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

Piecewise linear manifold

In mathematics, a piecewise linear manifold is a topological manifold together with a piecewise linear structure on it. Such a structure can be defined by means of an atlas, such that one can pass from chart to chart in it by piecewise linear functions.An isomorphism of PL manifolds is called a PL...

 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 geometry
  Digital geometry deals with discrete 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...
  
  
• Digital topology
  Digital topology
  Digital topology deals with properties and features of two-dimensional or three-dimensional digital imagesthat correspond to topological properties or topological features of objects....
  
  
• Topological data analysis
  Topological data analysis
  Topological data analysis is a new area of study aimed at having applications in areas such as data mining and computer vision.The main problems are:# how one infers high-dimensional structure from low-dimensional representations; and...
  
  
• Topology
  Topology
  Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
  
  
• Discrete mathematics
  Discrete mathematics
  Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...