数字拓扑中的保连通性多值函数
Connectivity Preserving Multivalued Functions in Digital Topology
摘要：
我们研究数字图像之间的连通性保持多值函数。这个概念推广了大多数在数字平面$Z^2$上研究的连续多值函数的概念。我们表明，连接保持多值函数，连续多值函数，是合适的模型，数字形态学操作。与连续性不同的是，连通性保持是通过组合来保持的，并且很容易推广到高维和任意邻接关系。
英文摘要：
We study connectivity preserving multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morpholological operations. Connectivity preservation, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
