Journal of Mathematical Imaging and Vision

, Volume 61, Issue 9, pp 1301–1321 | Cite as

Repairing 3D Binary Images Using the FCC Grid

  • Lidija Čomić
  • Paola MagilloEmail author


A 3D image I is well-composed if it does not contain critical edges or vertices (where the boundary of I is non-manifold). The process of transforming an image into a well composed one is called repairing. We propose to repair 3D images by associating the face-centered cubic grid (FCC grid) with the cubic grid. We show that the polyhedral complex in the FCC grid, obtained by our repairing algorithm, is well-composed and homotopy equivalent to the complex naturally associated with the given image I with edge-adjacency (18-adjacency). We illustrate an application on two tasks related to the repaired image: boundary reconstruction and computation of its Euler characteristic.


Digital topology Discrete geometry Cubic grid Face-centered cubic (FCC) grid Well-composed images Repairing 3D binary images 



We thank Andrija Blesić for implementing the coordinate system and topological relations for the FCC grid.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia
  2. 2.Department of Computer Science, Bioengineering, Robotics, and Systems EngineeringUniversity of GenovaGenovaItaly

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