Graph Signal Processing for Geometric Data and Beyond: Theory and Applications

• URL: http://arxiv.org/abs/2008.01918v3
• Date: Sat, 4 Sep 2021 17:35:02 GMT
• Title: Graph Signal Processing for Geometric Data and Beyond: Theory and Applications
• Authors: Wei Hu, Jiahao Pang, Xianming Liu, Dong Tian, Chia-Wen Lin, Anthony Vetro
• Abstract summary: Graph Signal Processing (GSP) enables processing signals that reside on irregular domains. GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs. Recently developed Graph Neural Networks (GNNs) interpret the operation of these networks from the perspective of GSP.
• Score: 55.81966207837108
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Geometric data acquired from real-world scenes, e.g., 2D depth images, 3D point clouds, and 4D dynamic point clouds, have found a wide range of applications including immersive telepresence, autonomous driving, surveillance, etc. Due to irregular sampling patterns of most geometric data, traditional image/video processing methodologies are limited, while Graph Signal Processing (GSP) -- a fast-developing field in the signal processing community -- enables processing signals that reside on irregular domains and plays a critical role in numerous applications of geometric data from low-level processing to high-level analysis. To further advance the research in this field, we provide the first timely and comprehensive overview of GSP methodologies for geometric data in a unified manner by bridging the connections between geometric data and graphs, among the various geometric data modalities, and with spectral/nodal graph filtering techniques. We also discuss the recently developed Graph Neural Networks (GNNs) and interpret the operation of these networks from the perspective of GSP. We conclude with a brief discussion of open problems and challenges.

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