scholarly journals Background modeling from video sequences via online motion-aware RPCA

2021 ◽  
pp. 29-29
Author(s):  
Xu Weiyao ◽  
Xia Ting ◽  
Jing Changqiang
Keyword(s):  
Principal Component ◽  
Background Modeling ◽  
Low Rank ◽  
Video Frame ◽  
Robust Principal Component Analysis ◽  
Online Application ◽  
Rank Matrix ◽  
Computer Vision Applications ◽  
Low Rank Matrix ◽  
Nuclear Norm Regularization

Background modeling of video frame sequences is a prerequisite for computer vision applications. Robust principal component analysis(RPCA), which aims to recover low rank matrix in applications of data mining and machine learning, has shown improved background modeling performance. Unfortunately, The traditional RPCA method considers the batch recovery of low rank matrix of all samples, which leads to higher storage cost. This paper proposes a novel online motion-aware RPCA algorithm, named OM-RPCAT, which adopt truncated nuclear norm regularization as an approximation method for of low rank constraint. And then, Two methods are employed to obtain the motion estimation matrix, the optical flow and the frame selection, which are merged into the data items to separate the foreground and background. Finally, an efficient alternating optimization algorithm is designed in an online manner. Experimental evaluations of challenging sequences demonstrate promising results over state-of-the-art methods in online application.

scholarly journals A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
E. Zhu ◽  
M. Xu ◽  
D. Pi
Keyword(s):  
Principal Component Analysis ◽  
Principal Component ◽  
Component Analysis ◽  
Low Rank ◽  
Robust Principal Component Analysis ◽  
Approximation Function ◽  
Rank Matrix ◽  
Rank Approximation ◽  
Low Rank Matrix ◽  
Novel Model

Noise exhibits low rank or no sparsity in the low-rank matrix recovery, and the nuclear norm is not an accurate rank approximation of low-rank matrix. In the present study, to solve the mentioned problem, a novel nonconvex approximation function of the low-rank matrix was proposed. Subsequently, based on the nonconvex rank approximation function, a novel model of robust principal component analysis was proposed. Such model was solved with the alternating direction method, and its convergence was verified theoretically. Subsequently, the background separation experiments were performed on the Wallflower and SBMnet datasets. Furthermore, the effectiveness of the novel model was verified by numerical experiments.

A New Analysis of the Iterative Threshold Algorithm for RPCA by Primal-Dual Method

2014 ◽  
Vol 989-994 ◽  
pp. 2462-2466 ◽  
Author(s):  
Ru Ya Fan ◽  
Hong Xia Wang ◽  
Hui Zhang
Keyword(s):  
Gradient Method ◽  
Principal Component ◽  
Low Rank ◽  
Dual Method ◽  
Theoretical Derivation ◽  
Threshold Algorithm ◽  
Rank Matrix ◽  
Primal Dual ◽  
Low Rank Matrix ◽  
Iterative Threshold

This paper studies the iterative threshold algorithm (ITA) for solving the Robust Principal Component Analysis (RPCA) problems, which is to recover a low-rank matrix with a fraction of its entries being arbitrarily corrupted. By utilizing the primal-dual method, we analyze the ITA in a new way and prove that the ITA is essentially equivalent to gradient method applying to a dual problem. In the original ITA, it is hard to choose the parameters and hence it converges very slowly. Now, based on the new insight, existing techniques of the gradient method can be used to accelerate the ITA. We combine the theoretical derivation with the numerical simulation experiments to give an empirical guidance to set the parameters. As illustration, background modeling problem is solved by the ITA with optimal parameters.

Research on Background Modeling Based on Low-Rank Matrix Recovery

2014 ◽  
Vol 635-637 ◽  
pp. 1056-1059 ◽  
Author(s):  
Bao Yan Wang ◽  
Xin Gang Wang
Keyword(s):  
Sparse Matrix ◽  
Background Modeling ◽  
Low Rank ◽  
Complex Scene ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Training Samples ◽  
The Individual ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

Key and difficult points of background subtraction method lie in looking for an ideal background modeling under complex scene. Stacking the individual frames as columns of a big matrix, background parts can be viewed as a low-rank background matrix because of large similarity among individual frames, yet foreground parts can be viewed as a sparse matrix as foreground parts play a small role in individual frames. Thus the process of video background modeling is in fact a process of low-rank matrix recovery. Background modeling based on low-rank matrix recovery can separate foreground images from background at the same time without pre-training samples, besides, the approach is robust to illumination changes. However, there exist some shortcomings in background modeling based on low-rank matrix recovery by analyzing numerical experiments, which is developed from three aspects.

scholarly journals Robust Principal Component Thermography for Defect Detection in Composites

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2682
Author(s):  
Samira Ebrahimi ◽  
Julien Fleuret ◽  
Matthieu Klein ◽  
Louis-Daniel Théroux ◽  
Marc Georges ◽  
...  
Keyword(s):  
Defect Detection ◽  
Sparse Matrix ◽  
Research Effort ◽  
Principal Component ◽  
Low Rank ◽  
Computational Time ◽  
Rank Matrix ◽  
Detection Capabilities ◽  
Signal Processing Methods ◽  
Low Rank Matrix

