Functional properties of PDE-based group equivariant convolutional neural networks

DOI10.1007/978-3-031-38271-0_7OpenAlexW4385435120MaRDI QIDQ6178826

Remco Duits, Bart M. N. Smets, Gijs Bellaard, Gautam Pai

Publication date: 16 January 2024

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-38271-0_7

zbMATH Keywords

Riemannian geometryLie groupssemiringsPDE-based image processinggroup equivariant convolutional neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Computing methodologies for image processing (68U10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Cites Work

• Unnamed Item
• Morphological counterparts of linear shift-invariant scale-spaces
• Functional inequalities and Hamilton-Jacobi equations in geodesic spaces
• Equivariant deep learning via morphological and linear scale space PDEs on the space of positions and orientations
• A cortical based model of perceptual completion in the roto-translation space
• Morphology neural networks: An introduction with applications
• Scale equivariant neural networks with morphological scale-spaces
• On the axioms of scale space theory
• Left-invariant parabolic evolutions on $SE(2)$ and contour enhancement via invertible orientation scores Part I: Linear left-invariant diffusion equations on $SE(2)$
• Scale space and variational methods in computer vision. 9th international conference, SSVM 2023, Santa Margherita di Pula, Italy, May 21--25, 2023. Proceedings
• PDE-based group equivariant convolutional neural networks