A new approach to image segmentation is presented using a variation framework. Regarding the edge points as interpolating points and minimizing an energy functional to interpolate a smooth threshold surface it carries out the image segmentation. In order to preserve the edge information of the original image in the threshold surface, without unduly sharping the edge of the image, a non-convex energy functional is adopted. A relaxation algorithm with the property of global convergence, for solving the optimization problem, is proposed by introducing a binary energy. As a result the non-convex optimization problem is transformed into a series of convex optimization problems, and the problem of slow convergence or nonconvergence is solved. The presented method is also tested experimentally. Finally the method of determining the parameters in optimizing is also explored.
