Numerical Approaches for Linear Left-invariant Diffusions onSE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging

DOI10.4208/nmtma.2015.m1411zbMath1363.65008arXiv1403.3320OpenAlexW3102122047MaRDI QIDQ2825039

Gonzalo Sanguinetti, Jiong Zhang, Bart M. ter Haar Romeny, Remco Duits

Publication date: 6 October 2016

Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.3320

zbMATH Keywords

Brownian motionerror boundsMonte Carlo simulationsfinite difference methodsstochastic methodsEuclidean motion groupFourier methodsMathieu operatorshypo-elliptic diffusionMathematica algorithmsretinal imaging

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Discrete-time Markov processes on general state spaces (60J05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for discrete and fast Fourier transforms (65T50) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Hypoelliptic equations (35H10) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

Related Items (8)

Analysis of vessel connectivities in retinal images by cortically inspired spectral clustering ⋮ New exact and numerical solutions of the (convection-)diffusion kernels on \(\mathrm{SE}(3)\) ⋮ Retrieving challenging vessel connections in retinal images by line co-occurrence statistics ⋮ PDE-based group equivariant convolutional neural networks ⋮ A neuromathematical model for geometrical optical illusions ⋮ Cortical Spatiotemporal Dimensionality Reduction for Visual Grouping ⋮ Cortical-inspired Wilson-Cowan-type equations for orientation-dependent contrast perception modelling ⋮ Nilpotent approximations of sub-Riemannian distances for fast perceptual grouping of blood vessels in 2D and 3D

Uses Software

• Mathematica

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