Adaptive variational curve smoothing based on level set method

Authors:
Yu Wang;Songhe Song;Zhijun Tan;Desheng Wang
Affiliations:
Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore;Department of Mathematics and System Science, School of Science, National University of Defense and Technology, Changsha, Hunan 410073, China;Singapore-MIT Alliance, 4 Engineering Drive 3, National University of Singapore, Singapore 117576, Singapore;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Venue:
Journal of Computational Physics
Year:
2009

Citing 12
Cited 2

Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

Journal of Computational Physics
A signal processing approach to fair surface design

SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Geodesic Active Contours

International Journal of Computer Vision
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains

Journal of Computational Physics
Weighted essentially non-oscillatory schemes on triangular meshes

Journal of Computational Physics
Implicit fairing of irregular meshes using diffusion and curvature flow

Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Anisotropic geometric diffusion in surface processing

Proceedings of the conference on Visualization '00
Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum

Journal of Computational Physics
Geometric surface smoothing via anisotropic diffusion of normals

Proceedings of the conference on Visualization '02
A three-dimensional adaptive method based on the iterative grid redistribution

Journal of Computational Physics
Mesh Generation: Application to Finite Elements

Mesh Generation: Application to Finite Elements
Fast Sweeping Methods for Eikonal Equations on Triangular Meshes

SIAM Journal on Numerical Analysis

On Variational Curve Smoothing and Reconstruction

Journal of Mathematical Imaging and Vision
Generalized edge-weighted centroidal Voronoi tessellations for geometry processing

Computers & Mathematics with Applications

Quantified Score

Hi-index	31.45

Visualization

Abstract

This paper presents an adaptive method for variational curve smoothing based on level set implementation. A suitable cost functional is minimized via solving the derived Euler-Lagrangian equation, of which the discretization is conducted on unstructured triangular meshes by employing a simple and effective finite volume scheme. Through adaptive refinement of the mesh, the geometry features of the given curve can be well resolved in a cost-effective way. Various numerical experiments demonstrate the effectiveness and efficiency of the proposed approach.