Time Discrete Geodesic Paths in the Space of Images

DOI10.1137/140970719zbMath1325.65031arXiv1503.02001OpenAlexW2963593874MaRDI QIDQ3192660

Martin Rumpf, Benjamin Berkels, Alexander Effland

Publication date: 13 October 2015

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

Full work available at URL: https://arxiv.org/abs/1503.02001

zbMATH Keywords

convergencenumerical exampleRiemannian manifoldfinite elementgeodesic pathshape spacemetamorphosisvariational time discretizationimage transportimage matching functional

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Geodesics in global differential geometry (53C22)

Related Items (14)

On a spatial-temporal decomposition of optical flow ⋮ Splines for image metamorphosis ⋮ Weight metamorphosis of varifolds and the LDDMM-Fisher-Rao metric ⋮ An Image Registration Model in Electron Backscatter Diffraction ⋮ Convergence of functions and their Moreau envelopes on Hadamard spaces ⋮ Numerical accuracy of ladder schemes for parallel transport on manifolds ⋮ Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds ⋮ HV geometry for signal comparison ⋮ Regularization of inverse problems via time discrete geodesics in image spaces ⋮ Applied harmonic analysis and data processing. Abstracts from the workshop held March 25--31, 2018 ⋮ Incorporation of a deformation prior in image reconstruction ⋮ Image Extrapolation for the Time Discrete Metamorphosis Model: Existence and Applications ⋮ Image morphing in deep feature spaces: theory and applications ⋮ Morphing of Manifold-Valued Images Inspired by Discrete Geodesics in Image Spaces

Uses Software

• LDDMM

Cites Work

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• A computational model of multidimensional shape
• A continuum mechanical approach to geodesics in shape space
• A metric on shape space with explicit geodesics
• Shape metrics based on elastic deformations
• An introduction to \(\Gamma\)-convergence
• Topological methods in hydrodynamics
• Curvature based image registration
• On the \(\Gamma\)-convergence of discrete dynamics and variational integrators
• Group actions, homeomorphisms, and matching: A general framework
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Riemannian geometries on spaces of plane curves
• 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
• Sard's theorem for mappings in Hölder and Sobolev spaces
• Computing large deformation metric mappings via geodesic flows of diffeomorphisms
• Landmark matching via large deformation diffeomorphisms
• Discrete Geodesic Calculus in Shape Space and Applications in the Space of Viscous Fluidic Objects
• Variational time discretization of geodesic calculus
• Discrete mechanics and optimal control: An analysis
• A New Geometric Metric in the Space of Curves, and Applications to Tracking Deforming Objects by Prediction and Filtering
• Variational time integrators
• Multipolar viscous fluids
• Global invertibility of Sobolev functions and the interpenetration of matter
• Variational problems on flows of diffeomorphisms for image matching
• The Euler-Poincaré theory of metamorphosis
• Finite Elemente
• Geometric Numerical Integration
• Local Geometry of Deformable Templates
• Variational, Geometric, and Level Set Methods in Computer Vision

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