Enhanced optimal delaunay triangulation methods with connectivity regularization

In this paper, we study the underlying properties of optimal Delaunay triangulations (ODT) and propose enhanced ODT methods combined with connectivity regularization. Based on optimizing node positions and Delaunay triangulation iteratively, ODT methods are very effective in mesh improvement. This paper demonstrates that the energy function minimized by ODT is nonconvex and unsmooth, thus, ODT methods suffer the problem of falling into a local minimum inevitably. Unlike general ways that minimize the ODT energy function in terms of mathematics directly, we take an outflanking strategy combining ODT methods with connectivity regularization for this issue. Connectivity regularization reduces the number of irregular nodes by basic topological operations, which can be regarded as a perturbation to help ODT methods jump out of a poor local minimum. Although the enhanced ODT methods cannot guarantee to obtain a global minimum, it starts a new viewpoint of minimizing ODT energy which uses topological operations but mathematical methods. And in terms of practical effect, several experimental results illustrate the enhanced ODT methods are capable of improving the mesh furtherly compared to general ODT methods.