Graph Signal Processing for Geometric Data and Beyond: Theory and Applications
This is an incremental contribution that provides a survey for researchers and practitioners in signal processing and geometric data applications.
The paper tackles the challenge of processing irregularly sampled geometric data like point clouds by providing a comprehensive overview of Graph Signal Processing (GSP) methodologies, bridging connections between geometric data, graphs, and techniques like Graph Neural Networks (GNNs). It aims to advance research in this field by unifying approaches and discussing open problems.
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.