Dynamic tree-structured sparse RPCA via column subset selection for background modeling and foreground detection

Video analysis often begins with background subtraction, which consists of creation of a background model that allows distinguishing foreground pixels. Recent evaluation of background subtraction techniques demonstrated that there are still considerable challenges facing these methods. Processing per-pixel basis from the background is not only time-consuming but also can dramatically affect foreground region detection, if region cohesion and contiguity is not considered in the model. We present a new method in which we regard the image sequence to be made up of the sum of a low-rank background matrix and a dynamic tree-structured sparse matrix, and solve the decomposition using our approximated Robust Principal Component Analysis method extended to handle camera motion. Furthermore, to reduce the curse of dimensionality and scale, we introduce a low-rank background modeling via Column Subset Selection that reduces the order of complexity, decreases computation time, and eliminates the huge storage need for large videos

A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain

Detecting camouflaged moving foreground objects has been known to be difficult due to the similarity between the foreground objects and the background. Conventional methods cannot distinguish the foreground from background due to the small differences between them and thus suffer from under-detection of the camouflaged foreground objects. In this paper, we present a fusion framework to address this problem in the wavelet domain. We first show that the small differences in the image domain can be highlighted in certain wavelet bands. Then the likelihood of each wavelet coefficient being foreground is estimated by formulating foreground and background models for each wavelet band. The proposed framework effectively aggregates the likelihoods from different wavelet bands based on the characteristics of the wavelet transform. Experimental results demonstrated that the proposed method significantly outperformed existing methods in detecting camouflaged foreground objects. Specifically, the average F-measure for the proposed algorithm was 0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI

Online Structured Sparsity-based Moving Object Detection from Satellite Videos

Inspired by the recent developments in computer vision, low-rank and structured sparse matrix decomposition can be potentially be used for extract moving objects in satellite videos. This set of approaches seeks for rank minimization on the background that typically requires batch-based optimization over a sequence of frames, which causes delays in processing and limits their applications. To remedy this delay, we propose an Online Low-rank and Structured Sparse Decomposition (O-LSD). O-LSD reformulates the batch-based low-rank matrix decomposition with the structured sparse penalty to its equivalent frame-wise separable counterpart, which then defines a stochastic optimization problem for online subspace basis estimation. In order to promote online processing, O-LSD conducts the foreground and background separation and the subspace basis update alternatingly for every frame in a video. We also show the convergence of O-LSD theoretically. Experimental results on two satellite videos demonstrate the performance of O-LSD in term of accuracy and time consumption is comparable with the batch-based approaches with significantly reduced delay in processing

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