A pair of equivalent sequential and fully parallel 3D surface-thinning algorithms

Abstract

Thinning is an iterative object reduction to obtain skeletons from binary digital pictures. The object boundary is traversed in an iteration step of a sequential thinning algorithm, and the actually visited single point is considered for possible removal. On the contrary, parallel thinning algorithms can remove a set of object points simultaneously. In fully parallel thinning algorithms, the same parallel reduction is applied in each iteration step, and it is repeated until stability is reached. Two thinning algorithms are said to be equivalent if they produce the same result for any input picture. This paper presents the first pair of equivalent sequential and fully parallel 3D surface-thinning algorithms. The proposed algorithms use the same deletion rule, and preserve topology for $(26,6)$  pictures.