Based on the idea that objects in a given image can be segmented by removing the background part, an unconstrained convex minimization problem is proposed. The penalization term added in the construction procedure of the proposed problem is proven to be viable, which is demonstrated by the experiment. At the computational level, a fixed-point operator and the corresponding algorithm are proposed by applying the theory of subdifferential and proximity operators, and Opial -averaged theorem. And then the convergence proof of the algorithm is given. Comparisons with other classical models show that the proposed segmentation model is more accurate. And the experiments also demonstrate that the fixed-point algorithm is faster than the gradient descent method and the split Bregman method. Moreover, the algorithm is robust to the initial curve and noise.