have led to significant progress. Following the rapid evolution of visual object tracking in the last decade, this survey presents a systematic and thorough review of more than 90 DCFs and Siamese trackers, based on results in nine tracking benchmarks. First, we present the background theory of both the DCF and Siamese tracking core formulations. Then, we distinguish and comprehensively review the shared as well as specific open research challenges in both these tracking paradigms. Furthermore, we thoroughly analyze the performance of DCF and Siamese trackers on nine benchmarks, covering different experimental aspects of visual tracking: datasets, evaluation metrics, performance, and speed comparisons. We finish the survey by presenting recommendations and suggestions for distinguished open challenges based on our analysis.