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

Abstract

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.

Keywords:

• Centroidal Voronoi tessellation
• image segmentation
• tetrahedral mesh
• hexahedral mesh
• quality improvement
• Giaquinta–Hildebrandt operator

Acknowledgements

The preliminary version of this paper was published in the CompImage’16 conference (Hu et al., 2016). The authors would like to thank Tao Liao for useful discussions on quality improvement techniques for tetrahedral mesh.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of K. Hu and Y. Zhang was supported in part by NSF CAREER Award [OCI-1149591]. G. Xu was supported in part by NSFC Fund for Creative Research Groups of China [grant number 11321061].