Math 671: Level set methods Variational level sets in shape reconstruction from unorganised data sets

Following in a vein similar to [Zhao et al., 2001], the goal of this project is to develop fast and accurate schemes to reconstruct shapes from unorganised data-sets using variational level set methods. The approach followed is based primarily on the gradient-flow scheme derived in class from variational considerations, and uses implementation details borrowed from [Zhao, 2004, Osher and Fedkiw, 2002]. Most notably, unlike the convection model followed in [Zhao et al., 2001], this current treatment also includes the curvature-based term (on the right hand side of Eq. (6)) neglected in their earlier work. Given an arbitrary set S = {points, curves, surfaces in N dimensions}, the basic problem at hand is the determination of an N dimensional surface Γ which minimises the error defined by