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E-grāmata: Graph Spectral Image Processing

(Politecnico di Torino, Italy), (University of California, Berkeley, USA)
  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Aug-2021
  • Izdevniecība: ISTE Ltd
  • Valoda: eng
  • ISBN-13: 9781119850823
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Graph Spectral Image ProcessingPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Aug-2021
  • Izdevniecība: ISTE Ltd
  • Valoda: eng
  • ISBN-13: 9781119850823
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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 graph signal processing – extending traditional Fourier analysis tools such as transforms and wavelets to handle data on irregular graph kernels – provides new flexible computational tools to analyze and process these varied types of imaging data. Recent methods combine graph signal processing ideas with deep neural network architectures for enhanced performances, with robustness and smaller memory requirements.

The book is divided into two parts. The first is centered on the fundamentals of graph signal processing theories, including graph filtering, graph learning and graph neural networks. The second part details several imaging applications using graph signal processing tools, including image and video compression, 3D image compression, image restoration, point cloud processing, image segmentation and image classification, as well as the use of graph neural networks for image processing.
Introduction to Graph Spectral Image Processing xi
Gene Cheung
Enrico Magli
Part 1 Fundamentals of Graph Signal Processing
1(72)
Chapter 1 Graph Spectral Filtering
3(28)
Yuichi Tanaka
1.1 Introduction
3(1)
1.2 Review: filtering of time-domain signals
4(1)
1.3 Filtering of graph signals
5(6)
1.3.1 Vertex domain filtering
6(2)
1.3.2 Spectral domain filtering
8(2)
1.3.3 Relationship between graph spectral filtering and classical filtering
10(1)
1.4 Edge-preserving smoothing of images as graph spectral filters
11(4)
1.4.1 Early works
11(1)
1.4.2 Edge-preserving smoothing
12(3)
1.5 Multiple graph filters: graph filter banks
15(5)
1.5.1 Framework
16(1)
1.5.2 Perfect reconstruction condition
17(3)
1.6 Fast computation
20(6)
1.6.1 Subdivision
20(1)
1.6.2 Downsampling
21(1)
1.6.3 Precomputing GFT
22(1)
1.6.4 Partial eigendecomposition
22(1)
1.6.5 Polynomial approximation
23(3)
1.6.6 Krylov subspace method
26(1)
1.7 Conclusion
26(1)
1.8 References
26(5)
Chapter 2 Graph Learning
31(32)
Xiaowen Dong
Dorina Thanou
Michael Rabbat
Pascal Frossard
2.1 Introduction
31(2)
2.2 Literature review
33(3)
2.2.1 Statistical models
33(2)
2.2.2 Physically motivated models
35(1)
2.3 Graph learning: a signal representation perspective
36(16)
2.3.1 Models based on signal smoothness
38(5)
2.3.2 Models based on spectral filtering of graph signals
43(5)
2.3.3 Models based on causal dependencies on graphs
48(2)
2.3.4 Connections with the broader literature
50(2)
2.4 Applications of graph learning in image processing
52(3)
2.5 Concluding remarks and future directions
55(2)
2.6 References
57(6)
Chapter 3 Graph Neural Networks
63(10)
Giulia Fracastoro
Diego Valsesia
3.1 Introduction
63(1)
3.2 Spectral graph-convolutional layers
64(2)
3.3 Spatial graph-convolutional layers
66(5)
3.4 Concluding remarks
71(1)
3.5 References
72(1)
Part 2 Imaging Applications of Graph Signal Processing
73(226)
Chapter 4 Graph Spectral Image and Video Compression
75(30)
Hilmi E. Egilmez
Yung-Hsuan Chao
Antonio Ortega
4.1 Introduction
75(4)
4.1.1 Basics of image and video compression
77(1)
4.1.2 Literature review
78(1)
4.1.3 Outline of the chapter
79(1)
4.2 Graph-based models for image and video signals
79(10)
4.2.1 Graph-based models for residuals of predicted signals
81(6)
4.2.2 DCT/DSTs as GFTs and their relation to ID models
87(1)
4.2.3 Interpretation of graph weights for predictive transform coding
88(1)
4.3 Graph spectral methods for compression
89(11)
4.3.1 GL-GFT design
89(3)
4.3.2 EA-GFT design
92(5)
4.3.3 Empirical evaluation of GL-GFT and EA-GFT
97(3)
4.4 Conclusion and potential future work
100(1)
4.5 References
101(4)
Chapter 5 Graph Spectral 3D Image Compression
105(28)
Thomas Maugey
Mira Rizkallah
Navid Mahmoudian Bidgoli
Aline Roumy
Christine Guillemot
5.1 Introduction to 3D images
106(4)
5.1.1 3D image definition
106(1)
5.1.2 Point clouds and meshes
106(1)
5.1.3 Omnidirectional images
107(2)
5.1.4 Light field images
109(1)
5.1.5 Stereo/multi-view images
110(1)
