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

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.

• 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