8 papers · 1 filter
Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images
Leanne Vis, Maxim Pisarenco, Bart M. N. Smets +2
Geodesic tracking on the projective line bundle has many uses, including the segmentation of objects in images. However, global tracking requires expensive dista…
Diffusion-Shock PDEs for Deep Learning on Position-Orientation Space
Finn M. Sherry, Kristina Schaefer, Remco Duits
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space [1] to position-orientation space . This has n…
Connected Components on Lie Groups and Applications to Multi-Orientation Image Analysis
Nicky J. van den Berg, Olga Mula, Leanne Vis +1
We develop and analyze a new algorithm to find the connected components of a compact set from a Lie group endowed with a left-invariant Riemannian distance. For a given $δ…
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…
Orientation Scores should be a Piece of Cake
Finn M. Sherry, Chase van de Geijn, Erik J. Bekkers +1
We axiomatically derive a family of wavelets for an orientation score, lifting from position space to position and orientation space , with f…
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…