The Euclidean Distance Transform Applied to the FCC and BCC Grids

Distance-Based Skeletonization on the BCC Grid

“…Here we note that d 8 and any a, b Chamfer distance have the same property [7]. Moreover, there are also linear time adaptations of the Euclidean distance transform on the BCC grid [20].…”

Generating Distance Maps with Neighbourhood Sequences

“…In [15], scanning masks to compute the Euclidean DT on the fcc and bcc grids were derived using the unfolded cube graph. Surprisingly, four scans are not sufficient for the bcc grid -five masks, i.e.…”

“…The following proposition follows directly from Theorem 3.5 in [18] (Z 2 and Z 3 ) and from the proofs of Theorem 2 and 5 in [15] for F and B respectively. Proposition 2.…”

“…One reason is that less samples can be used with the same representation/reconstruction quality compared to the cubic grid [12,13]. For example, image acquisition techniques [12,13], image processing algorithms [14,15,16] and visualization techniques [17] have been developed for these grids.…”

Distances in the face-centered cubic crystalline structure applying operational research

“…boundary tracking of objects built by Voronoi voxels of the f.c.c. lattice (Gardun ˜o et al, 1998;Herman, 1998), multispeed fuzzy segmentation algorithm (Carvalho et al, 2001), supercover (Linh et al, 2004), distance transform (Chen & Zhao, 2009;Fouard et al, 2007;Strand, 2005), surface skeletons (Strand, 2004;Karai, 2021), distance-driven curvethinning (Karai, 2022), topology-preserving marching cube like algorithms (Strand & Stelldinger, 2007), and ray-tracing and the object description method for objects sampled in the f.c.c. grid (Iba ´n ˜ez et al, 1997).…”