Graph Spectral Image Processing

Cover
Half-Title Page
Title Page
Copyright Page
Contents
Introduction to Graph Spectral Image Processing
	I.1. Introduction
	I.2. Graph definition
	I.3. Graph spectrum
	I.4. Graph variation operators
	I.5. Graph signal smoothness priors
	I.6. References
Part 1. Fundamentals of Graph Signal Processing
	Chapter 1. Graph Spectral Filtering
		1.1. Introduction
		1.2. Review: filtering of time-domain signals
		1.3. Filtering of graph signals
			1.3.1. Vertex domain filtering
			1.3.2. Spectral domain filtering
			1.3.3. Relationship between graph spectral filtering and classical filtering
		1.4. Edge-preserving smoothing of images as graph spectral filters
			1.4. Edge-preserving smoothing of images as graph spectral filters
			1.4.1. Early works
			1.4.2. Edge-preserving smoothing
		1.5. Multiple graph filters: graph filter banks
			1.5.1. Framework
			1.5.2. Perfect reconstruction condition
		1.6. Fast computation
			1.6.1. Subdivision
			1.6.3. Precomputing GFT
			1.6.4. Partial eigendecomposition
			1.6.5. Polynomial approximation
			1.6.6. Krylov subspace method
		1.7. Conclusion
		1.8. References
	Chapter 2. Graph Learning
		2.1. Introduction
		2.2. Literature review
			2.2.1. Statistical models
			2.2.2. Physically motivated models
		2.3. Graph learning: a signal representation perspective
			2.3.1. Models based on signal smoothness
			2.3.2. Models based on spectral filtering of graph signals
			2.3.3. Models based on causal dependencies on graphs
			2.3.4. Connections with the broader literature
		2.4. Applications of graph learning in image processing
		2.5. Concluding remarks and future directions
		2.6. References
	Chapter 3. Graph Neural Networks
		3.1. Introduction
		3.2. Spectral graph-convolutional layers
		3.3. Spatial graph-convolutional layers
		3.4. Concluding remarks
		3.5. References
Part 2. Imaging Applications of Graph Signal Processing
	Chapter 4. Graph Spectral Image and Video Compression
		4.1. Introduction
			4.1.1. Basics of image and video compression
			4.1.2. Literature review
			4.1.3. Outline of the chapter
		4.2. Graph-based models for image and video signals
			4.2.1. Graph-based models for residuals of predicted signals
			4.2.2. DCT/DSTs as GFTs and their relation to 1D models
			4.2.3. Interpretation of graph weights for predictive transform coding
		4.3. Graph spectral methods for compression
			4.3.1. GL-GFT design
			4.3.2. EA-GFT design
			4.3.3. Empirical evaluation of GL-GFT and EA-GFT
		4.4. Conclusion and potential future work
		4.5. References
	Chapter 5. Graph Spectral 3D Image Compression
		5.1. Introduction to 3D images
			5.1.1. 3D image definition
			5.1.2. Point clouds and meshes
			5.1.3. Omnidirectional images
			5.1.4. Light field images
			5.1.5. Stereo/multi-view images
		5.2. Graph-based 3D image coding: overview
		5.3. Graph construction
			5.3.1. Geometry-based approaches
			5.3.2. Joint geometry and color-based approaches
			5.3.3. Separable transforms
		5.4. Concluding remarks
		5.5. References
	Chapter 6. Graph Spectral Image Restoration
		6.1. Introduction
			6.1.1. A simple image degradation model
			6.1.2. Restoration with signal priors
			6.1.3. Restoration via filtering
			6.1.4. GSP for image restoration
		6.2. Discrete-domain methods
			6.2.1. Non-local graph-based transform for depth image denoising
			6.2.2. Doubly stochastic graph Laplacian
			6.2.3. Reweighted graph total variation prior
			6.2.4. Left eigenvectors of random walk graph Laplacian
			6.2.5. Graph-based image filtering
		6.3. Continuous-domain methods
			6.3.1. Continuous-domain analysis of graph Laplacian regularization
			6.3.2. Low-dimensional manifold model for image restoration
			6.3.3. LDMM as graph Laplacian regularization
		6.4. Learning-based methods
			6.4.1. CNN with GLR
			6.4.2. CNN with graph wavelet filter
		6.5. Concluding remarks
		6.6. References
	Chapter 7. Graph Spectral Point Cloud Processing
		7.1. Introduction
		7.2. Graph and graph-signals in point cloud processing
		7.3. Graph spectral methodologies for point cloud processing
			7.3.1. Spectral-domain graph filtering for point clouds
			7.3.2. Nodal-domain graph filtering for point clouds
			7.3.3. Learning-based graph spectral methods for point clouds
		7.4. Low-level point cloud processing
			7.4.1. Point cloud denoising
			7.4.2. Point cloud resampling
			7.4.3. Datasets and evaluation metrics
		7.5. High-level point cloud understanding
			7.5.1. Data auto-encoding for point clouds
			7.5.2. Transformation auto-encoding for point clouds
			7.5.3. Applications of GraphTER in point clouds
			7.5.4. Datasets and evaluation metrics
		7.6. Summary and further reading
		7.7. References
	Chapter 8. Graph Spectral Image Segmentation
		8.1. Introduction
		8.2. Pixel membership functions
			8.2.1. Two-class problems
			8.2.2. Multiple-class problems
			8.2.3. Multiple images
		8.3. Matrix properties
		8.4. Graph cuts
			8.4.1. The Mumford–Shah model
			8.4.2. Graph cuts minimization
		8.5. Summary
		8.6. References
	Chapter 9. Graph Spectral Image Classification
		9.1. Formulation of graph-based classification problems
			9.1.1. Graph spectral classifiers with noiseless labels
			9.1.2. Graph spectral classifiers with noisy labels
		9.2. Toward practical graph classifier implementation
			9.2.1. Graph construction
			9.2.2. Experimental setup and analysis
		9.3. Feature learning via deep neural network
			9.3.1. Deep feature learning for graph construction
			9.3.2. Iterative graph construction
			9.3.3. Toward practical implementation of deep feature learning
			9.3.4. Analysis on iterative graph construction for robust classification
			9.3.5. Graph spectrum visualization
			9.3.6. Classification error rate comparison using insufficient training data
			9.3.7. Classification error rate comparison using sufficient training data with label noise
		9.4. Conclusion
		9.5. References
	Chapter 10. Graph Neural Networks for Image Processing
		10.1. Introduction
		10.2. Supervised learning problems
			10.2.1. Point cloud classification
			10.2.2. Point cloud segmentation
			10.2.3. Image denoising
		10.3. Generative models for point clouds
			10.3.1. Point cloud generation
			10.3.2. Shape completion
		10.4. Concluding remarks
		10.5. References
List of Authors
Index
EULA