11 papers
Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images
Leanne Vis, Maxim Pisarenco, Bart M. N. Smets +2
Geodesic tracking on the projective line bundle has many uses, including the segmentation of objects in images. However, global tracking requires expensive dista…
Diffusion-Shock PDEs for Deep Learning on Position-Orientation Space
Finn M. Sherry, Kristina Schaefer, Remco Duits
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space [1] to position-orientation space . This has n…
Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields
Alejandro GarcÃa-Castellanos, Gijs Bellaard, Remco Duits +2
Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques d…
Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces
Alejandro GarcÃa-Castellanos, David R. Wessels, Nicky J. van den Berg +3
We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neura…
Connected Components on Lie Groups and Applications to Multi-Orientation Image Analysis
Nicky J. van den Berg, Olga Mula, Leanne Vis +1
We develop and analyze a new algorithm to find the connected components of a compact set from a Lie group endowed with a left-invariant Riemannian distance. For a given $δ…
Analysis and Computation of Geodesic Distances on Reductive Homogeneous Spaces
Remco Duits, Gijs Bellaard, Barbara Tumpach
Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is d…