Low-Rank Models in Visual Analysis

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

Appendices