CVT-Based 3D Image Segmentation for Quality Tetrahedral Meshing

  • Kangkang Hu
  • Yongjie Jessica ZhangEmail author
  • Guoliang Xu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10149)


Given an input 3D image, in this paper we first segment it into several clusters by extending the 2D harmonic edge-weighted centroidal Voronoi tessellation (HEWCVT) method to the 3D image domain. The Dual Contouring method is then applied to construct tetrahedral meshes by analyzing both material change edges and interior edges. An anisotropic Giaquinta-Hildebrandt operator (GHO) based geometric flow method is developed to smooth the surface with both volume and surface features preserved. Optimization based smoothing and topological optimizations are also applied to improve the quality of tetrahedral meshes. We have verified our algorithms by applying them to several datasets.


Centroidal voronoi tessellation Image segmentation Tetrahedral mesh Quality improvement Giaquinta-Hildebrandt operator 



The authors would like to thank Tao Liao for useful discussions on quality improvement techniques for tetrahedral mesh. The work of K. Hu and Y. Zhang was supported in part by NSF CAREER Award OCI-1149591. G. Xu was was supported in part by NSFC Fund for Creative Research Groups of China under the grant 11321061.


  1. 1.
    Arifin, A.Z., Asano, A.: Image segmentation by histogram thresholding using hierarchical cluster analysis. Pattern Recogn. Lett. 27(13), 1515–1521 (2006)CrossRefGoogle Scholar
  2. 2.
    Canann, S.A., Tristano, J.R., Staten, M.L.: An approach to combined Laplacian and optimization-based smoothing for triangular, quadrilateral, and quad-dominant meshes. In: 7th International Meshing Roundtable, pp. 479–494 (1998)Google Scholar
  3. 3.
    Chan, T.F., Vese, L.A.: Active contour and segmentation models using geometric PDEs for medical imaging. In: Malladi, R. (ed.) Geometric Methods in Bio-Medical Image Processing, pp. 63–75. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Cocosco, C.A., Kollokian, V., Kwan, R.K.S., Pike, G.B., Evans, A.C.: BrainWeb: online interface to a 3D MRI simulated brain database. NeuroImage 5(4), S425 (1997)Google Scholar
  5. 5.
    Du, Q., Faber, V., Gunzburger, M.: Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41(4), 637–676 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Du, Q., Gunzburger, M., Ju, L., Wang, X.: Centroidal Voronoi tessellation algorithms for image compression, segmentation, and multichannel restoration. J. Math. Imaging Vis. 24(2), 177–194 (2006)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Foteinos, P.A., Chrisochoides, N.P.: High quality real-time image-to-mesh conversion for finite element simulations. J. Parallel Distrib. Comput. 74(2), 2123–2140 (2014)CrossRefGoogle Scholar
  8. 8.
    Freitag, L.A.: On combining Laplacian and optimization-based mesh smoothing techniques. AMD-Vol. 220 Trends in Unstructured Mesh Generation, pp. 37–44 (1997)Google Scholar
  9. 9.
    Hu, K., Zhang, Y.: Image segmentation and adaptive superpixel generation based on harmonic edge-weighted centroidal Voronoi tessellation. Comput. Methods Biomech. Biomed. Eng.: Imaging Vis. 4(2), 46–60 (2016). The Special Issue of CompIMAGE’14Google Scholar
  10. 10.
    Leng, J., Zhang, Y., Xu, G.: A novel geometric flow approach for quality improvement of multi-component tetrahedral meshes. Comput. Aided Des. 45(10), 1182–1197 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Liao, T., Li, X., Xu, G., Zhang, Y.: Secondary Laplace operator and generalized Giaquinta-Hildebrandt operator with applications on surface segmentation and smoothing. Comput. Aided Des. 70, 56–66 (2016). A Special Issue of SIAM Conference on Geometric & Physical Modeling 2015MathSciNetCrossRefGoogle Scholar
  12. 12.
    Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Hege, H.C., Polthier, K. (eds.) Visualization and Mathematics III, pp. 35–57. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Pal, N.R., Pal, S.K.: A review on image segmentation techniques. Pattern Recogn. 26(9), 1277–1294 (1993)CrossRefGoogle Scholar
  14. 14.
    Pan, Q., Xu, G., Xu, G., Zhang, Y.: Isogeometric analysis based on extended Loop’s subdivision. J. Comput. Phys. 299, 731–746 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Pappas, T.N.: An adaptive clustering algorithm for image segmentation. IEEE Trans. Sig. Process. 40(4), 901–914 (1992)CrossRefGoogle Scholar
  16. 16.
    Ren, X., Malik, J.: Learning a classification model for segmentation. In: Ninth IEEE International Conference on Computer Vision, pp. 10–17 (2003)Google Scholar
  17. 17.
    Sijbers, J., Scheunders, P., Verhoye, M., der Linden, A.V., Dyck, D.V., Raman, E.: Watershed-based segmentation of 3D MR data for volume quantization. Magn. Reson. Imaging 15(6), 679–688 (1997)CrossRefGoogle Scholar
  18. 18.
    Tobias, O.J., Seara, R.: Image segmentation by histogram thresholding using fuzzy sets. IEEE Trans. Image Process. 11(12), 1457–1465 (2002)CrossRefGoogle Scholar
  19. 19.
    Tsuda, A., Filipovic, N., Haberthür, D., Dickie, R., Matsui, Y., Stampanoni, M., Schittny, J.C.: Finite element 3D reconstruction of the pulmonary acinus imaged by synchrotron X-ray tomography. J. Appl. Physiol. 105(3), 964–976 (2008)CrossRefGoogle Scholar
  20. 20.
    Wang, J., Ju, L., Wang, X.: An edge-weighted centroidal Voronoi tessellation model for image segmentation. IEEE Trans. Image Process. 18(8), 1844–1858 (2009)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Xu, G., Zhang, Q.: A general framework for surface modeling using geometric partial differential equations. Comput. Aided Geom. Des. 25(3), 181–202 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Zhang, Y., Bajaj, C., Sohn, B.S.: 3D finite element meshing from imaging data. Comput. Methods Appl. Mech. Eng. 194, 5083–5106 (2005)CrossRefzbMATHGoogle Scholar
  23. 23.
    Zhang, Y., Bajaj, C., Xu, G.: Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. Commun. Numer. Methods Eng. 25(1), 1–18 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Zhang, Y., Hughes, T., Bajaj, C.: An automatic 3D mesh generation method for domains with multiple materials. Comput. Methods Appl. Mech. Eng. 199(5–8), 405–415 (2010)CrossRefzbMATHGoogle Scholar
  25. 25.
    Zhang, Y., Qian, J.: Resolving topology ambiguity for multiple-material domains. Comput. Methods Appl. Mech. Eng. 247, 166–178 (2012)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Kangkang Hu
    • 1
  • Yongjie Jessica Zhang
    • 1
    Email author
  • Guoliang Xu
    • 2
  1. 1.Department of Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA
  2. 2.LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina

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