Repairing 3D Binary Images Using the FCC Grid

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.