Academia

Thesis

• Euclidean Equivariant Processing and Machine Learning on Position-Orientation Space
  Gijs Bellaard · 26 November 2025
  TU/e · PDF · Presentation

Publications

• Generalized Reduction to the Isotropy for Flexible Equivariant Neural Fields
  Alejandro García-Castellanos, Gijs Bellaard, Remco Duits, Daniel Pelt, Erik J Bekkers · ICLR 2026 Workshop GRaM · Published: 02 March 2026
  OpenReview
• Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
  Gijs Bellaard, Bart M. N. Smets, Remco Duits · Geometric Science of Information 2025 · Published: 20 October 2025
  Springer · arXiv
• Roto-Translation Invariant Metrics on Position-Orientation Space
  Gijs Bellaard, Bart M. N. Smets · Geometric Science of Information 2025 · Published: 20 October 2025
  Springer · arXiv
• Analysis and Computation of Geodesic Distances on Reductive Homogeneous Spaces
  Remco Duits, Gijs Bellaard, Barbara Tumpach · Geometric Science of Information 2025 · Published: 20 October 2025
  Springer · arXiv
• Entropic Optimal Transport with Data-Driven Metrics on the Roto-Translation Group
  Gautam Pai, Gijs Bellaard, Rick Sengers, Luc Florack, Remco Duits · Scale Space and Variational Methods in Computer Vision 2025 · Published: 17 May 2025
  Springer · PDF · Poster
• PDE-CNNs: Axiomatic Derivations and Applications
  Gijs Bellaard, Sei Sakata, Bart M. N. Smets, Remco Duits · Journal of Mathematical Imaging and Vision · Received: 15 April 2024 · Published: 30 January 2025
  Springer · arXiv
• Optimal Transport on the Lie Group of Roto-translations
  Daan Bon, Gautam Pai, Gijs Bellaard, Olga Mula, Remco Duits · SIAM Journal on Imaging Sciences · Received: 5 March 2024 · Published: 2 April 2025
  SIAM · arXiv
• Functional Properties of PDE-G-CNNs
  Gautam Pai, Gijs Bellaard, Bart M. N. Smets, Remco Duits · Geometric Science of Information 2023 · Received: 20 February 2023 · Published: 01 August 2023
  Springer · PDF
• Geometric Adaptations of PDE-G-CNNs
  Gijs 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 2023
  Springer · PDF · Poster
• Analysis of (sub-)Riemannian PDE-G-CNNs
  Gijs 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 2023
  Springer · arXiv

Supervision

• Distances on the Space of Positions and Orientations
  Axel Linders · Master Thesis · Remco Duits, Gijs Bellaard · 2025
  PDF
• Axiomatic PDE-G-CNNs on SE(2)
  Sei Sakata · Master Thesis · Remco Duits, Gijs Bellaard · 2023
  PDF · TU/e
• Classical and Quantum PDE-Based Neural Networks
  Tim Kraakman · Master Thesis · Remco Duits, Gautam Pai, Gijs Bellaard · 2023
  PDF · TU/e
• Analysis and Geometric Interpretation of PDE-G-CNNs
  Daan Bon · Master Thesis · Remco Duits, Gijs Bellaard · 2022
  PDF · TU/e

Teaching

• Differential Geometry for Image Processing
  TU/e · 2MMA70 · Instructor · 2023-2024
  Notes
• Advanced Calculus
  TU/e · 2DBN10 · Instructor · 2021-2023
• Complex Analysis
  TU/e · 2WA80 · Instructor · 2021-2023

Presentations

• Universal Collection of Euclidean Invariants between Pairs of Position-Orientations
  Geometric Science of Information 2025· 31 October 2025
  Slides
• Roto-Translation Invariant Metrics on Position-Orientation Space
  Geometric Science of Information 2025 · 31 October 2025
  Slides
• Geometric Invariants on Position-Orientation Space
  CASA day · 16 April 2025
  Slides
• Neurogeometry and PDE-Based Neural Networks
  Geometric Science of Information 2023 · 30 August 2023
  Slides (50MB!)
• Diffusion and Score Based Models
  AI Reading Group · TU/e · 24 March 2023
  Notes
• Equivariant Neural Networks
  AI Reading Group · TU/e · 04 November 2022
  Notes
• Analysis of PDE-G-CNNs
  CASA day · Evoluon Eindhoven · 13 April 2022
  Slides

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