A PDE Model for Smooth Surface Reconstruction from 2D Parallel Slices

In this letter, we propose a PDE model for 3D smooth surfaces reconstruction from 2D parallel slices. One of the terms in the PDE model is derived from a magnitude penalization term, which enforces the gradient magnitude of the volume to the minimum point of a well-defined potential function. This gives us smooth reconstructed surfaces when assuming that the surfaces are given by the zero-isosurfaces of the volumes. The PDE model has a second term whose parameter controls the ability of the reconstructed surfaces to satisfy the slices constraint. At the end of this letter, we show experiments of employing the proposed reconstruction model to reconstruct surfaces. The numerical results demonstrate the utility of the model.