Three-dimensional image reconstruction using the PF/MFS technique

We propose a geometric modeling method in R3R3 based on the so-called potential field (PF) modeling technique. The method is a new technique for surface reconstruction from a data set of scattered points taken on a surface. In this method, the construction of a geometric model is based on the solution of an elliptic boundary value problem determined using the method of fundamental solutions (MFS). We consider two such problems, Laplace's equation subject to Dirichlet boundary conditions and the biharmonic Dirichlet problem. We present the results of numerical experiments which demonstrate the efficacy of these approaches. We also identify differences and potential difficulties in the application of these approaches and propose ways of addressing them.