Constructing iso-surfaces satisfying the Delaunay constraint. Application to the skeleton computation

We design a new model for an image iso-surface which lies in the Delaunay graph of its vertices. Within each 8-cube of the image, a set of loops is computed according to the connectedness chosen for inner and outer voxels. Next, a triangulation is computed which respects the local geometry of these loops. Efficiency is obtained through the use of a look-up table which summarizes the algebraic tests that are required of each case. The inclusion of the iso-surface in the Delaunay triangulation has significant consequences. We derive a volume representation of the object, along with its skeleton. An example depicts the complete construction of our iso-surface, volume representation and skeleton computation.