CVT-based 3D image segmentation and quality improvement of tetrahedral/hexahedral meshes using anisotropic Giaquinta-Hildebrandt operator

Given an input three-dimensional (3D) image in this paper, we first segment it into several clusters by extending the two-dimensional harmonic edge-weighted centroidal Voronoi tessellation method to the 3D image domain.The dual contouring method is then applied to construct tetrahedral meshes by analysing both material change edges and interior edges. Hexahedral meshes can also be generated by analysing each interior grid point. An anisotropic Giaquinta-Hildebrandt operator-based geometric flow method is developed to smooth the surface with both volume and surface features preserved. Optimisation-based smoothing and topological optimisations are also applied to improve the quality of tetrahedral and hexahedral meshes. We have verified our algorithms by applying them to several data-sets.