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Low-Rank Models in Visual Analysis - 1st Edition - ISBN: 9780128127315, 9780128127322

Low-Rank Models in Visual Analysis

1st Edition

Theories, Algorithms, and Applications

Authors: Zhouchen Lin Hongyang Zhang
eBook ISBN: 9780128127322
Paperback ISBN: 9780128127315
Imprint: Academic Press
Published Date: 5th June 2017
Page Count: 260
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Table of Contents

1 Introduction

2 Linear Models

2.1 Single Subspace Models

2.2 Multi-Subspace Models

2.3 Theoretical Analysis

2.3.1 Exact Recovery

2.3.2 Closed-form Solutions

2.3.3 Block-diagonal Structure

3 Nonlinear Models

3.1 Kernel Methods

3.2 Laplacian and Hyper-Laplacian Methods

3.3 Locally Linear Representation

3.4 Transformation Invariant Clustering

4 Optimization Algorithms

4.1 Convex Algorithms

4.1.1 Accelerated Proximal Gradient

4.1.2 Frank-Wolfe Algorithm

4.1.3 Alternating Direction Method of Multipliers

4.1.4 Linearized Alternating Direction Method of Multipliers

4.1.5 Proximal Linearized Alternating Direction Method of Multiplier

4.2 Nonconvex Optimization Algorithms

4.2.1 Generalized Singular Value Thresholding

4.2.2 Truncated Nuclear Norm Minimization

4.2.3 Iteratively Reweighted Least Squares

4.2.4 Factorization Method

4.2.5 Iteratively Reweighted Nuclear Norm Algorithm

4.3 Convergence Analysis

4.4 Randomized Algorithms

4.4.1 `1 Filtering Algorithm

4.4.2 `2;1 Filtering Algorithm

4.4.3 Randomized Algorithm for Modi_ed LRR

5 Representative Applications

5.1 Video Denoising

5.1.1 Implement Details

5.1.2 Experiments

5.2 Background Modeling

5.2.1 Implement Details

5.2.2 Experiments

5.3 Robust Alignment by Sparse and Low-Rank Decomposition

5.3.1 Implement Details

5.3.2 Experiments

5.4 Transform Invariant Low-rank Textures

5.4.1 Implement Details

5.5 Motion Segmentation

5.6 Image Segmentation

5.7 Image Saliency Detection

5.8 Partial-Duplicate Image Retrieval

5.8.1 Implement Details

5.8.2 Experiments

5.9 Image Tag Completion and Re_nement

5.9.1 Implement Details

5.9.2 Experiments

5.10 Other Applications

6 Conclusions



Low-Rank Models in Visual Analysis: Theories, Algorithms, and Applications presents the state-of-the-art on low-rank models and their application to visual analysis. It provides insight into the ideas behind the models and their algorithms, giving details of their formulation and deduction. The main applications included are video denoising, background modeling, image alignment and rectification, motion segmentation, image segmentation and image saliency detection. Readers will learn which Low-rank models are highly useful in practice (both linear and nonlinear models), how to solve low-rank models efficiently, and how to apply low-rank models to real problems.

Key Features

  • Presents a self-contained, up-to-date introduction that covers underlying theory, algorithms and the state-of-the-art in current applications
  • Provides a full and clear explanation of the theory behind the models
  • Includes detailed proofs in the appendices


Researchers and graduate students in computer vision


No. of pages:
© Academic Press 2017
5th June 2017
Academic Press
eBook ISBN:
Paperback ISBN:

Ratings and Reviews

About the Authors

Zhouchen Lin

Zhouchen Lin received the Ph.D. degree in applied mathematics from Peking University in 2000. He is currently a Professor at Key Laboratory of Machine Perception (MOE), School of Electronics Engineering and Computer Science, Peking University. His research areas include computer vision, image processing, machine learning, pattern recognition, and numerical optimization. He is an area chair of CVPR 2014/2016, ICCV 2015 and NIPS 2015 and a senior program committee member of AAAI 2016/2017 and IJCAI 2016. He is an associate editor of IEEE Trans. Pattern Analysis and Machine Intelligence and International J. Computer Vision. He is an IAPR fellow.

Affiliations and Expertise

Professor, Key Laboratory of Machine Perception (MOE), School of Electronics Engineering and Computer Science, Peking University

Hongyang Zhang

Hongyang Zhang received the Master’s degree in computer science from Peking University, Beijing, China in 2015. He is now a Ph.D. candidate in Machine Learning Department, School of Computer Science, Carnegie Mellon University, Pittsburgh, USA. His research areas include machine learning, statistics, and optimization.

Affiliations and Expertise

Ph.D. student, Carnegie Mellon University