A geometric model for segmentation of images with missing boundaries is presented. Some classical problems of boundary completion in cognitive images, like the pop up of subjective contours in the famous triangle of Kanizsa, are faced from a surface evolution point of view. The method is based on the mean curvature evolution of a graph with respect to the Riemannian metric induced by the image. Existence, uniqueness and maximum principle of the parabolic partial differential equation are proved. A numerical scheme introduced by Osher and Sethian for evolution of fronts by curvature motion is adopted. Results are presented both for modal completion of cognitive objects and segmentation of medical images with missing boundaries.