A variational phase field method for curve smoothing

A variational phase field model is proposed for curve smoothing, in which a weight function is associated with the similarity measure term in the model so that important geometric features could be well preserved. Finite element approximation of the proposed model is given for its numerical implementation. Since the model has a linear weak variational form, the discretized system could be solved efficiently by many existing solution techniques. An effective algorithm is also developed, for the purpose of feature preservation, to automatically determine the weight from the given data. Various numerical examples are presented to demonstrate effectiveness and robustness of the proposed method.