Speakers

Klaus Hildebrandt

Title: Geometry Processing: Discretization, Learning and Analysis

Abstract: Advances in 3D capture, fabrication and display technologies over the past decade have led to the intensive use of 3D data in a variety of scientific disciplines and application domains posing a demand for computational methods for analysing and processing geometric data. This talk is divided into three parts. First, we discuss geometric properties of continuous surfaces and their discrete counterparts. In the second part, we look at the construction of convolutions on surfaces in the context of geometric deep learning. Finally, we discuss the analysis and synthesis of shapes using Riemannian shapes spaces.

Maosheng Yang

Title: Hodge-compositional Edge Gaussian Processes

Abstract: We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create Hodge-compositional edge GPs that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean current analysis and water supply networks.

Ruben Wiersma

Title: DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds

Abstract: Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D data. In this talk, we aim to construct anisotropic convolution layers that work directly on the surface derived from a point cloud. This is challenging because of the lack of a global coordinate system for tangential directions on surfaces. We describe DeltaConv, a convolution layer that combines geometric operators from vector calculus to enable the construction of anisotropic filters on point clouds. Because these operators are defined on scalar- and vector-fields, we separate the network into a scalar- and a vector-stream, which are connected by the operators. The vector stream enables the network to explicitly represent, evaluate, and process directional information. Our convolutions are robust and simple to implement and match or improve on state-of-the-art approaches on several benchmarks, while also speeding up training and inference.