Graph spectral image processing

Graph spectral image processing

Graph spectral image processing is the study of imaging data from a graph frequency perspective. Modern image sensors capture a wide range of visual data including high spatial resolution/high bit-depth 2D images and videos, hyperspectral images, light field images and 3D point clouds. The field of...

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Detalles Bibliográficos
Otros Autores: Magli, Enrico, editor (editor), Cheung, Gene, editor
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, New Jersey : John Wiley & Sons [2021]
Colección:Sciences. Image. Compression, coding and protection of images and videos
Materias:
Image processing.
Spectral imaging.
Graph theory.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009724215006719
Tabla de Contenidos:
  • 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.

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