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math.DG2025
Analysis and Computation of Geodesic Distances on Reductive Homogeneous Spaces
Remco Duits, Gijs Bellaard, Barbara Tumpach
Many geometric machine learning and image analysis applications, require a left-invariant metric on the 5D homogeneous space of 3D positions and orientations SE(3)/SO(2). This is d…
math.DG2025
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…
math.DG2025
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…