Skeleton Marching-based Parallel Vascular Geometry Reconstruction Using Implicit Functions

  • Quan Qi
  • Qing-De LiEmail author
  • Yongqiang Cheng
  • Qing-Qi Hong
Open Access
Review Special Issue on Improving Productivity Through Automation and Computing


Fast high-precision patient-specific vascular tissue and geometric structure reconstruction is an essential task for vascular tissue engineering and computer-aided minimally invasive vascular disease diagnosis and surgery. In this paper, we present an effective vascular geometry reconstruction technique by representing a highly complicated geometric structure of a vascular system as an implicit function. By implicit geometric modelling, we are able to reduce the complexity and level of difficulty of this geometric reconstruction task and turn it into a parallel process of reconstructing a set of simple short tubular-like vascular sections, thanks to the easy-blending nature of implicit geometries on combining implicitly modelled geometric forms. The basic idea behind our technique is to consider this extremely difficult task as a process of team exploration of an unknown environment like a cave. Based on this idea, we developed a parallel vascular modelling technique, called Skeleton Marching, for fast vascular geometric reconstruction. With the proposed technique, we first extract the vascular skeleton system from a given volumetric medical image. A set of sub-regions of a volumetric image containing a vascular segment is then identified by marching along the extracted skeleton tree. A localised segmentation method is then applied to each of these sub-image blocks to extract a point cloud from the surface of the short simple blood vessel segment contained in the image block. These small point clouds are then fitted with a set of implicit surfaces in a parallel manner. A high-precision geometric vascular tree is then reconstructed by blending together these simple tubular-shaped implicit surfaces using the shape-preserving blending operations. Experimental results show the time required for reconstructing a vascular system can be greatly reduced by the proposed parallel technique.


Vascular geometric reconstruction implicit modelling parallel computing high-performance high-accuracy 



This work was partly supported by National Natural Science Foundation of China (No. 61502402), and the Fundamental Research Funds for the Central Universities (No. 20720180073).

The authors would like to thank all the reviewers for their constructive comments.