Pulsed Thermography (PT) data are usually affected by noise and as such most of the research effort in the last few years has been directed towards the development of advanced signal processing methods to improve defect detection. Among the numerous techniques that have been proposed, principal component thermography (PCT)—based on principal component analysis (PCA)—is one of the most effective in terms of defect contrast enhancement and data compression. However, it is well-known that PCA can be significantly affected in the presence of corrupted data (e.g., noise and outliers). Robust PCA (RPCA) has been recently proposed as an alternative statistical method that handles noisy data more properly by decomposing the input data into a low-rank matrix and a sparse matrix. We propose to process PT data by RPCA instead of PCA in order to improve defect detectability. The performance of the resulting approach, Robust Principal Component Thermography (RPCT)—based on RPCA, was evaluated with respect to PCT—based on PCA, using a CFRP sample containing artificially produced defects. We compared results quantitatively based on two metrics, Contrast-to-Noise Ratio (CNR), for defect detection capabilities, and the Jaccard similarity coefficient, for defect segmentation potential. CNR results were on average 40% higher for RPCT than for PCT, and the Jaccard index was slightly higher for RPCT (0.7395) than for PCT (0.7010). In terms of computational time, however, PCT was 11.5 times faster than RPCT. Further investigations are needed to assess RPCT performance on a wider range of materials and to optimize computational time.

scholarly journals LOW-RANK MATRIX DECOMPOSITION WITH SUPERPIXEL-BASED STRUCTURED SPARSE REGULARIZATION FOR MOVING OBJECT DETECTION IN SATELLITE VIDEOS

2020 ◽  
Vol V-2-2020 ◽  
pp. 941-948
Author(s):  
J. Zhang ◽  
X. Jia ◽  
J. Hu
Keyword(s):  
Video Processing ◽  
Moving Objects ◽  
Matrix Decomposition ◽  
Moving Object ◽  
Low Rank ◽  
Machine Learning Techniques ◽  
Video Frame ◽  
Significant Saving ◽  
Rank Matrix ◽  
Low Rank Matrix

Abstract. With new accessibility to satellite videos, retrieving the dynamic information of moving objects over a vast territory becomes possible with the development of advanced video processing and machine learning techniques. Detecting moving objects can be based on the structures of both background and foreground of a satellite video, and the background is assumed to lay in a low dimensional subspace. As the moving objects in satellite videos are groups of neighbouring pixels other than isolated pixels, Low-rank and Structured Sparse Decomposition (LSD) with structured sparsity regularization on the foreground can suppress the false alarms caused by isolated outliers. However, in LSD, the groups of neighbouring pixels are extracted by a fixed sliding window over each video frame, which ignores the coherence on the appearance of a moving object. For example, a moving object can be in an irregular shape and arbitrary orientation. In this paper, we argue that the spatial groups on the foreground can be defined using the concept of superpixels, where each superpixel is formed by a group of spatially connected similar pixels obtained from over-segmentation. We conduct low-rank matrix decomposition at superpixel level, which is named as Superpixel-based LSD (S-LSD). To handle the variation in moving objects, we combine the superpixels at a range of scales in the superpixel-based spatial regularization on the foreground. With the reduction in the number of spatial groups, S-LSD presents reduced computation complexity. The results on two satellite videos show a satisfactory performance with a significant saving in processing time when the proposed S-LSD approach is applied.

scholarly journals New Robust Principal Component Analysis for Joint Image Alignment and Recovery via Affine Transformations, Frobenius and L2,1 Norms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Habte Tadesse Likassa
Keyword(s):  
Principal Component ◽  
Correlated Data ◽  
Image Alignment ◽  
Low Rank ◽  
Affine Transformations ◽  
Rank Matrix ◽  
Successful Approach ◽  
Potential Impact ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L2,1 norms. To attain this, affine transformations and Frobenius and L2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works.

Principal Component Pursuit with Weighted Nuclear Norm

2014 ◽  
Vol 513-517 ◽  
pp. 1722-1726
Author(s):  
Qing Shan You ◽  
Qun Wan
Keyword(s):  
Sparse Matrix ◽  
Principal Component ◽  
Low Rank ◽  
Linear Measurements ◽  
Alternating Direction ◽  
Rank Matrix ◽  
Small Set ◽  
Principal Component Pursuit ◽  
Low Dimensional ◽  
Low Rank Matrix

Principal Component Pursuit (PCP) recovers low-dimensional structures from a small set of linear measurements, such as low rank matrix and sparse matrix. Pervious works mainly focus on exact recovery without additional noise. However, in many applications the observed measurements are corrupted by an additional white Gaussian noise (AWGN). In this paper, we model the recovered matrix the sum a low-rank matrix, a sparse matrix and an AWGN. We propose a weighted PCP for the recovery matrix, which is solved by alternating direction method. Numerical results show that the reconstructions performance of weighted PCP outperforms the classical PCP in term of accuracy.

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