Some sequential algorithms for a generalized distance transformation based on Minkowski operations

A generalized distance transformation (GDT) of binary images and the related medial axis transformation (MAT) are discussed. These transformations are defined in a discrete space of arbitrary dimension and arbitrary grids. The GDT is based on successive morphological operations using alternatively N arbitrary structuring elements: N is called the period of the GDT. The GDT differs from the classical distance transformations based on a point-to-point distance. However, the well-known chessboard, city-block, and hexagonal distance transformations are special cases of the one-period GDT, whereas the octagonal distance transformation is a special case of the two-period GDT. In this paper, both one- and two-period GDTs are discussed. Different sequential algorithms are proposed for computing such GDTs. These algorithms need a maximum of two scannings of the image. The computation of the MAT is also discussed.>