Concepts and results of digital topology are used to specify and justify important (low-level) image analysis algorithms, including algorithms for thinning, border or surface tracing, counting of components or tunnels, or region-filling.
Digital topology was first studied in the late 1960s by the computer image analysis researcher Azriel Rosenfeld (1931–2004), whose publications on the subject played a major role in establishing and developing the field.
Theodosios Pavlidis (1982) suggested the use of graph-theoretic algorithms such as the depth-first search method for finding connected components.
He also proposed (2008) a more general axiomatic theory of locally finite topological spaces and abstract cell complexes formerly suggested by Ernst Steinitz (1908).
The book from 2008 contains new definitions of topological balls and spheres independent of a metric and numerous applications to digital image analysis.
David Morgenthaler and Rosenfeld (1981) gave a mathematical definition of surfaces in three-dimensional digital space.
A basic (early) result in digital topology says that 2D binary images require the alternative use of 4- or 8-adjacency or "pixel connectivity" (for "object" or "non-object" pixels) to ensure the basic topological duality of separation and connectedness.
This alternative use corresponds to open or closed sets in the 2D grid cell topology, and the result generalizes to 3D: the alternative use of 6- or 26-adjacency corresponds to open or closed sets in the 3D grid cell topology.