Roto-Translation Invariant Metrics on Position-Orientation Space
Riemannian metrics on the position-orientation space M(3) that are roto-translation group SE(3) invariant play a key role in image ā¦
Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
Euclidean E(3) equivariant neural networks that employ scalar fields on position-orientation space M(3) have been effectively applied ā¦
Flow Matching on Lie Groups
Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution š1 by flowing samples ā¦
PDE-CNNs: Axiomatic Derivations and Applications
PDE-based group convolutional neural networks (PDE-G-CNNs) use solvers of evolution PDEs as substitutes for the conventional components ā¦
Semiring Activation in Neural Networks
We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators ā¦
Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2)
Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the ā¦
Analysis of (sub-)Riemannian PDE-G-CNNs
Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs ā¦
Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking
We introduce a data-driven version of the plus Cartan connection on the 3D homogeneous space $\mathbb{M}_2$ of 2D positions and ā¦
PDE-based Group Equivariant Convolutional Neural Networks
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a ā¦
Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations (JMIV)
Two key ideas have greatly improved techniques for image enhancement and denoising: the lifting of image data to multi-orientation ā¦
Total Variation and Mean Curvature PDEs on $\mathbb{R}^d \rtimes S^{dā1}$ (SSVM)
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include ā¦
