scholarly journals Panning and Jitter Invariant Incremental Principal Component Pursuit for Video Background Modeling

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Gustavo Chau ◽  
Paul Rodríguez
Keyword(s):  
Reference Frame ◽  
Matrix Method ◽  
Moving Objects ◽  
State Of The Art ◽  
Principal Component ◽  
Background Modeling ◽  
The State ◽  
Low Rank ◽  
Current Reference ◽  
Principal Component Pursuit

Video background modeling is an important preprocessing stage for various applications, and principal component pursuit (PCP) is among the state-of-the-art algorithms for this task. One of the main drawbacks of PCP is its sensitivity to jitter and camera movement. This problem has only been partially solved by a few methods devised for jitter or small transformations. However, such methods cannot handle the case of moving or panning cameras in an incremental fashion. In this paper, we greatly expand the results of our earlier work, in which we presented a novel, fully incremental PCP algorithm, named incPCP-PTI, which was able to cope with panning scenarios and jitter by continuously aligning the low-rank component to the current reference frame of the camera. To the best of our knowledge, incPCP-PTI is the first low-rank plus additive incremental matrix method capable of handling these scenarios in an incremental way. The results on synthetic videos and Moseg, DAVIS, and CDnet2014 datasets show that incPCP-PTI is able to maintain a good performance in the detection of moving objects even when panning and jitter are present in a video. Additionally, in most videos, incPCP-PTI obtains competitive or superior results compared to state-of-the-art batch methods.

Computing Robust Principal Components by A* Search

2018 ◽  
Vol 27 (07) ◽  
pp. 1860013 ◽  
Author(s):  
Swair Shah ◽  
Baokun He ◽  
Crystal Maung ◽  
Haim Schweitzer
Keyword(s):  
State Of The Art ◽  
Principal Component ◽  
Low Rank ◽  
A Algorithm ◽  
Running Time ◽  
Current State ◽  
Dimensionality Reduction Technique ◽  
Related Variant ◽  
Low Rank Representation ◽  
The Cost

Principal Component Analysis (PCA) is a classical dimensionality reduction technique that computes a low rank representation of the data. Recent studies have shown how to compute this low rank representation from most of the data, excluding a small amount of outlier data. We show how to convert this problem into graph search, and describe an algorithm that solves this problem optimally by applying a variant of the A* algorithm to search for the outliers. The results obtained by our algorithm are optimal in terms of accuracy, and are shown to be more accurate than results obtained by the current state-of-the- art algorithms which are shown not to be optimal. This comes at the cost of running time, which is typically slower than the current state of the art. We also describe a related variant of the A* algorithm that runs much faster than the optimal variant and produces a solution that is guaranteed to be near the optimal. This variant is shown experimentally to be more accurate than the current state-of-the-art and has a comparable running time.

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 Improving One-Class Collaborative Filtering via Ranking-Based Implicit Regularizer

2019 ◽  
Vol 33 ◽  
pp. 37-44 ◽  
Author(s):  
Jin Chen ◽  
Defu Lian ◽  
Kai Zheng
Keyword(s):  
Collaborative Filtering ◽  
State Of The Art ◽  
Ground Truth ◽  
The State ◽  
Low Rank ◽  
Model Parameters ◽  
Music Recommendation ◽  
Low Rank Approximation ◽  
The Arts ◽  
Rank Approximation

One-class collaborative filtering (OCCF) problems are vital in many applications of recommender systems, such as news and music recommendation, but suffers from sparsity issues and lacks negative examples. To address this problem, the state-of-the-arts assigned smaller weights to unobserved samples and performed low-rank approximation. However, the ground-truth ratings of unobserved samples are usually set to zero but ill-defined. In this paper, we propose a ranking-based implicit regularizer and provide a new general framework for OCCF, to avert the ground-truth ratings of unobserved samples. We then exploit it to regularize a ranking-based loss function and design efficient optimization algorithms to learn model parameters. Finally, we evaluate them on three realworld datasets. The results show that the proposed regularizer significantly improves ranking-based algorithms and that the proposed framework outperforms the state-of-the-art OCCF algorithms.

scholarly journals Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Qingshan You ◽  
Qun Wan ◽  
Haiwen Xu
Keyword(s):  
Sparse Matrix ◽  
Principal Component ◽  
Restricted Isometry Property ◽  
Low Rank ◽  
Linear Measurements ◽  
Matrix Recovery ◽  
Strongly Convex ◽  
Rank Matrix ◽  
Principal Component Pursuit ◽  
Low Rank Matrix Recovery

The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP_RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming.

scholarly journals Video Foreground Detection Algorithm Based on Fast Principal Component Pursuit and Motion Saliency

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Rui Chen ◽  
Ying Tong ◽  
Jie Yang ◽  
Minghu Wu
Keyword(s):  
Principal Component ◽  
Detection Algorithm ◽  
Low Rank ◽  
Foreground Detection ◽  
Dynamic Background ◽  
Foreground Region ◽  
Principal Component Pursuit ◽  
Small Targets ◽  
Background Motion ◽  
Motion Saliency

Aiming at the shortcoming of being unsuitable for dynamic background and high computational complexity of the existing RPCA- (robust principal component analysis-) based block-sparse moving object detection method, this paper proposes a two-stage foreground detection framework based on motion saliency for video sequence. At the first stage, the observed image sequence is regarded as the sum of a low-rank background matrix and a sparse outlier matrix, and then the decomposition is solved by the RPCA method via fast PCP (principal component pursuit). At the second stage, the sparse foreground blocks are obtained according to the spectral residuals and the spatial correlation of the foreground region. Finally, the block-sparse RPCA algorithm through fast PCP is used to estimate foreground areas dynamically and to reconstruct the foreground objects. Extensive experiments demonstrate that our method can exclude the interference of background motion and change, simultaneously improving the detection rate of small targets.

scholarly journals Simultaneously Low Rank and Group Sparse Decomposition for Rolling Bearing Fault Diagnosis

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5541
Author(s):  
Kai Zheng ◽  
Yin Bai ◽  
Jingfeng Xiong ◽  
Feng Tan ◽  
Dewei Yang ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
State Of The Art ◽  
Hankel Matrix ◽  
Rolling Bearing ◽  
The State ◽  
Low Rank ◽  
Sparse Decomposition ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
Value Decomposition

Singular value decomposition (SVD) methods have aroused wide concern to extract the periodic impulses for bearing fault diagnosis. The state-of-the-art SVD methods mainly focus on the low rank property of the Hankel matrix for the fault feature, which cannot achieve satisfied performance when the background noise is strong. Different to the existing low rank-based approaches, we proposed a simultaneously low rank and group sparse decomposition (SLRGSD) method for bearing fault diagnosis. The major contribution is that the simultaneously low rank and group sparse (SLRGS) property of the Hankel matrix for fault feature is first revealed to improve performance of the proposed method. Firstly, we exploit the SLRGS property of the Hankel matrix for the fault feature. On this basis, a regularization model is formulated to construct the new diagnostic framework. Furthermore, the incremental proximal algorithm is adopted to achieve a stationary solution. Finally, the effectiveness of the SLRGSD method for enhancing the fault feature are profoundly validated by the numerical analysis, the artificial bearing fault experiment and the wind turbine bearing fault experiment. Simulation and experimental results indicate that the SLRGSD method can obtain superior results of extracting the incipient fault feature in both performance and visual quality as compared with the state-of-the-art methods.

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