Discrete Delaunay: Boundary extraction from voxel objects

Abstract

We present a discrete approach for boundary extraction from 3D image data. The proposed technique is based on the duality between the Voronoi graph computed accross the digital boundary and the Delaunay triangulation. The originality of the approach is that algorithms perform only integer arithmetic and the method does not suffer from standard round problems and numerical instabilities in the case of floating point computations. This method has been applied both on segmented anatomical structures and on manufactured objects presenting corners and edges. The experimental results show that the method allows to produce a polygonal boundary representation which is guaranteed to be a 2-manifold. This representation is successfully transformed into a triangular quality mesh which meets all topological and geometrical requirements of applications such as augmented reality or simulation.