Bezier Curve Based Continuous Medial Representation for Shape Analysis: A Theoretical Framework

  • Leonid Mesteskiy
  • B. H. Shekar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10682)


In this paper, we introduce a continuous medial representation (skeleton + radial function) to compute the description of a given bitmap image. The computational geometry based mathematical model is proposed to obtain the continuous medial representation unlike traditional algorithms which are used to estimate medial representation of bitmap image in a discrete/heuristic manner. The skeleton of the polygonal figure is represented by straight line control graph of a compound Bezier curve which results in simple and accurate description. The process of pruning is devised to eliminate the spurious branches which are quite often exist while processing shapes in real scenario and hence continuous skeleton regularization is achieved for its accurate representation.


Skeleton Medial axis Radial function Continuous representation Bezier curve Shape analysis 



This work is supported by Russian Foundation for Basic Research, RFBR Grant No. 16-57-45054 and Department of Science and Technology Grant No. INT/RUS/RFBR/P-248.


  1. 1.
    Blum, H., et al.: A transformation for extracting new descriptors of shape. In: Models for the Perception of Speech and Visual Form, vol. 19, no. 5, pp. 362–380 (1967)Google Scholar
  2. 2.
    da Fona Costa, L., Cesar Jr., R.M.: Shape analysis and classification: theory and practice. CRC Press, Inc. (2000)Google Scholar
  3. 3.
    Deng, W., Iyengar, S.S., Brener, N.E.: A fast parallel thinning algorithm for the binary image skeletonization. Int. J. High Perform. Comput. Appl. 14(1), 65–81 (2000)CrossRefGoogle Scholar
  4. 4.
    Goutsias, J., Schonfeld, D.: Morphological representation of discrete and binary images. IEEE Trans. Signal Process. 39(6), 1369–1379 (1991)CrossRefGoogle Scholar
  5. 5.
    Lee, D.-T.: Medial axis transformation of a planar shape. IEEE Trans. Pattern Anal. Mach. Intell. 4, 363–369 (1982)CrossRefzbMATHGoogle Scholar
  6. 6.
    Lee, D.-T., Drysdale III, R.L.: Generalization of Voronoi diagrams in the plane. SIAM J. Comput. 10(1), 73–87 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Mestetskiy, L.M.: Skeletonization of a multiply-connected polygonal domain based on its boundary adjacent tree. Sibirskii Zhurnal Vychislitel’noi Matematiki 9(3), 299–314 (2006)zbMATHGoogle Scholar
  8. 8.
    Siddiqi, K., Pizer, S.M.: Medial Representations: Mathematics, Algorithms and Applications, vol. 37. Springer, Dordrecht (2008)zbMATHGoogle Scholar
  9. 9.
    Strzodka, R., Telea, A.: Generalized distance transforms and skeletons in graphics hardware. In: Proceedings of the Sixth Joint Eurographics-IEEE TCVG conference on Visualization. Eurographics Association, pp. 221–230 (2004)Google Scholar
  10. 10.
    Chazelle, B.: A theorem on polygon cutting with applications. In: Proceedings 23th IEEE Symposium on Foundations of Computer Science, Chicago, pp. 339–349 (1982)Google Scholar
  11. 11.
    Mestetskii, L.M.: Representation of segment Voronoi diagram by Bezier curves. Program. Comput. Softw. 41(5), 279–288 (2015)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Mangalore UniversityMangaloreIndia

Personalised recommendations