Computing the Number of Bubbles and Tunnels of a 3-D Binary Object

  • Humberto SossaEmail author
  • Hermilo Sánchez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10163)


We present two formulations and two procedures that can be used for computing the number of bubbles and tunnels of a 3-D binary object. The first formulation is useful to determine the number of bubbles of an object, while the second one can be used to calculate the number of tunnels of an object. Both formulations are formally demonstrated. Examples are provided to numerically validate the functioning of both formulations. On the other hand, the first procedure allows obtaining the number of bubbles and tunnels of a 3-D object while the second procedure allows computing the number of bubbles and tunnels of several 3-D objects. Examples with 3-D images are provided to illustrate the utility and validity of the second procedure.


Betti Number Euler Number Vertical Slice Human Trabecular Bone Maximal Ball 
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.



H. Sossa thanks COFAA-IPN, SIP-IPN and CONACYT under Grants 20151187, 20161126, 155014 and 65 (Frontiers of Science), respectively, for the economic support to carry out this research. E. Sánchez thanks the Centro de Ciencias Básicas of the Universidad Autónoma de Aguascalientes for the support.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Instituto Politécnico Nacional-CICMexico CityMexico
  2. 2.Centro de Ciencias BásicasUniversidad Autónoma de AguascalientesAguascalientesMexico

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