Shape splines and stochastic shape evolutions: A second order point of view

DOI10.1090/S0033-569X-2012-01250-4zbMath1259.65104arXiv1003.3895OpenAlexW2964177960WikidataQ56624067 ScholiaQ56624067MaRDI QIDQ2892167

Alain Trouvé, François-Xavier Vialard

Publication date: 18 June 2012

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.3895

zbMATH Keywords

Hamiltonian equations for landmarksshape spline esitmationstochastic shape evolutions

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Numerical optimization and variational techniques (65K10) Optimization of shapes other than minimal surfaces (49Q10) Numerical solutions to stochastic differential and integral equations (65C30) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items (22)

Smooth interpolation of key frames in a Riemannian shell space ⋮ Splines for image metamorphosis ⋮ Diffeomorphic Surface Registration with Atrophy Constraints ⋮ Diffusion Bridges for Stochastic Hamiltonian Systems and Shape Evolutions ⋮ Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data ⋮ A reparameterisation based approach to geodesic constrained solvers for curve matching ⋮ A geometric framework for stochastic shape analysis ⋮ Minimizing acceleration on the group of diffeomorphisms and its relaxation ⋮ Moment evolution equations and moment matching for stochastic image EPDiff ⋮ Extension to infinite dimensions of a stochastic second-order model associated with shape splines ⋮ Statistical models for deformable templates in image and shape analysis ⋮ Existence of variationally defined curves with higher order elliptic Lagrangians ⋮ Invariant higher-order variational problems. II ⋮ Langevin Equations for Landmark Image Registration with Uncertainty ⋮ Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics ⋮ Analysing `simple' image registrations ⋮ String methods for stochastic image and shape matching ⋮ Second-order models for optimal transport and cubic splines on the Wasserstein Space ⋮ Riemannian cubics close to geodesics at the boundaries ⋮ Estimation of a growth development with partial diffeomorphic mappings ⋮ Shape deformation analysis from the optimal control viewpoint ⋮ Collision Avoidance of Multiagent Systems on Riemannian Manifolds

Uses Software

• LDDMM

Cites Work

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