Digital Jordan Curve Theorems

@incollection{citeulike:2572978, abstract = {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 restricted class of Jordan curves.}, author = {Kiselman, Christer }, citeulike-article-id = {2572978}, doi = {10.1007/3-540-44438-6\_5}, journal = {Discrete Geometry for Computer Imagery}, keywords = {combinatorics, topology}, pages = {46--56}, posted-at = {2008-03-22 18:15:58}, priority = {2}, title = {Digital Jordan Curve Theorems}, url = {http://dx.doi.org/10.1007/3-540-44438-6\_5}, year = {2000} }

TY - CHAP ID - citeulike:2572978 L3 - citeulike-article-id:2572978 TI - Digital Jordan Curve Theorems JF - Discrete Geometry for Computer Imagery SP - 46 EP - 56 N2 - 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 restricted class of Jordan curves. KW - combinatorics KW - topology AU - Kiselman, Christer PY - 2000/// UR - http://dx.doi.org/10.1007/3-540-44438-6_5 ER -