5.2 Graph-based 3D image coding: overview
110(5)
5.3 Graph construction
115(11)
5.3.1 Geometry-based approaches
117(4)
5.3.2 Joint geometry and color-based approaches
121(4)
5.3.3 Separable transforms
125(1)
5.4 Concluding remarks
126(2)
5.5 References
128(5)
Chapter 6 Graph Spectral Image Restoration
133(48)
Jiahao Pang
Jin Zeng
6.1 Introduction
133(8)
6.1.1 A simple image degradation model
133(2)
6.1.2 Restoration with signal priors
135(2)
6.1.3 Restoration via filtering
137(3)
6.1.4 GSP for image restoration
140(1)
6.2 Discrete-domain methods
141(14)
6.2.1 Non-local graph-based transform for depth image denoising
141(1)
6.2.2 Doubly stochastic graph Laplacian
142(3)
6.2.3 Reweighted graph total variation prior
145(5)
6.2.4 Left eigenvectors of random walk graph Laplacian
150(5)
6.2.5 Graph-based image filtering
155(1)
6.3 Continuous-domain methods
155(12)
6.3.1 Continuous-domain analysis of graph Laplacian regularization
156(7)
6.3.2 Low-dimensional manifold model for image restoration
163(2)
6.3.3 LDMM as graph Laplacian regularization
165(2)
6.4 Learning-based methods
167(5)
6.4.1 CNN with GLR
169(2)
6.4.2 CNN with graph wavelet filter
171(1)
6.5 Concluding remarks
172(1)
6.6 References
173(8)
Chapter 7 Graph Spectral Point Cloud Processing
181(40)
Wei Hu
Siheng Chen
Dong Tian
7.1 Introduction
181(2)
7.2 Graph and graph-signals in point cloud processing
183(2)
7.3 Graph spectral methodologies for point cloud processing
185(5)
7.3.1 Spectral-domain graph filtering for point clouds
185(3)
7.3.2 Nodal-domain graph filtering for point clouds
188(1)
7.3.3 Learning-based graph spectral methods for point clouds
189(1)
7.4 Low-level point cloud processing
190(9)
7.4.1 Point cloud denoising
191(2)
7.4.2 Point cloud resampling
193(5)
7.4.3 Datasets and evaluation metrics
198(1)
7.5 High-level point cloud understanding
199(14)
7.5.1 Data auto-encoding for point clouds
199(7)
7.5.2 Transformation auto-encoding for point clouds
206(5)
7.5.3 Applications of GraphTER in point clouds
211(1)
7.5.4 Datasets and evaluation metrics
211(2)
7.6 Summary and further reading
213(1)
7.7 References
214(7)
Chapter 8 Graph Spectral Image Segmentation
221(20)
Michael Ng
8.1 Introduction
221(1)
8.2 Pixel membership functions
222(8)
8.2.1 Two-class problems
222(4)
8.2.2 Multiple-class problems
226(1)
8.2.3 Multiple images
227(3)
8.3 Matrix properties
230(2)
8.4 Graph cuts
232(5)
8.4.1 The Mumford-Shah model
234(1)
8.4.2 Graph cuts minimization
235(2)
8.5 Summary
237(1)
8.6 References
237(4)
Chapter 9 Graph Spectral Image Classification
241(36)
Minxiang Ye
Vladimir Stankovic
Lina Stankovic
Gene Cheung
9.1 Formulation of graph-based classification problems
243(4)
9.1.1 Graph spectral classifiers with noiseless labels
243(3)
9.1.2 Graph spectral classifiers with noisy labels
246(1)
9.2 Toward practical graph classifier implementation
247(8)
9.2.1 Graph construction
247(2)
9.2.2 Experimental setup and analysis
249(6)
9.3 Feature learning via deep neural network
255(16)
9.3.1 Deep feature learning for graph construction
258(2)
9.3.2 Iterative graph construction
260(2)
9.3.3 Toward practical implementation of deep feature learning
262(5)
9.3.4 Analysis on iterative graph construction for robust classification
267(2)
9.3.5 Graph spectrum visualization
269(1)
9.3.6 Classification error rate comparison using insufficient training data
270(1)
9.3.7 Classification error rate comparison using sufficient training data with label noise
270(1)
9.4 Conclusion
271(1)
9.5 References
272(5)
Chapter 10 Graph Neural Networks for Image Processing
277(22)
Giulia Fracastoro
Diego Valsesia
10.1 Introduction
277(1)
10.2 Supervised learning problems
278(8)
10.2.1 Point cloud classification
278(3)
10.2.2 Point cloud segmentation
281(2)
10.2.3 Image denoising
283(3)
10.3 Generative models for point clouds
286(8)
10.3.1 Point cloud generation
286(5)
10.3.2 Shape completion
291(3)
10.4 Concluding remarks
294(1)
10.5 References
294(5)
List of Authors 299(2)
Index 301
Gene Cheung received his PhD in Electrical Engineering and Computer Science from the University of California, Berkeley, USA. He is Associate Professor at York University, Canada, and an IEEE fellow. His research interests include image and graph signal processing.

Enrico Magli is Full Professor at Politecnico di Torino, Italy, and is an IEEE fellow. His research interests are within the field of graph signal processing and deep learning for image and video analysis.
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