We propose a new robust and accurate method for the numerical solution of medical image segmentation. The modified Allen-Cahn equation is used to model the boundaries of the image regions. Its numerical algorithm is based on operator splitting techniques. In the first step of the splitting scheme, we implicitly solve the heat equation with the variable diffusive coefficient and a source term. Then, in the second step, using a closed-form solution for the nonlinear equation, we get an analytic solution. We overcome the time step constraint associated with most numerical implementations of geometric active contours. We demonstrate performance of the proposed image segmentation algorithm on several artificial as well as real image examples.