Digital manifold
Special kind of combinatorial manifold which is defined in grid cell space
title: "Digital manifold" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["digital-topology", "digital-geometry"] description: "Special kind of combinatorial manifold which is defined in grid cell space" topic_path: "science/mathematics" source: "https://en.wikipedia.org/wiki/Digital_manifold" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Special kind of combinatorial manifold which is defined in grid cell space ::
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.
References
::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::