Digital manifold


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 -cell. In other words, if A and B are two i-cells
and A is a parallel-move of B, then is an -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:
any two k-cells are -connected, every -cell has
only one or two parallel-moves, and M does not contain any -cells.