Reconstruction of Surfaces from Cross Sections Using Skeleton Information

  • Joaquín Pina Amargós
  • René Alquézar Mancho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2905)


Surface reconstruction from parallel cross sections is an important problem in medical imaging and other object-modeling applications. Shape and topological differences between object contours in adjacent sections cause severe difficulties in the reconstruction process. A way to approach this problem is using the skeleton to create intermediate sections that represent the place where the ramifications occur. Several authors have proposed previously the use of some type of skeleton to face the problem, but in an intuitive way and without giving a basis that guarantees a complete and correct use. In this paper, the foundations of the use of the skeleton to reconstruct a surface from cross sections are expounded. Some results of an algorithm that is based on these foundations and has been recently proposed by the authors are shown that illustrate the excellent performance of the method in especially difficult cases not solved previously.


Surface Reconstruction Medial Axis Adjacent Section Distance Field Intermediate Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bajaj, C.L., Coyle, E.J., Lin, K.N.: Arbitrary topology shape reconstruction from planar cross sections. Graphical Models and Image Processing 58, 524–543 (1996)CrossRefGoogle Scholar
  2. 2.
    Christiansen, H.N., Sederberg, T.W.: Conversion of contour line definitions into polygonal element mosaics. Computer Graphics 13, 187–192 (1978)CrossRefGoogle Scholar
  3. 3.
    Foley, J.D., Van Dam, A., Feinier, S.K., Hughes, J.F.: Computer Graphics: Principles and Practice, 2nd edn. in C. Addison-Wesley, Reading (1996)zbMATHGoogle Scholar
  4. 4.
    Geiger, B.: Tree-dimensional modeling of human organs and its applications to diagnosis and surgical planning. Technical report, 2105, INRIA, France (1993)Google Scholar
  5. 5.
    Kégl, B., Krzyzak, A.: Piecewise linear skeletonization using principal curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(1), 59–74 (2002)CrossRefGoogle Scholar
  6. 6.
    Klein, R., Schilling, A., Straßen, W.: Reconstruction and simplification of surface from contours. Graphical Models 62(6), 429–443 (2000)zbMATHCrossRefGoogle Scholar
  7. 7.
    Lee, S.W., Lam, L., Suen, C.: A systematic evaluation of skeletonization algorithms. Int. J. of Pattern Recognition and Artificial Intelligence 7(5), 1203–1225 (1993)CrossRefGoogle Scholar
  8. 8.
    Levin, D.: Multidimensional reconstruction by set-valued approximation. IMA J. Numerical Analysis (6), 173–184 (1986)Google Scholar
  9. 9.
    Meyers, D.: Reconstruction of surfaces from planar contours. Doctoral dissertation. University of Washington (1994)Google Scholar
  10. 10.
    Oliva, J.M., Perrin, M., Coquillart, S.: 3D reconstruction of complex polyhedral shapes from contours using a simplified generalized Voronoi diagram. Comp. Graphics Forum 15(3), C397–C408 (1996)Google Scholar
  11. 11.
    Pina, J., Alquézar, R.: Results of a new method for surface reconstruction from tomographic images. In: Proc., V Cong. Soc. Cub. de Bioingeniería, T0090, Havana, Cuba (2003)Google Scholar
  12. 12.
    Ritter, G.X., Wilson, J.N.: Handbook of Computer Vision Algorithms in Image Algebra, 2nd edn. CRC Press, Boca Raton (2001)zbMATHGoogle Scholar
  13. 13.
    Sloan, K.R., Hrechanyk, L.M.: Surface reconstruction from sparse data. In: Proc., IEEE Conf. on Patt. Recog. and Image Processing, Dallas, pp. 45–48 (1981)Google Scholar
  14. 14.
    Suzuki, S., Abe, K.: Sequential thinning of binary pictures using distance transformation. In: Proceedings of the 8th Int. Conf. on Patt. Recog., pp. 289–292 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Joaquín Pina Amargós
    • 1
  • René Alquézar Mancho
    • 2
  1. 1.Centro de Estudios de Ingeniería y Sistemas (CEIS)Polytechnic Institute “José A Echeverría” (CUJAE)HavanaCuba
  2. 2.Departament de Llenguatges i Sistemes Informàtics (LSI)Universitat Politècnica de Catalunya (UPC)BarcelonaSpain

Personalised recommendations