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 …
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 …
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 …
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 …
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 …
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 …
Total Variation and Mean Curvature PDEs on $\mathbb{R}^d \rtimes S^{d−1}$ (SSVM)
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include …
