Topological properties of closed digital spaces: One method of constructing digital models of closed continuous surfaces by using covers

@article{citeulike:2572995, abstract = {This paper studies properties of closed digital n-dimensional spaces, which are digital models of continuous n-dimensional closed surfaces. We show that the minimal number of points in a closed digital n-dimensional space is 2n + 2 points. A closed digital n-dimensional space with 2n + 2 points is the minimal n-dimensional sphere, which is the join of n + 1 copies of the 0-dimensional sphere. We prove that a closed digital n-dimensional space cannot contain a closed digital n-dimensional subspace, which is different from the space itself. We introduce the general definition of a closed digital space and prove that a closed digital space is necessarily a closed digital n-dimensional space. Finally, we present conditions which guarantee that every digitization process preserves important topological and geometric properties of continuous closed 2-surfaces. These conditions also allow us to determine the correct digitization resolution for a given closed 2-surface.}, author = {Evako, Alexander V. }, citeulike-article-id = {2572995}, doi = {10.1016/j.cviu.2003.11.003}, journal = {Computer Vision and Image Understanding}, keywords = {combinatorics, topology}, month = {May}, number = {2}, pages = {134--144}, posted-at = {2008-03-22 18:17:53}, priority = {2}, title = {Topological properties of closed digital spaces: One method of constructing digital models of closed continuous surfaces by using covers}, url = {http://dx.doi.org/10.1016/j.cviu.2003.11.003}, volume = {102}, year = {2006} }

TY - JOUR ID - citeulike:2572995 L3 - citeulike-article-id:2572995 TI - Topological properties of closed digital spaces: One method of constructing digital models of closed continuous surfaces by using covers JF - Computer Vision and Image Understanding VL - 102 IS - 2 SP - 134 EP - 144 N2 - This paper studies properties of closed digital n-dimensional spaces, which are digital models of continuous n-dimensional closed surfaces. We show that the minimal number of points in a closed digital n-dimensional space is 2n + 2 points. A closed digital n-dimensional space with 2n + 2 points is the minimal n-dimensional sphere, which is the join of n + 1 copies of the 0-dimensional sphere. We prove that a closed digital n-dimensional space cannot contain a closed digital n-dimensional subspace, which is different from the space itself. We introduce the general definition of a closed digital space and prove that a closed digital space is necessarily a closed digital n-dimensional space. Finally, we present conditions which guarantee that every digitization process preserves important topological and geometric properties of continuous closed 2-surfaces. These conditions also allow us to determine the correct digitization resolution for a given closed 2-surface. KW - combinatorics KW - topology AU - Evako, Alexander PY - 2006/05// UR - http://dx.doi.org/10.1016/j.cviu.2003.11.003 ER -