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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., boundaries) of objects. 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. == History == 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. The term "digital topology" was itself invented by Rosenfeld, who used it in a 1973 publication for the first time. A related work called the grid cell topology appeared in Alexandrov-Hopf's book Topologie I (1935) can be considered as a link to classic combinatorial topology. Rosenfeld ''et al.'' proposed digital connectivity such as 4-connectivity and 8-connectivity in two dimensions as well as 6-connectivity and 26-connectivity in three dimensions. The labeling method for inferring a connected component was studied in the 1970s. T. Pavlidis (1982) suggested the use of graph-theoretic algorithms such as the depth-first search method for finding connected components. V. Kovalevsky (1989) extended Alexandrov-Hopf's 2D grid cell topology to three and higher dimensions. He also proposed (2008) a more general axiomatic theory of locally finite topological spaces and abstract cell complexes formerly suggested by Steinitz (1908). It is the Alexandrov topology. The book of 2008 contains new definitions of topological balls and spheres independent of a metric and numerous applications to digital image analysis. In the early 1980s, digital surfaces were studied. Morgenthaler and Rosenfeld (1981) gave a mathematical definition of surfaces in three-dimensional digital space. This definition contains a total of nine types of digital surfaces. The digital manifold was studied in the 1990s. A recursive definition of the digital k-manifold was proposed intuitively by Chen and Zhang in 1993. Many applications were found in image processing and computer vision. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Digital topology」の詳細全文を読む スポンサード リンク
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