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

机译:基于Minkowski运算的广义距离变换的一些顺序算法

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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.
机译:讨论了二值图像的广义距离变换(GDT)和相关的中间轴变换(MAT)。这些变换是在任意尺寸和任意网格的离散空间中定义的。 GDT基于交替使用N个任意结构元素的连续形态运算:N称为GDT的周期。 GDT与基于点对点距离的经典距离转换不同。但是,众所周知的棋盘,城市街区和六边形距离变换是一周期GDT的特例,而八边形距离变换是二周期GDT的特例。在本文中,将讨论一期和两期GDT。提出了用于计算这样的GDT的不同的顺序算法。这些算法最多需要对图像进行两次扫描。还讨论了MAT的计算。

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