An efficient iterative method for reconstructing surface from point clouds
This work addresses a fundamental problem in computer vision for applications requiring surface reconstruction, presenting an incremental improvement with a novel iterative approach.
The paper tackles surface reconstruction from point clouds by developing an efficient iterative method based on a variational model with implicit indicator functions and heat kernel convolutions, achieving simplicity, efficiency, and accuracy in numerical experiments across 2D and 3D spaces.
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.