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Thinning on cell complexes from polygonal tilings

机译：通过多边形平铺细化细胞复合物

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This paper provides a theoretical foundation of a thinning method due to Kovalevsky for 2D digital binary images modelled by cell complexes or, equivalently, by Alexandroff To topological spaces, whenever these are constructed from polygonal tilings. We analyze the relation between local and global simplicity of cells, and prove their equivalence under certain conditions. For the proof we apply a digital Jordan theorem due to Neumann-Lara/Wilson which is valid in any connected planar locally Hamiltonian graph. Therefore we first prove that the incidence graph of the cell complex constructed from any polygonal tiling has these properties, showing that it is a triangulation of the plane. Moreover, we prove that the parallel performance of Kovalevsky's thinning method preserves topology in the sense that the numbers of connected components, for both the object and of the background, remain the same.
机译：本文提供了一种稀疏方法的理论基础，这种稀疏方法是基于Kovalevsky的二维数字二进制图像的建模，该二维二进制二进制图像由单元复合物或等效地由Alexandroff建模，只要它们是由多边形平铺构造的。我们分析了单元格的局部和全局简单性之间的关系，并证明了它们在某些条件下的等效性。为了证明这一点，我们根据Neumann-Lara / Wilson应用了数字约旦定理，该定理在任何连接的平面局部哈密顿图中均有效。因此，我们首先证明由任何多边形平铺构造的细胞复合体的入射图具有这些特性，表明它是平面的三角剖分。此外，我们证明了Kovalevsky的细化方法的并行性能在某种意义上保持了拓扑结构，即对象和背景的连接组件数保持不变。

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