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

摘要

Abstract 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.