62 citations · 65 across the 12 of their papers we have counts for
12 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…
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…
Flow Matching on Lie Groups
Finn M. Sherry, Bart M. N. Smets
Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution by flowing samples from some distribution $\mathfrak…
Semiring Activation in Neural Networks
Bart M. N. Smets, Peter D. Donker, Jim W. Portegies
We introduce a class of trainable nonlinear operators based on semirings that are suitable for use in neural networks. These operators generalize the traditional alternation of lin…
Mathematics of Neural Networks (Lecture Notes Graduate Course)
Bart M. N. Smets
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an int…
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…
Analysis of (sub-)Riemannian PDE-G-CNNs
Gijs Bellaard, Daan L. J. Bon, Gautam Pai +2
Group equivariant convolutional neural networks (G-CNNs) have been successfully applied in geometric deep learning. Typically, G-CNNs have the advantage over CNNs that they do not…
Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking
Nicky van den Berg, Bart Smets, Gautam Pai +2
We introduce a data-driven version of the plus Cartan connection on the homogeneous space of 2D positions and orientations. We formulate a theorem that describes all…
PDE-based Group Equivariant Convolutional Neural Networks
Bart Smets, Jim Portegies, Erik Bekkers +1
We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where…
Total Variation and Mean Curvature PDEs on
Remco Duits, Etienne St-Onge, Jim Portegies +1
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curviline…
Investigation on Demand Side Management Techniques in the Smart Grid using Game Theory and ICT Concepts
Bart Smets
This paper investigates how concepts from game theory and ICT can contribute to solve challenges in demand side management, an important concept in the upcoming smart grid. Demand…