A Geodesic Landmark Shooting Algorithm for Template Matching and Its Applications

DOI10.1137/15M104373XzbMath1366.65085OpenAlexW2595196388MaRDI QIDQ5266376

Dongyang Kuang, Long Lee, Roberto Camassa

Publication date: 2 June 2017

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m104373x

zbMATH Keywords

algorithmconvergenceneural networksdeformationnumerical experimenttemplate matchingparticle systemmultiscale decompositiongeodesic shootinglandmarkHamiltonian metric

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Neural networks for/in biological studies, artificial life and related topics (92B20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Uses Software

• LDDMM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Group actions, homeomorphisms, and matching: A general framework
• A reparameterisation based approach to geodesic constrained solvers for curve matching
• A kernel class allowing for fast computations in shape spaces induced by diffeomorphisms
• Matrix-valued kernels for shape deformation analysis
• Landmark-free statistical analysis of the shape of plant leaves
• Shape deformation analysis from the optimal control viewpoint
• Geodesic shooting for computational anatomy
• Computing large deformation metric mappings via geodesic flows of diffeomorphisms
• Landmark matching via large deformation diffeomorphisms
• An Invariant Approach to Statistical Analysis of Shapes
• Integration of the EPDiff equation by particle methods
• Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
• Solitary Waves and N ‐Particle Algorithms for a Class of Euler–Poincaré Equations
• N-particle dynamics of the Euler equations for planar diffeomorphisms
• Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
• Variational problems on flows of diffeomorphisms for image matching
• Computational anatomy: an emerging discipline
• The Euler-Poincaré theory of metamorphosis
• Shapes and diffeomorphisms