A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
✍ Scribed by Karol Mikula; Daniel S̆evc̆ovic̆
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 495 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.514
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✦ Synopsis
Abstract
A new method for solution of the evolution of plane curves satisfying the geometric equation v=β(x,k,ν), where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ⊂ ℝ^2^ at the point x∈Γ, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non‐trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd.