In mathematics, a digital manifold is a special kind of combinatorial manifold which is defined in digital space i.e. grid cell space. A combinatorial manifold is a kind of manifold which is a discretization of a manifold. It usually means a piecewise linear manifold made by simplicial complexes.
Concepts
Parallel-move is used to extend an i-cell to (i+1)-cell. In other words, if A and B are two i-cells and A is a parallel-move of B, then {A,B} is an (i+1)-cell. Therefore, k-cells can be defined recursively.
Basically, a connected set of grid points M can be viewed as a digital k-manifold if: (1) any two k-cells are (k-1)-connected, (2) every (k-1)-cell has only one or two parallel-moves, and (3) M does not contain any (k+1)-cells.
See also
Digital geometry
Digital topology
Topological data analysis
Topology
Discrete mathematics
References
Chen, L.; Zhang, J. (1993). "Digital manifolds: an intuitive definition and some properties". Proceedings on the second ACM symposium on Solid modeling and applications, Montreal, Quebec, Canada: 459–460.
Chen, L. (2014). "Digital and Discrete Geometry". Springer.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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