Multiscale Nonrigid Point Cloud Registration Using Rotation-Invariant Sliced-Wasserstein Distance via Laplace--Beltrami Eigenmap

DOI10.1137/16M1068827zbMath1365.65246arXiv1406.3758MaRDI QIDQ5266381

Rongjie Lai, Hong-Kai Zhao

Publication date: 2 June 2017

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

Full work available at URL: https://arxiv.org/abs/1406.3758

zbMATH Keywords

algorithmeigenvalueeigenfunctioncomputational efficiencyoptimal transportationnonrigid registrationpoint cloudsLaplace-Beltrami eigenmaprotation-invariant sliced Wasserstein distance

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Complexity and performance of numerical algorithms (65Y20)

Related Items

A Nonlocal Stokes System with Volume Constraints, Entropical optimal transport, Schrödinger's system and algorithms, The diffusion geometry of fibre bundles: horizontal diffusion maps, A second-order nonlocal approximation for Poisson model with Dirichlet boundary, Solving Partial Differential Equations on Manifolds From Incomplete Interpoint Distance, Nonisometric surface registration via conformal Laplace-Beltrami basis pursuit

Uses Software

• SCAPE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A feasible method for optimization with orthogonality constraints
• Best bases for signal spaces
• A local mesh method for solving PDEs on point clouds
• A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching
• Solving eigenvalue problems on curved surfaces using the closest point method
• Riemannian coverings and isospectral manifolds
• Geodesic length functions and Teichmüller spaces
• Embedding Riemannian manifolds by their heat kernel
• Affine invariant geometry for non-rigid shapes
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Sliced and Radon Wasserstein barycenters of measures
• Diffusion maps
• A theoretical and computational framework for isometry invariant recognition of point cloud data
• Solving Partial Differential Equations on Point Clouds
• Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels
• Assignment Problems
• Numerical Geometry of Non-Rigid Shapes
• Shape distributions
• Two-Point Step Size Gradient Methods
• Can One Hear the Shape of a Drum? Revisited
• One cannot hear the shape of a drum
• Generic Properties of Eigenfunctions
• Mathématiques/Mathematics Shape optimization solutions via Monge-Kantorovich equation
• The Variational Formulation of the Fokker--Planck Equation
• A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching
• Can One Hear the Shape of a Drum?
• Optimal Transport