digital manifold
{{short description|Special kind of combinatorial manifold which is defined in grid cell space}}
{{No footnotes|date=December 2022}}
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
References
- {{cite conference |author1=Chen, L. |author2=Zhang, J. | contribution=Digital manifolds: an intuitive definition and some properties | title=Proceedings on the second ACM symposium on Solid modeling and applications, Montreal, Quebec, Canada | year=1993 | pages=459–460|publisher=Association for Computing Machinery}}
- {{cite book |author1=Chen, L. | title= Digital and Discrete Geometry | publisher=Springer | year=2014}}