Conformal curvature flows: from phase transitions to active vision
From MaRDI portal
Publication:1815420
DOI10.1007/BF00379537zbMath0937.53029MaRDI QIDQ1815420
Arun Kumar, Satyanad Kichenassamy, Peter J. Olver, Allen Tannenbaum, Anthony J. Yezzi
Publication date: 11 December 1996
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Computing methodologies for image processing (68U10) Stefan problems, phase changes, etc. (80A22) Curves in Euclidean and related spaces (53A04) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items
Shock capturing, level sets, and PDE based methods in computer vision and image processing: A review of Osher's contributions ⋮ Adaptive cell-centered finite volume method for diffusion equations on a consistent quadtree grid ⋮ An analysis of the Perona-Malik scheme ⋮ An automated segmentation of NATURA 2000 habitats from sentinel-2 optical data ⋮ Semi-automatic segmentation of NATURA 2000 habitats in sentinel-2 satellite images by evolving open curves ⋮ Stability and consistency of the semi-implicit co-volume scheme for regularized mean curvature flow equation in level set formulation. ⋮ Geometrical image segmentation by the Allen-Cahn equation ⋮ Unnamed Item ⋮ Texture-oriented anisotropic filtering and geodesic active contours in breast tumor ultrasound segmentation ⋮ Segmentation of vectorial image features using shape gradients and information measures ⋮ Unnamed Item ⋮ Multiscale active contours ⋮ Recent advances of variational models in medical imaging and applications to computer aided surgery ⋮ A High-Order Scheme for Image Segmentation via a Modified Level-Set Method ⋮ Amoeba Techniques for Shape and Texture Analysis ⋮ Efficient 3D volume reconstruction from a point cloud using a phase-field method ⋮ Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case ⋮ Analysis of linearized version of active contours without gradient ⋮ An improved region-based model with local statistical features for image segmentation ⋮ Geodesic active contour under geometrical conditions: theory and 3D applications ⋮ A discrete level set approach to image segmentation ⋮ Automatic solution of jigsaw puzzles ⋮ Error estimates of the finite volume scheme for the nonlinear tensor-driven anisotropic diffusion ⋮ An unconditionally stable numerical method for bimodal image segmentation ⋮ Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods ⋮ Total Variation in Imaging ⋮ 3D edge detection by selection of level surface patches ⋮ A variational model for object segmentation using boundary information and shape prior driven by the Mumford-Shah functional ⋮ Inflow-implicit/outflow-explicit finite volume methods for solving advection equations ⋮ Evolution of curves on a surface driven by the geodesic curvature and external force ⋮ Active contour directed by the Poisson gradient vector field and edge tracking ⋮ Numerical algorithm for tracking cell dynamics in 4D biomedical images ⋮ Mathematical methods in medical image processing ⋮ Long time behavior of Riemannian mean curvature flow of graphs ⋮ Nonlinear PDE based numerical methods for cell tracking in zebrafish embryogenesis ⋮ Analysis of amoeba active contours
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Multiphase thermomechanics with interfacial structure. I: Heat conduction and the capillary balance law
- Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
- The maximum principle for semicontinuous functions
- Flow by mean curvature of convex surfaces into spheres
- Curve shortening makes convex curves circular
- Motion of level sets by mean curvature. I
- On the formation of singularities in the curve shortening flow
- Some recent developments in differential geometry
- Flow of nonconvex hypersurfaces into spheres
- Deforming convex hypersurfaces by the \(n\)th root of the Gaussian curvature
- The heat equation shrinking convex plane curves
- Curvature and the evolution of fronts
- Constraints on deformable models: Recovering 3D shape and nonrigid motion
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- The heat equation shrinks embedded plane curves to round points
- Toward a nonequilibrium thermodynamics of two-phase materials
- A short note on the evolution of a surface by its mean curvature
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Crystal growth and dendritic solidification
- On the evolution of curves via a function of curvature. I: The classical case
- Shortening embedded curves
- Axioms and fundamental equations of image processing
- On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
- A dynamic mesh algorithm for curvature dependent evolving interfaces
- Feature-Oriented Image Enhancement Using Shock Filters
- Fast Reaction, Slow Diffusion, and Curve Shortening
- Riemann Solvers, the Entropy Condition, and Difference
- The Equations for Large Vibrations of Strings
- Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II
- User’s guide to viscosity solutions of second order partial differential equations
- Phase transitions and generalized motion by mean curvature
- The Motion of a Surface by Its Mean Curvature. (MN-20)
- Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations
- What is the Best Causal Scale Space for Three-Dimensional Images?
- Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
- Numerical Methods in Fluid Dynamics