Digital topology deals with properties and features of two-dimensional (2D) or three-dimensional (3D) digital images that correspond to topological properties (e.g., connectedness) or topological features (e.g., frontiers) of objects. Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... 3-D or 3D abbreviates three dimensional and is often related to a stereoscopic display that exploits binocular vision. ... A digital image is a representation of a two-dimensional image as a finite set of digital values, called picture elements or pixels. ... In topology and related branches of mathematics, a topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. ... Frontiers - April 2006 Issue Frontiers is Southern Californias largest LGBT magazine. ...

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. Image analysis is the extraction of useful information from images; mainly from digital images by means of digital image processing techniques. ...

Digital topology was first studied in the late 1960's 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. The term digital topology was itself invented by Rosenfeld, who used it in a 1973 publication for the first time.

A basic (early) result in digital topology says that 2D binary images require the alternative use of 4- or 8-adjacency (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. Grid cell topology also applies to multilevel (e.g., color) 2D or 3D images, for example based on a total order of possible image values. A pixel (a contraction of picture element) is one of the many tiny dots that make up the representation of a picture in a computers memory. ...

See also: digital geometry, topology, and discrete mathematics. 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. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. ...

Books

• Kong, T.Y., and A. Rosenfeld (editors) (1996). Topological Algorithms for Digital Image Processing. Elsevier. ISBN 0-44489-754-2.

• Voss, K. (1993). Discrete Images, Objects, and Functions in Zn. Springer. ISBN 0-38755-943-4.

• Klette, R., and A. Rosenfeld (2004). Digital Geometry. Morgan Kaufmann. ISBN 1-55860-861-3.