Invertible Polygonalization of 3D Planar Digital Curves and Application to Volume Data Reconstruction

In this paper, we describe a new algorithm to compute in linear time a 3D planar polygonal curve from a planar digital curve, that is a curve which belongs to a digital plane. Based on this algorithm, we propose a new method for converting the boundary of digital volumetric objects into polygonal meshes which aims at providing a topologically consistent and invertible reconstruction, i.e. the digitization of the obtained object is equal to the original digital data. Indeed, we do not want any information to be added or lost. In order to limit the number of generated polygonal faces, our approach is based on the use of digital geometry tools which allow the reconstruction of large pieces of planes.