Geodesic distance and curves through isotropic and anisotropic heat equations on images and surfaces

DOI10.1007/s10851-015-0621-9zbMath1338.65216OpenAlexW2276917074MaRDI QIDQ283012

Fang Yang, Laurent D. Cohen

Publication date: 13 May 2016

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

Full work available at URL: https://doi.org/10.1007/s10851-015-0621-9

zbMATH Keywords

algorithmnumerical exampleminimal pathsgeodesicheat diffusionanisotropicautomatic geodesic extractiongeodesic votingisotropickey points

Mathematics Subject Classification ID

Heat equation (35K05) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Geodesics in global differential geometry (53C22) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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Cites Work

• Unnamed Item
• A note on two problems in connexion with graphs
• Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression
• Off diagonal asymptotics of hypoelliptic diffusion equations and singular Riemannian geometry
• Coherence-enhancing diffusion filtering.
• Heat kernel expansion: user's manual
• Affine invariant geometry for non-rigid shapes
• Sparse non-negative stencils for anisotropic diffusion
• Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction
• Geodesic Methods in Computer Vision and Graphics
• Stochastic partial differential equations and filtering of diffusion processes
• Computing Discrete Minimal Surfaces and Their Conjugates
• Fast methods for the Eikonal and related Hamilton– Jacobi equations on unstructured meshes
• A fast marching level set method for monotonically advancing fronts.
• Approximate solutions to second order parabolic equations. I: Analytic estimates
• Restricted delaunay triangulations and normal cycle
• On the Partial Difference Equations of Mathematical Physics
• Diffusion processes in a small time interval

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