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 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
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Digital geometry
Digital geometry deals with discrete sets (usually discrete point sets) considered to be digitized models or images of objects of the 2D or 3D Euclidean space.
Simply put, ''digitizing'' is replacing an object by a discrete set of its points. ...
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Digital topology
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Topological data analysis
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Topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...
References
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*{{cite book , author1=Chen, L. , title= Digital and Discrete Geometry , publisher=Springer , year=2014
Digital topology
Digital geometry