A Nonlinear Elastic Shape Averaging Approach

DOI10.1137/080738337zbMath1219.49035OpenAlexW2080179319MaRDI QIDQ3183409

Benedikt Wirth, Martin Rumpf

Publication date: 19 October 2009

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

Full work available at URL: https://semanticscholar.org/paper/2aba53741971cc087547fcf508d0f04a9ed4d7f5

zbMATH Keywords

finite element discretizationnonlinear elasticityphase field approximationnonrigid registrationshape averagingMumford-Shah approach

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Computing methodologies for image processing (68U10) Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Optimization of shapes other than minimal surfaces (49Q10) Variational principles of physics (49S05)

Related Items (16)

Elastic 3D-2D image registration ⋮ An elasticity-based covariance analysis of shapes ⋮ A Variational Model Dedicated to Joint Segmentation, Registration, and Atlas Generation for Shape Analysis ⋮ On diffeologies from infinite dimensional geometry to PDE constrained optimization ⋮ On diffeologies for power sets and measures ⋮ A non-local topology-preserving segmentation-guided registration model ⋮ Shape-aware matching of implicit surfaces based on thin shell energies ⋮ Suitable spaces for shape optimization ⋮ Symmetry and scaling limits for matching of implicit surfaces based on thin shell energies ⋮ A lattice Boltzmann method applied to the fluid image registration ⋮ Variational Methods in Shape Analysis ⋮ A Joint Segmentation/Registration Model Based on a Nonlocal Characterization of Weighted Total Variation and Nonlocal Shape Descriptors ⋮ An SL(2) invariant shape median ⋮ Real-Time Nonlinear Shape Interpolation ⋮ An Inexact Newton--Krylov Algorithm for Constrained Diffeomorphic Image Registration ⋮ Algorithmically generated rodent hepatic vascular trees in arbitrary detail

Uses Software

• LDDMM

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