A Spatial Convexity Descriptor for Object Enlacement

  • Sara Brunetti
  • Péter BalázsEmail author
  • Péter Bodnár
  • Judit Szűcs
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


In (Brunetti et al.: Extension of a one-dimensional convexity measure to two dimensions, LNCS 10256 (2017) 105–116) a spatial convexity descriptor is designed which provides a quantitative representation of an object by means of relative positions of its points. The descriptor uses so-called Quadrant-convexity and therefore, it is an immediate two-dimensional convexity descriptor. In this paper we extend the definition to spatial relations between objects and consider complex spatial relations like enlacement and interlacement. This approach permits to easily model these kinds of configurations as highlighted by the examples, and it allows us to define two interlacement descriptors which differ in the normalization. Experiments show a good behavior of them in the studied cases, and compare their performances.


Shape descriptor Spatial relations Q-convexity 


  1. 1.
    Balázs, P., Brunetti, S.: A measure of Q-convexity. In: Normand, N., Guédon, J., Autrusseau, F. (eds.) DGCI 2016. LNCS, vol. 9647, pp. 219–230. Springer, Cham (2016). Scholar
  2. 2.
    Balázs, P., Brunetti, S.: A new shape descriptor based on a Q-convexity measure. In: Kropatsch, W.G., Artner, N.M., Janusch, I. (eds.) DGCI 2017. LNCS, vol. 10502, pp. 267–278. Springer, Cham (2017). Scholar
  3. 3.
    Balázs, P., Ozsvár, Z., Tasi, T.S., Nyúl, L.G.: A measure of directional convexity inspired by binary tomography. Fundam. Inform. 141(2–3), 151–167 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bloch, I.: Fuzzy sets for image processing and understanding. Fuzzy Sets Syst. 281, 280–291 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bloch, I., Colliot, O., Cesar Jr., R.M.: On the ternary spatial relation “between”. IEEE Trans. Syst. Man Cybern. B Cybern. 36(2), 312–327 (2006)CrossRefGoogle Scholar
  6. 6.
    Boxer, L.: Computing deviations from convexity in polygons. Pattern Recogn. Lett. 14, 163–167 (1993)CrossRefGoogle Scholar
  7. 7.
    Brunetti, S., Balázs, P., Bodnár, P.: Extension of a one-dimensional convexity measure to two dimensions. In: Brimkov, V.E., Barneva, R.P. (eds.) IWCIA 2017. LNCS, vol. 10256, pp. 105–116. Springer, Cham (2017). Scholar
  8. 8.
    Brunetti, S., Daurat, A.: An algorithm reconstructing convex lattice sets. Theor. Comput. Sci. 304(1–3), 35–57 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Brunetti, S., Daurat, A.: Reconstruction of convex lattice sets from tomographic projections in quartic time. Theor. Comput. Sci. 406(1–2), 55–62 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Clement, M., Poulenard, A., Kurtz, C., Wendling, L.: Directional enlacement histograms for the description of complex spatial configurations between objects. IEEE Trans. Pattern Anal. Mach. Intell. 39, 2366–2380 (2017)CrossRefGoogle Scholar
  11. 11.
    Clément, M., Kurtz, C., Wendling, L.: Fuzzy directional enlacement landscapes. In: Kropatsch, W.G., Artner, N.M., Janusch, I. (eds.) DGCI 2017. LNCS, vol. 10502, pp. 171–182. Springer, Cham (2017). Scholar
  12. 12.
    Daurat, A.: Salient points of Q-convex sets. Int. J. Pattern Recognit. Artif. Intell. 15, 1023–1030 (2001)CrossRefGoogle Scholar
  13. 13.
    Daurat, A., Nivat, M.: Salient and reentrant points of discrete sets. Electron. Notes Discret. Math. 12, 208–219 (2003)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Frank, E., Hall, M.A., Witten, I.H.: The WEKA Workbench. Online Appendix for “Data Mining: Practical Machine Learning Tools and Techniques”, 4th edn. Morgan Kaufmann, Burlington (2016)Google Scholar
  15. 15.
    Fraz, M.M., et al.: An ensemble classification-based approach applied to retinal blood vessel segmentation. IEEE Trans. Biomed. Eng. 59(9), 2538–2548 (2012)CrossRefGoogle Scholar
  16. 16.
    Gorelick, L., Veksler, O., Boykov, Y., Nieuwenhuis, C.: Convexity shape prior for segmentation. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8693, pp. 675–690. Springer, Cham (2014). Scholar
  17. 17.
    Gorelick, L., Veksler, O., Boykov, Y., Nieuwenhuis, C.: Convexity shape prior for binary segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39, 258–271 (2017)CrossRefGoogle Scholar
  18. 18.
    Latecki, L.J., Lakamper, R.: Convexity rule for shape decomposition based on discrete contour evolution. Comput. Vis. Image Underst. 73(3), 441–454 (1999)CrossRefGoogle Scholar
  19. 19.
    Matsakis, P., Wendling, L., Ni, J.: A general approach to the fuzzy modeling of spatial relationships. In: Jeansoulin, R., Papini, O., Prade, H., Schockaert, S. (eds.) Methods for Handling Imperfect Spatial Information, vol. 256, pp. 49–74. Springer, Heidelberg (2010). Scholar
  20. 20.
    Odstrcilik, J., et al.: Retinal vessel segmentation by improved matched filtering: evaluation on a new high-resolution fundus image database. IET Image Process. 7(4), 373–383 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Rahtu, E., Salo, M., Heikkila, J.: A new convexity measure based on a probabilistic interpretation of images. IEEE Trans. Pattern Anal. 28(9), 1501–1512 (2006)CrossRefGoogle Scholar
  22. 22.
    Rosin, P.L., Zunic, J.: Probabilistic convexity measure. IET Image Process. 1(2), 182–188 (2007)CrossRefGoogle Scholar
  23. 23.
    Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis, and Machine Vision, 3rd edn. Thomson Learning, Toronto (2008)Google Scholar
  24. 24.
    Staal, J.J., Abramoff, M.D., Niemeijer, M., Viergever, M.A., Van Ginneken, B.: Ridge based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 23(4), 501–509 (2004)CrossRefGoogle Scholar
  25. 25.
    Stern, H.: Polygonal entropy: a convexity measure. Pattern Recogn. Lett. 10, 229–235 (1998)CrossRefGoogle Scholar
  26. 26.
    Tasi, T.S., Nyúl, L.G., Balázs, P.: Directional convexity measure for binary tomography. In: Ruiz-Shulcloper, J., Sanniti di Baja, G. (eds.) CIARP 2013. LNCS, vol. 8259, pp. 9–16. Springer, Heidelberg (2013). Scholar
  27. 27.
    Vanegas, M.C., Bloch, I., Inglada, J.: A fuzzy definition of the spatial relation “surround” - application to complex shapes. In: Proceedings of EUSFLAT, pp. 844–851 (2011)Google Scholar
  28. 28.
    Zunic, J., Rosin, P.L.: A new convexity measure for polygons. IEEE Trans. Pattern Anal. 26(7), 923–934 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sara Brunetti
    • 1
  • Péter Balázs
    • 2
    Email author
  • Péter Bodnár
    • 2
  • Judit Szűcs
    • 2
  1. 1.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheSienaItaly
  2. 2.Department of Image Processing and Computer GraphicsUniversity of SzegedSzegedHungary

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