A direct method for solving an anisotropic mean curvature flow of plane curves with an external force

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.