6 papers
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…
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…
Roto-Translation Invariant Metrics on Position-Orientation Space
Gijs Bellaard, Bart M. N. Smets
Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image analysis tasks like enhancement, denoising, and s…
Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
Gijs Bellaard, Bart M. N. Smets, Remco Duits
Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied to tasks such as predicting molecular dynamics…
PDE-CNNs: Axiomatic Derivations and Applications
Gijs Bellaard, Sei Sakata, Bart M. N. Smets +1
PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) use solvers of evolution PDEs as substitutes for the conventional components in G-CNNs. PDE-G-CNNs can offer several bene…
Optimal Transport on the Lie Group of Roto-translations
Daan Bon, Gautam Pai, Gijs Bellaard +2
The roto-translation group SE2 has been of active interest in image analysis due to methods that lift the image data to multi-orientation representations defined on this Lie group.…