  1. [1]
    WHO. Cardiovascular Diseases (CVDs), [Online], Available:, July 4, 2017.Google Scholar
  2. [2]
    WHO. World Health Statistics 2017, Geneva, Switzerland: World Health Organization, 2017.Google Scholar
  3. [3]
    A. Alwan. Global Status Report on Noncommunicable Diseases 2010, Technical Report, World Health Organization, Geneva, Switzerland, 2011.Google Scholar
  4. [4]
    D. Lesage, E. D. Angelini, I. Bloch, G. Funka-Lea. A review of 3D vessel lumen segmentation techniques: Models, features and extraction schemes. Medical Image Analysis, vol. 13, no. 6, pp. 819–845, 2009. DOI: Scholar
  5. [5]
    M. R. Jr. Lepore, M. Yoselevitz, W. C. Sternbergh III, S. R. Money. Minimally invasive vascular techniques. The Ochsner Journal, vol. 2, no. 3, pp. 145–152, 2000.Google Scholar
  6. [6]
    B. Preim and S. Oeltze. 3D visualization of vasculature: An overview. Visualization in Medicine and Life Sciences, L. Linsen, H. Hagen, B. Hamann, Eds., Berlin Heidelberg, Germany: Springer, pp. 39–59, 2008. DOI: Scholar
  7. [7]
    J. Bloomenthal. Skeletal Design of Natural Forms, Ph. D. dissertation, Department of Computer Science, University of Calgary, Calgary, Canada, 1995.Google Scholar
  8. [8]
    J. Bloomenthal, C. Bajaj. Introduction to Implicit Surfaces, San Francisco, USA: Morgan Kaufmann, 1997.zbMATHGoogle Scholar
  9. [9]
    Q. Li. Smooth piecewise polynomial blending operations for implicit shapes. Computer Graphics Forum, vol. 26, no. 2, pp. 157–171, 2007. DOI: Scholar
  10. [10]
    X. L. Wu, V. Luboz, K. Krissian, S. Cotin, S. Dawson. Segmentation and reconstruction of vascular structures for 3D real-time simulation. Medical Image Analysis, vol. 15, no. 1, pp. 22–34, 2011. DOI: Scholar
  11. [11]
    Q. Q. Hong, Q. D. Li, J. Tian. Implicit reconstruction of vasculatures using bivariate piecewise algebraic splines. IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp. 543–553, 2012. DOI: Scholar
  12. [12]
    J. Kretschmer, C. Godenschwager, B. Preim, M. Stamminger. Interactive patient-specific vascular modeling with sweep surfaces. IEEE Transactions on Visualization and Computer Graphics, vol. 19, no. 12, pp. 2828–2837, 2013. DOI: Scholar
  13. [13]
    W. E. Lorensen, H. E. Cline. Marching cubes: A high resolution 3D surface construction algorithm. ACM SIGGRAPH Computer Graphics, vol. 21, no. 4, pp. 163–169, 1987. DOI: Scholar
  14. [14]
    Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, H. P. Seidel. Multi-level partition of unity implicits. ACM Transactions on Graphics, vol. 22, no. 3, pp. 463–470, 2003. DOI: Scholar
  15. [15]
    Q. Qi, Q. D. Li, Q. Q. Hong. Skeleton marching: A high-performance parallel vascular geometry reconstruction technique. In Proceedings of the 24th International Conference on Automation and Computing, ICAC, Newcastle Upon Tyne, UK, pp. 1–6, 2018.Google Scholar
  16. [16]
    H. K. Zhao, S. Osher, R. Fedkiw. Fast surface reconstruction using the level set method. In Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision, IEEE, Vancouver, Canada, pp. 194–201, 2001. DOI: Scholar
  17. [17]
    M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, C. T. Silva. Computing and rendering point set surfaces. IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 1, pp. 3–15, 2003. DOI: Scholar
  18. [18]
    G. Guennebaud, M. Gross. Algebraic point set surfaces. ACM Transactions on Graphics, vol. 26, no. 3, Article number 23, 2007. DOI:
  19. [19]
    G. Turk, J. F. O’Brien. Variational Implicit Surfaces, Technical Report GIT-GVU-99-15, Georgia Institute of Technology, USA, 1999.Google Scholar
  20. [20]
    S. F. Frisken, R. N. Perry, A. P. Rockwood, T. R. Jones. Adaptively sampled distance fields: A general representation of shape for computer graphics. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, ACM, New Orleans, USA, pp. 249–254, 2000. DOI: Scholar
  21. [21]
    J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, T. R. Evans. Reconstruction and representation of 3D objects with radial basis functions. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, ACM, Los Angeles, USA, pp. 67–76, 2001. DOI: Scholar
  22. [22]
    Q. Li, D. Wills, R. Phillips, W. J. Viant, J. G. Griffiths, J. W. Ward. Implicit fitting using radial basis functions with ellipsoid constraint. Computer Graphics Forum, vol. 23, no. 1, pp. 55–69, 2004. DOI: Scholar
  23. [23]
    W. J. Schroeder, W. E. Lorensen, S. Linthicum. Implicit modeling of swept surfaces and volumes. In Proceedings of the Conference on Visualization’94, IEEE, Washington DC, USA, USA, pp. 40–45, 1994. DOI: Scholar
  24. [24]
    Q. D. Li, J. Tian. 2D piecewise algebraic splines for implicit modeling. ACM Transactions on Graphics, vol. 28, no. 2, Article number 13, 2009. DOI:
  25. [25]
    C. Twigg. Catmull-Rom splines. Computer, vol. 41, no. 6, pp. 4–6, 2003.Google Scholar
  26. [26]
    O. Gourmel, L. Barthe, M. P. Cani, B. Wyvill, A. Bernhardt, M. Paulin, H. Grasberger. A gradient-based implicit blend. ACM Transactions on Graphics, vol. 32, no. 2, Article number 12, 2013. DOI:
  27. [27]
    A. Pressley. Elementary Differential Geometry, London, UK: Springer, 2010. DOI: Scholar
  28. [28]
    L. Antiga, M. Piccinelli, L. Botti, B. Ene-Iordache, A. Remuzzi, D. A. Steinman. An image-based modeling framework for patient-specific computational hemodynamics. Medical & Biological Engineering & Computing, vol. 46, no. 11, pp. 1097–1112, 2008. DOI: Scholar
  29. [29]
    G. S. Almasi, A. Gottlieb. Highly Parallel Computing, Redwood City, USA: Benjamin-Cummings Publishing Co., Inc., 1989.zbMATHGoogle Scholar
  30. [30]
    J. D. Owens, D. Luebke, N. Govindaraju, M. Harris, J. Kruger, A. E. Lefohn, T. J. Purcell. A survey of general-purpose computation on graphics hardware. Computer Graphics Forum, vol. 26, no. 1, pp. 80–113, 2007. DOI: Scholar
  31. [31]
    B. X. Wu, S. U. Ay, A. Abdel-Rahim. Pedestrian height estimation and 3D reconstruction using pixel-resolution mapping method without special patterns. International Journal of Automation and Computing, vol. 16, no. 4, pp. 449–361, 2019. DOI: Scholar

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Authors and Affiliations

  1. 1.College of Information Science and TechnologyShihezi UniversityShiheziChina
  2. 2.Department of Computer Science and TechnologyUniversity of HullHullUK
  3. 3.Software SchoolXiamen UniversityXiamenChina

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