Currents and finite elements as tools for shape space

DOI10.1007/s10851-019-00896-xzbMath1468.65018arXiv1702.02780OpenAlexW3102538218MaRDI QIDQ2331093

Stephen Marsland, Olivier Verdier, Klas Modin, Robert I. Mclachlan, James Benn

Publication date: 25 October 2019

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.02780

zbMATH Keywords

finite elementscurrentsimage analysisshape space

Mathematics Subject Classification ID

Random fields; image analysis (62M40) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Spaces of embeddings and immersions (58D10) Currents in global analysis (58A25)

Related Items (4)

The measurement and analysis of shapes. An application of hydrodynamics and probability theory ⋮ A relaxed approach for curve matching with elastic metrics ⋮ Unnamed Item ⋮ femshape

Uses Software

• DOLFIN
• FEniCS
• GitHub
• Deformetrica

Cites Work

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• Large deformation diffeomorphic metric curve mapping
• Partial differential equations. I: Basic theory
• Surface matching using normal cycles
• Numerically invariant signature curves
• Functional currents: a new mathematical tool to model and analyse functional shapes
• Saving phase: injectivity and stability for phase retrieval
• Shape analysis on Lie groups with applications in computer animation
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Constructing reparameterization invariant metrics on spaces of plane curves
• Computing large deformation metric mappings via geodesic flows of diffeomorphisms
• The Varifold Representation of Nonoriented Shapes for Diffeomorphic Registration

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