Abstract: Active contour models are successfully and widely used in image segmentation. However, they always get local minima which make wrong segmentation results. In this paper, based on previous work named background removed model, a convex energy which is obtained by approximating the Heaviside function in the previous nonconvex energy is proposed. By minimizing it, the evolution equation is given. Experimental results show that the proposed method is accurate, fast and antinoise. Moreover, it is not sensitive to the location of the initial curve.