A fast level-set approach to 2D and 3D reconstruction from unorganized sample points

In this paper we propose a novel algorithm for the reconstruction of surfaces from sets of unorganized sample points, based on the temporal evolution of a volumetric function´s level-set. The evolving front can be thought of as the surface that separates two different fluids that obey specific laws of fluid dynamics. One remarkable feature of this approach is its ability to model complex topologies thanks to a novel strategy that allows us to steer the front evolution using Voronoi surfaces in 3D space. Another remarkable feature of this algorithm is its computational efficiency, which proved to between one and two orders of magnitude better than traditional level-set approaches J.A. Sethian (1999).