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<p>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.</p>
mathematical morphology; image processing; sequential algorithms; generalized distance transformation; Minkowski operations; binary images; medial axis transformation; point-to-point distance; image processing; mathematical morphology; transforms

G. Bertrand and X. Wang, "Some Sequential Algorithms for a Generalized Distance Transformation Based on Minkowski Operations," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 14, no. , pp. 1114-1121, 1992.
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