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.
@cite_18: Object detection is a fundamental step for automated video analysis in many vision applications. Object detection in a video is usually performed by object detectors or background subtraction techniques. Often, an object detector requires manually labeled examples to train a binary classifier, while background subtraction needs a training sequence that contains no objects to build a background model. To automate the analysis, object detection without a separate training phase becomes a critical task. People have tried to tackle this task by using motion information. But existing motion-based methods are usually limited when coping with complex scenarios such as nonrigid motion and dynamic background. In this paper, we show that the above challenges can be addressed in a unified framework named DEtecting Contiguous Outliers in the LOw-rank Representation (DECOLOR). This formulation integrates object detection and background learning into a single process of optimization, which can be solved by an alternating algorithm efficiently. We explain the relations between DECOLOR and other sparsity-based methods. Experiments on both simulated data and real sequences demonstrate that DECOLOR outperforms the state-of-the-art approaches and it can work effectively on a wide range of complex scenarios.
@cite_14: We study the problem of online subspace learning in the context of sequential observations involving structured perturbations. In online subspace learning, the observations are an unknown mixture of two components presented to the model sequentially - the main effect which pertains to the subspace and a residual error term. If no additional requirement is imposed on the residual, it often corresponds to noise terms in the signal which were unaccounted for by the main effect. To remedy this, one may impose "structural" contiguity, which has the intended effect of leveraging the secondary terms as a covariate that helps the estimation of the subspace itself, instead of merely serving as a noise residual. We show that the corresponding online estimation procedure can be written as an approximate optimization process on a Grassmannian. We propose an efficient numerical solution, GOSUS, Grassmannian Online Subspace Updates with Structured-sparsity, for this problem. GOSUS is expressive enough in modeling both homogeneous perturbations of the subspace and structural contiguities of outliers, and after certain manipulations, solvable via an alternating direction method of multipliers (ADMM). We evaluate the empirical performance of this algorithm on two problems of interest: online background subtraction and online multiple face tracking, and demonstrate that it achieves competitive performance with the state-of-the-art in near real time.
@cite_26: We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of l∞-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when the groups are disjoint or embedded in a specific hierarchical structure, we address here the case of general overlapping groups. To this end, we show that the corresponding optimization problem is related to network flow optimization. More precisely, the proximal problem associated with the norm we consider is dual to a quadratic min-cost flow problem. We propose an efficient procedure which computes its solution exactly in polynomial time. Our algorithm scales up to millions of variables, and opens up a whole new range of applications for structured sparse models. We present several experiments on image and video data, demonstrating the applicability and scalability of our approach for various problems.
@cite_24: Background Subtraction (BS) is one of the key steps in video analysis. Many background models have been proposed and achieved promising performance on public data sets. However, due to challenges such as illumination change, dynamic background etc. the resulted foreground segmentation often consists of holes as well as background noise. In this regard, we consider generalized fused lasso regularization to quest for intact structured foregrounds. Together with certain assumptions about the background, such as the low-rank assumption or the sparse-composition assumption (depending on whether pure background frames are provided), we formulate BS as a matrix decomposition problem using regularization terms for both the foreground and background matrices. Moreover, under the proposed formulation, the two generally distinctive background assumptions can be solved in a unified manner. The optimization was carried out via applying the augmented Lagrange multiplier (ALM) method in such a way that a fast parametric-flow algorithm is used for updating the foreground matrix. Experimental results on several popular BS data sets demonstrate the advantage of the proposed model compared to state-of-the-arts.
@cite_19: Low rank and sparse representation based methods, which make few specific assumptions about the background, have recently attracted wide attention in background modeling. With these methods, moving objects in the scene are modeled as pixel-wised sparse outliers. However, in many practical scenarios, the distributions of these moving parts are not truly pixel-wised sparse but structurally sparse. Meanwhile a robust analysis mechanism is required to handle background regions or foreground movements with varying scales. Based on these two observations, we first introduce a class of structured sparsity-inducing norms to model moving objects in videos. In our approach, we regard the observed sequence as being constituted of two terms, a low-rank matrix (background) and a structured sparse outlier matrix (foreground). Next, in virtue of adaptive parameters for dynamic videos, we propose a saliency measurement to dynamically estimate the support of the foreground. Experiments on challenging well known data sets demonstrate that the proposed approach outperforms the state-of-the-art methods and works effectively on a wide range of complex videos.
@cite_12: Abstract Extracting moving objects from a video sequence and estimating the background of each individual image are fundamental issues in many practical applications such as visual surveillance, intelligent vehicle navigation, and traffic monitoring. Recently, some methods have been proposed to detect moving objects in a video via low-rank approximation and sparse outliers where the background is modeled with the computed low-rank component of the video and the foreground objects are detected as the sparse outliers in the low-rank approximation. Many of these existing methods work in a batch manner, preventing them from being applied in real time and long duration tasks. To address this issue, some online methods have been proposed; however, existing online methods fail to provide satisfactory results under challenging conditions such as dynamic background scene and noisy environments. In this paper, we present an online sequential framework, namely contiguous outliers representation via online low-rank approximation (COROLA), to detect moving objects and learn the background model at the same time. We also show that our model can detect moving objects with a moving camera. Our experimental evaluation uses simulated data and real public datasets to demonstrate the superior performance of COROLA to the existing batch and online methods in terms of both accuracy and efficiency.
@cite_17: Matrix factorization is a fundamental problem that is often encountered in many computer vision and machine learning tasks. In recent years, enhancing the robustness of matrix factorization methods has attracted much attention in the research community. To benefit from the strengths of full Bayesian treatment over point estimation, we propose here a full Bayesian approach to robust matrix factorization. For the generative process, the model parameters have conjugate priors and the likelihood (or noise model) takes the form of a Laplace mixture. For Bayesian inference, we devise an efficient sampling algorithm by exploiting a hierarchical view of the Laplace distribution. Besides the basic model, we also propose an extension which assumes that the outliers exhibit spatial or temporal proximity as encountered in many computer vision applications. The proposed methods give competitive experimental results when compared with several state-of-the-art methods on some benchmark image and video processing tasks.
The third group of methods also imposed the connectivity constraint on @math @cite_14 @cite_17 @cite_18 @cite_12 @cite_24 @cite_19 using other formulations than the second group. For example, Liu et al @cite_19 attempted to use a structured sparsity norm @cite_26 and a motion saliency map, to improve the accuracy of moving object segmentation under sudden illumination changes. However, this method still cannot handle shadows and severe illumination changes, especially in time-lapse sequences with independent object locations among the images in the sequence that change similarly to shadow and illumination. In general, although the low-rank framework is well-known to be robust against moderate illumination changes in frame-rate sequences, the existing methods are still not able to handle discontinuous change in illumination and shadow, especially in time-lapse sequences.