A method for recovering a contour using combinatorial optimization includes receiving an input image, initializing functions for gradient f, smooth background g, and contour r, determining an optimum of the gradient f of a region R in the input image, extending the optimum of the gradient f of region R to a complement of R, determining an optimum of the smooth background function g for a region Q corresponding to the complement of R, extending the optimum of the smooth background function g of region Q to a complement of Q, and determining an optimum contour r according to the optimum of the gradient f and the optimum of the smooth background function g.