Digital topology
Overview
Three-dimensional space
Three-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...
(3D) digital images
that correspond to topological properties (e.g., connectedness
Connectedness
In mathematics, connectedness is used to refer to various properties meaning, in some sense, "all one piece". When a mathematical object has such a property, we say it is connected; otherwise it is disconnected...
) or topological features (e.g., boundaries
Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary...
) of objects.
Concepts and results of digital topology are used to specify and justify important (low-level) image analysis
Image analysis
Image analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques...
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
Azriel Rosenfeld
Professor Dr. Azriel Rosenfeld was an American Research Professor, a Distinguished University Professor, and Director of the Center for Automation Research at the University of Maryland in College Park, Maryland, where he also held affiliate professorships in the Departments of Computer Science,...
(1931–2004), whose publications on the subject played a major role in establishing and developing the field.
