In this talk, we present some efficient numerical solvers for active contour models for multi-phase image segmentation problems. Iterative methods will be employed to minimize the given energy functionals. The proposed minimization algorithms enjoy the energy-decaying property under some conditions and have highly efficient performance in the segmentation. To overcome the initialization issue of active contour models, we develop a multi-phase inhomogeneous graph Laplacian initialization method to give the initial contour of numerical solvers. Numerical experiments are conducted on synthetic images and real images to demonstrate the capability of our initialization method, and the effectiveness of the numerical solvers in the image segmentation.