# Repairing 3D Binary Images Using the FCC Grid

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## Abstract

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.

## Keywords

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

### Acknowledgements

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

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