Academia
Publications
-
Universal Collection of Euclidean Invariants between Pairs of Position-OrientationsGijs Bellaard, Bart M. N. Smets, Remco Duits · Submitted to: Geometric Science of Information 2025arXiv
-
Roto-Translation Invariant Metrics on Position-Orientation SpaceGijs Bellaard, Bart M. N. Smets · Submitted to: Geometric Science of Information 2025arXiv
-
Analysis and Computation of Geodesic Distances on Reductive Homogeneous SpacesRemco Duits, Gijs Bellaard, Barbara Tumpach · Submitted to: Geometric Science of Information 2025arXiv
-
Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation GroupGautam Pai, Gijs Bellaard, Rick Sengers, Luc Florack, Remco Duits · Scale Space and Variational Methods in Computer Vision 2025Springer · PDF · Poster
-
PDE-CNNs: Axiomatic Derivations and ApplicationsGijs Bellaard, Sei Sakata, Bart M. N. Smets, Remco Duits · Journal of Mathematical Imaging and Vision · Received: 15 April 2024 · Published: 30 January 2025Springer · arXiv
-
Optimal Transport on the Lie Group of Roto-translationsDaan Bon, Gautam Pai, Gijs Bellaard, Olga Mula, Remco Duits · SIAM Journal on Imaging Sciences · Received: 5 March 2024 · Published: 2 April 2025SIAM · arXiv
-
Functional Properties of PDE-G-CNNsGautam Pai, Gijs Bellaard, Bart M. N. Smets, Remco Duits · Geometric Science of Information 2023 · Received: 20 February 2023 · Published: 01 August 2023Springer · PDF
-
Geometric Adaptations of PDE-G-CNNsGijs Bellaard, Gautam Pai, Javier Olivan Bescos, and Remco Duits · Scale Space and Variational Methods in Computer Vision 2023 · Received: 30 January 2023 · Published: 10 May 2023Springer · PDF · Poster
-
Analysis of (sub-)Riemannian PDE-G-CNNsGijs Bellaard, Daan L. J. Bon, Gautam Pai, Bart M. N. Smets, Remco Duits · Journal of Mathematical Imaging and Vision · Received: 21 October 2022 · Published: 16 April 2023Springer · arXiv
Supervision
-
Axiomatic PDE-G-CNNs on SE(2)Sei Sakata · Master Thesis · Remco Duits, Gijs Bellaard · 2023PDF · TU/E
-
Classical and Quantum PDE-Based Neural NetworksTim Kraakman · Master Thesis · Remco Duits, Gautam Pai, Gijs Bellaard · 2023PDF · TU/E
-
Analysis and Geometric Interpretation of PDE-G-CNNsDaan Bon · Master Thesis · Remco Duits, Gijs Bellaard · 2022PDF · TU/E
Teaching
-
Differential Geometry for Image ProcessingTU/e · 2MMA70 · Instructor · 2023-2024Notes
-
Advanced CalculusTU/e · 2DBN10 · Instructor · 2021-2023
-
Complex AnalysisTU/e · 2WA80 · Instructor · 2021-2023
Presentations
-
Geometric Invariants on Position-Orientation SpaceCASA day · 16 April 2025Slides
-
Neurogeometry and PDE-Based Neural NetworksGSI 2023 · 30 August 2023Slides (50MB!)
-
Diffusion and Score Based ModelsAI Reading Group · TU/e · 24 March 2023Notes
-
Equivariant Neural NetworksAI Reading Group · TU/e · 04 November 2022Notes
-
Analysis of PDE-G-CNNsCASA day · Evoluon Eindhoven · 13 April 2022Slides
Other
-
My bachelor final project is about neighbor-swap graphs.
Tom Verhoeff was my supervisor during this project.
A Dutch introduction to this topic can be read in the so-called "A4-populair",
which is meant for high schoolers in the Netherlands.
Paper · Presentation · A4-Populair -
My master thesis is about the simulation of viscoplastic materials using smoothed particle hydrodynamics.
This thesis was done under the supervision of Bas van der Linden at Sioux Mathware.
Thesis · Presentation -
My friend Sander Spoelstra's bachelor final project is about the Union-Closed conjecture which I am also interested in.
I followed the writing of his paper closely and he allowed me to share it here.
Paper