Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable non-convex approach, coined Learned Robust Matrix Completion (LRMC), for large-scale RMC problems. LRMC enjoys low computational complexity with linear convergence. Motivated by the proposed theorem, the free parameters of LRMC can be effectively learned via deep unfolding to achieve optimum performance. Furthermore, this paper proposes a flexible feedforward-recurrent-mixed neural network framework that extends deep unfolding from fix-number iterations to infinite iterations. The superior empirical performance of LRMC is verified with extensive experiments against state-of-the-art on synthetic datasets and real applications, including video background subtraction, ultrasound imaging, face modeling, and cloud removal from satellite imagery.
Background subtraction refers to extracting the foreground from an observed video, and is the fundamental problem of various applications. There are two kinds of popular methods to deal with background separation, namely, robust principal component analysis (RPCA) and low-rank matrix factorization (LRMF). Nevertheless, the drawback of RPCA requires tuning penalty parameter to attain an ideal result. Compared with RPCA, the ℓ1 -norm based LRMF does not involve extra parameters tuning, but it is challenging to optimize the ℓ1 -norm based minimization because of the nonsmooth ℓ1 -norm. In addition, it becomes time-consuming to find the optimal solution. In this work, we propose to employ smooth ℓ1,ϵ -norm, an approximation of ℓ1 -norm, to tackle background subtraction. Thus, the proposed model inherits the superiority of LRMF and even becomes tractable. Then the resultant optimization problem is solved by alternating minimization and gradient descent where the step-size of the gradient descent is adaptively updated via backtracking line searching approach. The proposed method is proved to be locally convergent. Experimental results on synthetic and real-world data demonstrate that our method outperforms the state-of-the-art algorithms in terms of reconstruction loss, computational speed and hardware performance.
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.
Foreground-background segmentation has been an active research area over the years. However, conventional models fail to produce accurate results when challenged with the videos of challenging illumination conditions. In this paper, we present a robust model that allows accurately extracting the foreground even in exceptionally dark or bright scenes and in continuously varying illumination in a video sequence. This is accomplished by a triple multi-task generative adversarial network (TMT-GAN) that effectively models the semantic relationship between the dark and bright images and performs binary segmentation end-to-end. Our contribution is twofold: first, we show that by jointly optimizing the GAN loss and the segmentation loss, our network simultaneously learns both tasks that mutually benefit each other. Second, fusing features of images with varying illumination into the segmentation branch vastly improve the performance of the network. Comparative evaluations on highly challenging real and synthetic benchmark datasets (ESI and SABS) demonstrate the robustness of TMT-GAN and its superiority over state-of-the-art approaches.
In video analysis, background models have many applications such as background/foreground separation, change detection, anomaly detection, tracking, and more. However, while learning such a model in a video captured by a static camera is a fairly-solved task, in the case of a Moving-camera Background Model (MCBM), the success has been far more modest due to algorithmic and scalability challenges that arise due to the camera motion. Thus, existing MCBMs are limited in their scope and their supported camera-motion types. These hurdles also impeded the employment, in this unsupervised task, of end-to-end solutions based on deep learning (DL). Moreover, existing MCBMs usually model the background either on the domain of a typically-large panoramic image or in an online fashion. Unfortunately, the former creates several problems, including poor scalability, while the latter prevents the recognition and leveraging of cases where the camera revisits previously-seen parts of the scene. This paper proposes a new method, called DeepMCBM, that eliminates all the aforementioned issues and achieves state-of-the-art results. Concretely, first we identify the difficulties associated with joint alignment of video frames in general and in a DL setting in particular. Next, we propose a new strategy for joint alignment that lets us use a spatial transformer net with neither a regularization nor any form of specialized (and non-differentiable) initialization. Coupled with an autoencoder conditioned on unwarped robust central moments (obtained from the joint alignment), this yields an end-to-end regularization-free MCBM that supports a broad range of camera motions and scales gracefully. We demonstrate DeepMCBM's utility on a variety of videos, including ones beyond the scope of other methods. Our code is available at https://github.com/BGU-CS-VIL/DeepMCBM .
