The goal of this presentation is to introduce a broad framework called geometric data processing which encapsulates many research trends focused on the processing of point clouds in vector spaces of arbitrary dimensions. Such point clouds often arise as a representation of 3D scenes in computer vision or as embeddings of datasets processed by neural networks.
The first part of the presentation will be devoted to motivating examples. I will present recent success stories in applications of neural networks and give a motivation for working with 3D point clouds instead of 2D images. Next, I will present a high-level overview of mathematical tools which are useful for geometric data processing and review tasks that are routinely being solved using these tools.
My aim is to present possible meeting points for engineering and theory-driven researchers at our institute.