Publications

2025

1. Roto-Translation Invariant Metrics on Position-Orientation Space G. Bellaard, B.M.N. Smets Conference International Conference on Geometric Science of Information 2025 arXiv DOI
2. Universal Collection of Euclidean Invariants between Pairs of Position-Orientations G. Bellaard, B.M.N. Smets, R. Duits Conference International Conference on Geometric Science of Information 2025 arXiv DOI
3. Flow Matching on Lie Groups F.M. Sherry, B.M.N. Smets Conference International Conference on Geometric Science of Information 2025 arXiv DOI
4. PDE-CNNs: Axiomatic Derivations and Applications G. Bellaard, S. Sakata, B.M.N. Smets, R. Duits Journal Journal of Mathematical Imaging and Vision 2025 PDF DOI LieTorch

2024

1. Geometric Partial Differential Equations in Deep Learning & Image Processing B.M.N. Smets ThesisPhD thesis, Eindhoven University of Technology 2024 PDF TU/e repository LieTorch
2. Semiring Activation in Neural Networks B.M.N. Smets, P.D. Donker, J.W. Portegies Preprint2024 PDF arXiv SemiTorch
3. Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking N.J. van den Berg, B.M.N. Smets, G. Pai, J.-M. Mirebeau, R. Duits Journal Journal of Mathematical Imaging and Vision 2024 arXiv DOI

2023

1. Geodesic Tracking of Retinal Vascular Trees with Optical and TV-Flow Enhancement in SE(2) N.J. van den Berg, S. Zhang, B.M.N. Smets, T.J.M. Berendschot, R. Duits Conference International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 2023 DOI
2. Analysis of (sub-)Riemannian PDE-G-CNNs G. Bellaard, D.L.J. Bon, G. Pai, B.M.N. Smets, R. Duits Journal Journal of Mathematical Imaging and Vision 2023 DOI LieTorch
3. Functional Properties of PDE-Based Group Equivariant Convolutional Neural Networks G. Pai, G. Bellaard, B.M.N. Smets, R. Duits Conference International Conference on Geometric Science of Information 2023 DOI

2022

1. PDE-based Group Equivariant Convolutional Neural Networks B.M.N. Smets, J.W. Portegies, E.J. Bekkers, R. Duits Journal Journal of Mathematical Imaging and Vision 2022 PDF arXiv DOI LieTorch

2021

1. Recent Geometric Flows in Multi-orientation Image Processing via a Cartan Connection R. Duits, B.M.N. Smets, A.J. Wemmenhove, J.W. Portegies, E.J. Bekkers Book chapter Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging 2021 Springer
2. Equivariant Deep Learning via Morphological and Linear Scale Space PDEs on the Space of Positions and Orientations R. Duits, B.M.N. Smets, E.J. Bekkers, J.W. Portegies Conference International Conference on Scale Space and Variational Methods In Computer Vision 2021 DOI

2020

1. Total Variation and Mean Curvature PDEs on the Homogeneous Space of Positions and Orientations B.M.N. Smets, R. Duits, E. St-Onge, J.W. Portegies Journal Journal of Mathematical Imaging and Vision 2020 PDF DOI Code (Mathematica)

2019

1. Geometric Image Denoising and Machine Learning B.M.N. Smets Thesis MSc thesis, Eindhoven University of Technology 2019 PDF Slides
2. Total Variation and Mean Curvature PDEs on ${ℝ}^d⋊S^{d-1}$ R. Duits, E. St-Onge, J.W. Portegies, B.M.N. Smets Conference International Conference on Scale Space and Variational Methods in Computer Vision (SSVM) 2019 PDF arXiv DOI

2017

1. Improving on Vascular Tracking using Sub-Riemannian Geodesics B.M.N. Smets ThesisBSc thesis (bachelor end project), Eindhoven University of Technology 2017 PDF