Graph Spectral Image Processing

Graph Spectral Image Processing

by Gene Cheung, Enrico Magli
Released August 2021
Publisher(s): Wiley-ISTE
ISBN: 9781789450286

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Book description

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.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Introduction to Graph Spectral Image Processing
    1. I.1. Introduction
    2. I.2. Graph definition
    3. I.3. Graph spectrum
    4. I.4. Graph variation operators
    5. I.5. Graph signal smoothness priors
    6. I.6. References
  5. PART 1 Fundamentals of Graph Signal Processing
    1. 1 Graph Spectral Filtering
      1. 1.1. Introduction
      2. 1.2. Review: filtering of time-domain signals
      3. 1.3. Filtering of graph signals
      4. 1.4. Edge-preserving smoothing of images as graph spectral filters
      5. 1.5. Multiple graph filters: graph filter banks
      6. 1.6. Fast computation
      7. 1.7. Conclusion
      8. 1.8. References
    2. 2 Graph Learning
      1. 2.1. Introduction
      2. 2.2. Literature review
      3. 2.3. Graph learning: a signal representation perspective
      4. 2.4. Applications of graph learning in image processing
      5. 2.5. Concluding remarks and future directions
      6. 2.6. References
    3. 3 Graph Neural Networks
      1. 3.1. Introduction
      2. 3.2. Spectral graph-convolutional layers
      3. 3.3. Spatial graph-convolutional layers
      4. 3.4. Concluding remarks
      5. 3.5. References
  6. PART 2 Imaging Applications of Graph Signal Processing
    1. 4 Graph Spectral Image and Video Compression
      1. 4.1. Introduction
      2. 4.2. Graph-based models for image and video signals
      3. 4.3. Graph spectral methods for compression
      4. 4.4. Conclusion and potential future work
      5. 4.5. References
    2. 5 Graph Spectral 3D Image Compression
      1. 5.1. Introduction to 3D images
      2. 5.2. Graph-based 3D image coding: overview
      3. 5.3. Graph construction
      4. 5.4. Concluding remarks
      5. 5.5. References
    3. 6 Graph Spectral Image Restoration
      1. 6.1. Introduction
      2. 6.2. Discrete-domain methods
      3. 6.3. Continuous-domain methods
      4. 6.4. Learning-based methods
      5. 6.5. Concluding remarks
      6. 6.6. References
    4. 7 Graph Spectral Point Cloud Processing
      1. 7.1. Introduction
      2. 7.2. Graph and graph-signals in point cloud processing
      3. 7.3. Graph spectral methodologies for point cloud processing
      4. 7.4. Low-level point cloud processing
      5. 7.5. High-level point cloud understanding
      6. 7.6. Summary and further reading
      7. 7.7. References
    5. 8 Graph Spectral Image Segmentation
      1. 8.1. Introduction
      2. 8.2. Pixel membership functions
      3. 8.3. Matrix properties
      4. 8.4. Graph cuts
      5. 8.5. Summary
      6. 8.6. References
    6. 9 Graph Spectral Image Classification
      1. 9.1. Formulation of graph-based classification problems
      2. 9.2. Toward practical graph classifier implementation
      3. 9.3. Feature learning via deep neural network
      4. 9.4. Conclusion
      5. 9.5. References
    7. 10 Graph Neural Networks for Image Processing
      1. 10.1. Introduction
      2. 10.2. Supervised learning problems
      3. 10.3. Generative models for point clouds
      4. 10.4. Concluding remarks
      5. 10.5. References
  7. List of Authors
  8. Index
  9. End User License Agreement

Product information

  • Title: Graph Spectral Image Processing
  • Author(s): Gene Cheung, Enrico Magli
  • Release date: August 2021
  • Publisher(s): Wiley-ISTE
  • ISBN: 9781789450286