We consider a segmentation problem which arises in medical imaging and liver surgery. The model problem is based on an active contour without edges technique formulated in a level set dictionary. Previous work indicates that a feasible solution can be obtained solving the gradient descent equation associated to the original minimization problem but the convergence of the algorithm is too slow for practical clinical purposes. Here, we study the implementation of multigrid methods to the elliptic problem and the numerical results are compared with the parabolic approach
