Although low-rank and sparse decomposition based methods have been successfully applied to the problem of moving object detection using structured sparsity-inducing norms, they are still vulnerable to significant illumination changes that arise in certain applications. We are interested in moving object detection in applications involving time-lapse image sequences for which current methods mistakenly group moving objects and illumination changes into foreground. Our method relies on the multilinear (tensor) data low-rank and sparse decomposition framework to address the weaknesses of existing methods. The key to our proposed method is to create first a set of prior maps that can characterize the changes in the image sequence due to illumination. We show that they can be detected by a k-support norm. To deal with concurrent, two types of changes, we employ two regularization terms, one for detecting moving objects and the other for accounting for illumination changes, in the tensor low-rank and sparse decomposition formulation. Through comprehensive experiments using challenging datasets, we show that our method demonstrates a remarkable ability to detect moving objects under discontinuous change in illumination, and outperforms the state-of-the-art solutions to this challenging problem.
The second group of methods used the additional prior knowledge on the spatial continuity of objects to constrain sparse matrix @math and improve the detection accuracy @cite_34 @cite_6 . Using spatial continuity (e.g., @math -norm in @cite_34 ) to enforce the block-sparsity of the foreground, results become more stable than conventional RPCA in the presence of illumination changes. However, it remains a challenge to handle moving shadows or significant changes in illumination. Furthermore, the position of an object in a time-lapse image sequence is discontinuous from one image to another so that the continuity assumption is invalid as a way to separate moving objects and changes in illumination.
@cite_34 @cite_6
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Low-rank and sparse representation based methods have attracted wide attention in background subtraction and moving object detection, where moving objects in the scene are modeled as pixel-wise sparse outliers. Since in real scenarios moving objects are also structurally sparse, recently researchers have attempted to extract moving objects using structured sparse outliers. Although existing methods with structured sparsity-inducing norms produce promising results, they are still vulnerable to various illumination changes that frequently occur in real environments, specifically for time-lapse image sequences where assumptions about sparsity between images such as group sparsity are not valid. In this paper, we first introduce a prior map obtained by illumination invariant representation of images. Next, we propose a low-rank and invariant sparse decomposition using the prior map to detect moving objects under significant illumination changes. Experiments on challenging benchmark datasets demonstrate the superior performance of our proposed method under complex illumination changes. Abstract Foreground detection is the first step in video surveillance system to detect moving objects. Recent research on subspace estimation by sparse representation and rank minimization represents a nice framework to separate moving objects from the background. Robust Principal Component Analysis (RPCA) solved via Principal Component Pursuit decomposes a data matrix A in two components such that A = L + S , where L is a low-rank matrix and S is a sparse noise matrix. 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. To date, many efforts have been made to develop Principal Component Pursuit (PCP) methods with reduced computational cost that perform visually well in foreground detection. However, no current algorithm seems to emerge and to be able to simultaneously address all the key challenges that accompany real-world videos. This is due, in part, to the absence of a rigorous quantitative evaluation with synthetic and realistic large-scale dataset with accurate ground truth providing a balanced coverage of the range of challenges present in the real world. In this context, this work aims to initiate a rigorous and comprehensive review of RPCA-PCP based methods for testing and ranking existing algorithms for foreground detection. For this, we first review the recent developments in the field of RPCA solved via Principal Component Pursuit. Furthermore, we investigate how these methods are solved and if incremental algorithms and real-time implementations can be achieved for foreground detection. Finally, experimental results on the Background Models Challenge (BMC) dataset which contains different synthetic and real datasets show the comparative performance of these recent methods. 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 ( (2010); (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 ( (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 datasets Accurate detection of moving objects is an important precursor to stable tracking or recognition. In this paper, we present an object detection scheme that has three innovations over existing approaches. First, the model of the intensities of image pixels as independent random variables is challenged and it is asserted that useful correlation exists in intensities of spatially proximal pixels. This correlation is exploited to sustain high levels of detection accuracy in the presence of dynamic backgrounds. By using a nonparametric density estimation method over a joint domain-range representation of image pixels, multimodal spatial uncertainties and complex dependencies between the domain (location) and range (color) are directly modeled. We propose a model of the background as a single probability density. Second, temporal persistence is proposed as a detection criterion. Unlike previous approaches to object detection which detect objects by building adaptive models of the background, the foregrounds modeled to augment the detection of objects (without explicit tracking) since objects detected in the preceding frame contain substantial evidence for detection in the current frame. Finally, the background and foreground models are used competitively in a MAP-MRF decision framework, stressing spatial context as a condition of detecting interesting objects and the posterior function is maximized efficiently by finding the minimum cut of a capacitated graph. Experimental validation of the proposed method is performed and presented on a diverse set of dynamic scenes.