Well-Shaped, Stable, and Reversible Skeletons from the (3, 4)-Distance Transform

Abstract The skeleton of a digital pattern is extracted from the distance transform of the pattern, computed according to a quasi-Euclidean distance function. The pattern can be quite faithfully reconstructed by applying the reverse distance transformation to the skeleton, since this includes almost all the centers of the maximal discs of the pattern. The shape characterizing the discs is rounded, due the use of a quasi-Euclidean distance function, so that skeleton stability under pattern rotation is greatly favored. A pruning step, which makes it possible to simplify the structure of the skeleton without losing significant information, and a beautifying step, which is aimed at reducing the jaggedness possibly affecting some skeleton branches, are added to the process to improve the well-shapedness of the resulting skeleton.