Even after decades of research, dynamic scene background reconstruction and foreground object segmentation are still considered as open problems due various challenges such as illumination changes, camera movements, or background noise caused by air turbulence or moving trees. We propose in this paper to model the background of a frame sequence as a low dimensional manifold using an autoencoder and compare the reconstructed background provided by this autoencoder with the original image to compute the foreground/background segmentation masks. The main novelty of the proposed model is that the autoencoder is also trained to predict the background noise, which allows to compute for each frame a pixel-dependent threshold to perform the foreground segmentation. Although the proposed model does not use any temporal or motion information, it exceeds the state of the art for unsupervised background subtraction on the CDnet 2014 and LASIESTA datasets, with a significant improvement on videos where the camera is moving. It is also able to perform background reconstruction on some non-video image datasets.
The robust tensor completion (RTC) problem, which aims to reconstruct a low-rank tensor from partially observed tensor contaminated by a sparse tensor, has received increasing attention. In this paper, by leveraging the superior expression of the fully-connected tensor network (FCTN) decomposition, we propose a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{c}$onvex optimization model (RC-FCTN) for the RTC problem. Then, we rigorously establish the exact recovery guarantee for the RC-FCTN. For solving the constrained optimization model RC-FCTN, we develop an alternating direction method of multipliers (ADMM)-based algorithm, which enjoys the global convergence guarantee. Moreover, we suggest a $\textbf{FCTN}$-based $\textbf{r}$obust $\textbf{n}$on$\textbf{c}$onvex optimization model (RNC-FCTN) for the RTC problem. A proximal alternating minimization (PAM)-based algorithm is developed to solve the proposed RNC-FCTN. Meanwhile, we theoretically derive the convergence of the PAM-based algorithm. Comprehensive numerical experiments in several applications, such as video completion and video background subtraction, demonstrate that proposed methods are superior to several state-of-the-art methods.
We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm, coined Robust Tensor CUR (RTCUR), for large-scale TRPCA problems. RTCUR considers a framework of alternating projections and utilizes the recently developed tensor Fiber CUR decomposition to dramatically lower the computational complexity. The performance advantage of RTCUR is empirically verified against the state-of-the-arts on the synthetic datasets and is further demonstrated on the real-world application such as color video background subtraction.
Background modeling and subtraction is a promising research area with a variety of applications for video surveillance. Recent years have witnessed a proliferation of effective learning-based deep neural networks in this area. However, the techniques have only provided limited descriptions of scenes' properties while requiring heavy computations, as their single-valued mapping functions are learned to approximate the temporal conditional averages of observed target backgrounds and foregrounds. On the other hand, statistical learning in imagery domains has been a prevalent approach with high adaptation to dynamic context transformation, notably using Gaussian Mixture Models (GMM) with its generalization capabilities. By leveraging both, we propose a novel method called CDN-MEDAL-net for background modeling and subtraction with two convolutional neural networks. The first architecture, CDN-GM, is grounded on an unsupervised GMM statistical learning strategy to describe observed scenes' salient features. The second one, MEDAL-net, implements a light-weighted pipeline of online video background subtraction. Our two-stage architecture is small, but it is very effective with rapid convergence to representations of intricate motion patterns. Our experiments show that the proposed approach is not only capable of effectively extracting regions of moving objects in unseen cases, but it is also very efficient.
In this paper, we consider the compressed video background subtraction problem that separates the background and foreground of a video from its compressed measurements. The background of a video usually lies in a low dimensional space and the foreground is usually sparse. More importantly, each video frame is a natural image that has textural patterns. By exploiting these properties, we develop a message passing algorithm termed offline denoising-based turbo message passing (DTMP). We show that these structural properties can be efficiently handled by the existing denoising techniques under the turbo message passing framework. We further extend the DTMP algorithm to the online scenario where the video data is collected in an online manner. The extension is based on the similarity/continuity between adjacent video frames. We adopt the optical flow method to refine the estimation of the foreground. We also adopt the sliding window based background estimation to reduce complexity. By exploiting the Gaussianity of messages, we develop the state evolution to characterize the per-iteration performance of offline and online DTMP. Comparing to the existing algorithms, DTMP can work at much lower compression rates, and can subtract the background successfully with a lower mean squared error and better visual quality for both offline and online compressed video background subtraction.
