Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "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 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 robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "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.Comment: To appear, IEEE Signal Processing Magazine, July 201

Robust Principal Component Analysis for Background Subtraction: Systematic Evaluation and Comparative Analysis

The analysis and understanding of video sequences is currently quite an active research field. Many applications such as video surveillance, optical motion capture or those of multimedia need to first be able to detect the objects moving in a scene filmed by a static camera. This requires the basic operation that consists of separating the moving objects called "foreground" from the static information called "background". Many background subtraction methods have been developed (Bouwmans et al. (2010); Bouwmans et al. (2008)). A recent survey (Bouwmans (2009)) shows that subspace learning models are well suited for background subtraction. Principal Component Analysis (PCA) has been used to model the background by significantly reducing the data's dimension. To perform PCA, different Robust Principal Components Analysis (RPCA) models have been recently developed in the literature. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. However, authors compare their algorithm only with the PCA (Oliver et al. (1999)) or another RPCA model. Furthermore, the evaluation is not made with the datasets and the measures currently used in the field of background subtraction. Considering all of this, we propose to evaluate RPCA models in the field of video-surveillance. Contributions of this chapter can be summarized as follows: 1) A survey regarding robust principal component analysis and 2) An evaluation and comparison on different video surveillance dataset

Discovering Local Binary Pattern Equation for Foreground Object Removal in Videos

Designing a novel Local Binary Pattern (LBP) process usually relies heavily on human experts' knowledge and experience in the area. Even experts are often left with tedious episodes of trial and error until they identify an optimal LBP for a particular dataset. To address this problem, we present a novel symbolic regression able to automatically discover LBP formulas to remove the moving parts of a scene by segmenting it into a background and a foreground. Experimental results conducted on real videos of outdoor urban scenes under various conditions show that the LBPs discovered by the proposed approach significantly outperform the previous state-of-the-art LBP descriptors both qualitatively and quantitatively. Our source code and data will be available online.Comment: arXiv admin note: substantial text overlap with arXiv:2104.0863

Human Pose Estimation from Monocular Images : a Comprehensive Survey

Human pose estimation refers to the estimation of the location of body parts and how they are connected in an image. Human pose estimation from monocular images has wide applications (e.g., image indexing). Several surveys on human pose estimation can be found in the literature, but they focus on a certain category; for example, model-based approaches or human motion analysis, etc. As far as we know, an overall review of this problem domain has yet to be provided. Furthermore, recent advancements based on deep learning have brought novel algorithms for this problem. In this paper, a comprehensive survey of human pose estimation from monocular images is carried out including milestone works and recent advancements. Based on one standard pipeline for the solution of computer vision problems, this survey splits the problema into several modules: feature extraction and description, human body models, and modelin methods. Problem modeling methods are approached based on two means of categorization in this survey. One way to categorize includes top-down and bottom-up methods, and another way includes generative and discriminative methods. Considering the fact that one direct application of human pose estimation is to provide initialization for automatic video surveillance, there are additional sections for motion-related methods in all modules: motion features, motion models, and motion-based methods. Finally, the paper also collects 26 publicly available data sets for validation and provides error measurement methods that are frequently used

Time-varying Signals Recovery via Graph Neural Networks

The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.Comment: Published in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2023, Greec

Tutorial on Evaluation of Background Subtraction Algorithms

The tutorial focused on the BGSLibrary (https://github.com/andrewssobral/bgslibrary) and the CDnet 2014 dataset (http://www.changedetection.net), and answered three questions: how to install the BGSLibrary? How to add your own code in the BGSLibrary? How to use the CDnet 2014 dataset and its metrics