The fshape framework for the variability analysis of functional shapes

DOI10.1007/s10208-015-9288-2zbMath1376.49054arXiv1404.6039OpenAlexW2963466111MaRDI QIDQ2397743

Nicolas Charon, Benjamin Charlier, Alain Trouvé

Publication date: 23 May 2017

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.6039

zbMATH Keywords

shape analysisvarifoldsmetamorphosesKarcher meansexistence of an optimal solutionlarge deformation modelsatlas estimation algorithmssignals on manifolds

Mathematics Subject Classification ID

Computing methodologies for image processing (68U10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Optimization of shapes other than minimal surfaces (49Q10) Geometry of quantum groups (58B32) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Discrete approximations in optimal control (49M25)

Related Items (13)

Metamorphoses of functional shapes in Sobolev spaces ⋮ A Riemann manifold model framework for longitudinal changes in physical activity patterns ⋮ HV geometry for signal comparison ⋮ Statistical Analysis of Functions on Surfaces, With an Application to Medical Imaging ⋮ Nonlinear flag manifolds as coadjoint orbits ⋮ Metrics, quantization and registration in varifold spaces ⋮ A numerical framework for elastic surface matching, comparison, and interpolation ⋮ Functional random effects modeling of brain shape and connectivity ⋮ Representation of surfaces with normal cycles and application to surface registration ⋮ Estimation of a growth development with partial diffeomorphic mappings ⋮ A Coherent Framework for Learning Spatiotemporal Piecewise-Geodesic Trajectories from Longitudinal Manifold-Valued Data ⋮ Kernel Metrics on Normal Cycles and Application to Curve Matching ⋮ Mechanistic Modeling of Longitudinal Shape Changes: Equations of Motion and Inverse Problems

Uses Software

• LDDMM
• fshapesTk
• GitHub

Cites Work

• Functional currents: a new mathematical tool to model and analyse functional shapes
• Shape deformation analysis from the optimal control viewpoint
• A zoo of diffeomorphism groups on \(\mathbb R^n\)
• Geodesic shooting for computational anatomy
• Metamorphoses through Lie group action
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• On the first variation of a varifold
• Computing large deformation metric mappings via geodesic flows of diffeomorphisms
• The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration
• VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES AND UNIVERSALITY
• Variational problems on flows of diffeomorphisms for image matching
• Shape Spaces
• Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups
• Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds
• Universality, Characteristic Kernels and RKHS Embedding of Measures
• Local Geometry of Deformable Templates
• Theory of Reproducing Kernels
• Shapes and diffeomorphisms
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