Graph spectral image processing / / edited by Gene Cheung, Enrico Magli

• Record Nr.: UNINA9910555108603321
• Pubbl/distr/stampa: Hoboken, New Jersey : , : John Wiley & Sons, , [2021]; ©2021
• ISBN: 1-119-85081-9; 1-119-85083-5; 1-119-85082-7
• Descrizione fisica: 1 online resource (325 pages)
• Disciplina: 621.367
• Soggetti: Image processing; Graph theory; Spectral imaging; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Includes index.
• Nota di contenuto: 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.