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= (x; k; ), where v is the normal velocity, k and are the curvature and tangential angle of a plane curve ⊂R2 at the point x∈ , is proposed. We derive a governing system of partial di erential 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 nd a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright ? 2004 John Wiley & Sons, Ltd.