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Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

Machine Learning · Computer Science 2011-01-04 Huan Xu , Constantine Caramanis , Sujay Sanghavi

The singular value decomposition (SVD) is a crucial tool in machine learning and statistical data analysis. However, it is highly susceptible to outliers in the data matrix. Existing robust SVD algorithms often sacrifice speed for…

Machine Learning · Statistics 2024-02-16 Sangil Han , Kyoowon Kim , Sungkyu Jung

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…

Machine Learning · Statistics 2021-04-08 Long Feng , Junhui Wang

Moving object detection is critical for automated video analysis in many vision-related tasks, such as surveillance tracking, video compression coding, etc. Robust Principal Component Analysis (RPCA), as one of the most popular moving…

Computer Vision and Pattern Recognition · Computer Science 2020-06-16 Zerui Shao , Yifei Pu , Jiliu Zhou , Bihan Wen , Yi Zhang

Background foreground separation (BFS) is a popular computer vision problem where dynamic foreground objects are separated from the static background of a scene. Typically, this is performed using consumer cameras because of their low cost,…

Image and Video Processing · Electrical Eng. & Systems 2021-08-16 Spencer Markowitz , Corey Snyder , Yonina C. Eldar , Minh N. Do

In the evolving landscape of video enhancement and editing methodologies, a majority of deep learning techniques often rely on extensive datasets of observed input and ground truth sequence pairs for optimal performance. Such reliance often…

Computer Vision and Pattern Recognition · Computer Science 2024-12-10 Gaurav Shrivastava , Ser-Nam Lim , Abhinav Shrivastava

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

Machine Learning · Computer Science 2015-08-03 Ohad Shamir

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern…

Machine Learning · Computer Science 2018-04-17 Shuai Zheng , Chris Ding , Feiping Nie

In video analysis, background models have many applications such as background/foreground separation, change detection, anomaly detection, tracking, and more. However, while learning such a model in a video captured by a static camera is a…

Computer Vision and Pattern Recognition · Computer Science 2022-09-19 Guy Erez , Ron Shapira Weber , Oren Freifeld

Moving target detection is a challenging computer vision task aimed at generating accurate segmentation maps in diverse in-the-wild color videos captured by static cameras. If backgrounds and targets can be simultaneously extracted and…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Liyang Wang , Shiqian Wu , Shun Fang , Qile Zhu , Jiaxin Wu , Sos Again

The t-SVD based Tensor Robust Principal Component Analysis (TRPCA) decomposes low rank multi-linear signal corrupted by gross errors into low multi-rank and sparse component by simultaneously minimizing tensor nuclear norm and l 1 norm. But…

Computer Vision and Pattern Recognition · Computer Science 2017-07-11 M. Baburaj , Sudhish N. George

Sparse decomposition has been widely used for different applications, such as source separation, image classification, image denoising and more. This paper presents a new algorithm for segmentation of an image into background and foreground…

Computer Vision and Pattern Recognition · Computer Science 2016-07-28 Shervin Minaee , Yao Wang

In the recent work of Candes et al, the problem of recovering low rank matrix corrupted by i.i.d. sparse outliers is studied and a very elegant solution, principal component pursuit, is proposed. It is motivated as a tool for video…

Computer Vision and Pattern Recognition · Computer Science 2015-03-17 Chenlu Qiu , Namrata Vaswani

This paper considers how to separate text and/or graphics from smooth background in screen content and mixed document images and proposes two approaches to perform this segmentation task. The proposed methods make use of the fact that the…

Computer Vision and Pattern Recognition · Computer Science 2016-07-12 Shervin Minaee , Yao Wang

We propose an algorithm for separating the foreground (mainly text and line graphics) from the smoothly varying background in screen content images. The proposed method is designed based on the assumption that the background part of the…

Computer Vision and Pattern Recognition · Computer Science 2015-02-20 Shervin Minaee , Yao Wang

With the advancement of deep learning-driven video editing technology, security risks have emerged. Malicious video tampering can lead to public misunderstanding, property losses, and legal disputes. Currently, detection methods are mostly…

Computer Vision and Pattern Recognition · Computer Science 2024-09-06 Pengfei Pei

Video segmentation consists of a frame-by-frame selection process of meaningful areas related to foreground moving objects. Some applications include traffic monitoring, human tracking, action recognition, efficient video surveillance, and…

Computer Vision and Pattern Recognition · Computer Science 2022-12-22 Daniel F. S. Santos , Rafael G. Pires , Danilo Colombo , João P. Papa

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Numerical Analysis · Mathematics 2021-02-02 Ningyu Sha , Lei Shi , Ming Yan

This paper introduces an unsupervised framework to extract semantically rich features for video representation. Inspired by how the human visual system groups objects based on motion cues, we propose a deep convolutional neural network that…

Computer Vision and Pattern Recognition · Computer Science 2017-07-18 Xunyu Lin , Victor Campos , Xavier Giro-i-Nieto , Jordi Torres , Cristian Canton Ferrer

Although it has been widely discussed in video surveillance, background subtraction is still an open problem in the context of complex scenarios, e.g., dynamic backgrounds, illumination variations, and indistinct foreground objects. To…

Computer Vision and Pattern Recognition · Computer Science 2015-02-03 Liang Lin , Yuanlu Xu , Xiaodan Liang , Jianhuang Lai