Sajid Javed

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.

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.

Background estimation and foreground segmentation are important steps in many high-level vision tasks. Many existing methods estimate background as a low-rank component and foreground as a sparse matrix without incorporating the structural information. Therefore, these algorithms exhibit degraded performance in the presence of dynamic backgrounds, photometric variations, jitter, shadows, and large occlusions. We observe that these backgrounds often span multiple manifolds. Therefore, constraints that ensure continuity on those manifolds will result in better background estimation. Hence, we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis (RPCA) framework. To that end, we compute a spatial and temporal graph for a given sequence using motion-aware correlation coefficient. The information captured by both graphs is utilized by estimating the proximity matrices using both the normalized Euclidean and geodesic distances. The low-rank component must be able to efficiently partition the spatiotemporal graphs using these Laplacian matrices. Embedded with the RPCA objective function, these Laplacian matrices constrain the background model to be spatially and temporally consistent, both on linear and nonlinear manifolds. The solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme. Experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state-of-the-art methods. The results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation.