Digital Jordan curves
نویسندگان
چکیده
منابع مشابه
Jordan Curves in the Digital Plane
Abstract. We discuss certain interrelated pretopologies on the digital plane Z2 including the Khalimsky topology and several other topologies on Z2 . We present a digital analogue of the Jordan curve theorem for each of the pretopologies to demonstrate that they can provide background structures on Z2 convenient for the study of geometric and topological properties of two-dimensional digital im...
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Efim Khalimsky’s digital Jordan curve theorem states that the complement of a Jordan curve in the digital plane equipped with the Khalimsky topology has exactly two connectivity components. We present a new, short proof of this theorem using induction on the Euclidean length of the curve. We also prove that the theorem holds with another topology on the digital plane but then only for a restric...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2006
ISSN: 0166-8641
DOI: 10.1016/j.topol.2005.10.011