  Surface reconstruction from point clouds is a fundamental step in many
applications in computer vision. In this paper, we develop an efficient
iterative method on a variational model for the surface reconstruction from
point clouds. The surface is implicitly represented by indicator functions and
the energy functional is then approximated based on such representations using
heat kernel convolutions. We then develop a novel iterative method to minimize
the approximate energy and prove the energy decaying property during each
iteration. We then use asymptotic expansion to give a connection between the
proposed algorithm and active contour models. Extensive numerical experiments
are performed in both 2- and 3- dimensional Euclidean spaces to show that the
proposed method is simple, efficient, and accurate.