A core challenge in background subtraction (BGS) is handling videos with sudden illumination changes in consecutive frames. In this paper, we tackle the problem from a data point-of-view using data augmentation. Our method performs data augmentation that not only creates endless data on the fly, but also features semantic transformations of illumination which enhance the generalisation of the model. It successfully simulates flashes and shadows by applying the Euclidean distance transform over a binary mask that is randomly generated. Such data allows us to effectively train an illumination-invariant deep learning model for BGS. Experimental results demonstrate the contribution of the synthetics in the ability of the models to perform BGS even when significant illumination changes take place. The source code of the project is made publicly available at https://github.com/dksakkos/illumination_augmentation.
Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.
Conventional neural networks show a powerful framework for background subtraction in video acquired by static cameras. Indeed, the well-known SOBS method and its variants based on neural networks were the leader methods on the largescale CDnet 2012 dataset during a long time. Recently, convolutional neural networks which belong to deep learning methods were employed with success for background initialization, foreground detection and deep learned features. Currently, the top current background subtraction methods in CDnet 2014 are based on deep neural networks with a large gap of performance in comparison on the conventional unsupervised approaches based on multi-features or multi-cues strategies. Furthermore, a huge amount of papers was published since 2016 when Braham and Van Droogenbroeck published their first work on CNN applied to background subtraction providing a regular gain of performance. In this context, we provide the first review of deep neural network concepts in background subtraction for novices and experts in order to analyze this success and to provide further directions. For this, we first surveyed the methods used background initialization, background subtraction and deep learned features. Then, we discuss the adequacy of deep neural networks for background subtraction. Finally, experimental results are presented on the CDnet 2014 dataset.
The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help distinguish signal from noise. One way to achieve this goal is to perform subspace learning to estimate a small set of latent features that capture the majority of the variance in the original data. Most existing subspace learning models, such as PCA, assume that the data can be fully represented by its embedding in one or more latent subspaces. However, in this work, we argue that this assumption is not suitable for many high-dimensional datasets; often only some variables can easily be projected to a low-dimensional space. We propose a hybrid dimensionality reduction technique in which some features are mapped to a low-dimensional subspace while others remain in the original space. Our model leads to more accurate estimation of the latent space and lower reconstruction error. We present a simple optimization procedure for the resulting biconvex problem and show synthetic data results that demonstrate the advantages of our approach over existing methods. Finally, we demonstrate the effectiveness of this method for extracting meaningful features from both gene expression and video background subtraction datasets.
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear dynamical model. Our algorithm, based on recent theoretical results for $\ell_1$-$\ell_1$ minimization, is recursive and computes the number of measurements to be taken at each time on-the-fly. As an example, we apply the algorithm to compressive video background subtraction, a problem that can be stated as follows: given a set of measurements of a sequence of images with a static background, simultaneously reconstruct each image while separating its foreground from the background. The performance of our method is illustrated on sequences of real images: we observe that it allows a dramatic reduction in the number of measurements with respect to state-of-the-art compressive background subtraction schemes.
Security concerns has been kept on increasing, so it is important for everyone to keep their property safe from thefts and destruction. So the need for surveillance techniques are also increasing. The system has been developed to detect the motion in a video. A system has been developed for real time applications by using the techniques of background subtraction and frame differencing. In this system, motion is detected from the webcam or from the real time video. Background subtraction and frames differencing method has been used to detect the moving target. In background subtraction method, current frame is subtracted from the referenced frame and then the threshold is applied. If the difference is greater than the threshold then it is considered as the pixel from the moving object, otherwise it is considered as background pixel. Similarly, two frames difference method takes difference between two continuous frames. Then that resultant difference frame is thresholded and the amount of difference pixels is calculated.