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The grid cell topology is studied in digital topology as part of the theoretical basis for (low-level) algorithms in computer image analysis or computer graphics. The elements of the ''n''-dimensional grid cell topology (''n'' ≥ 1) are all ''n''-dimensional grid cubes and their ''k''-dimensional faces ( for 0 ≤ ''k'' ≤ ''n''−1); between these a partial order ''A'' ≤ ''B'' is defined if ''A'' is a subset of ''B'' (and thus also dim(''A'') ≤ dim(''B'')). The grid cell topology is the Alexandrov topology (open sets are up-sets) with respect to this partial order. (See also poset topology.) Alexandrov and Hopf first introduced the grid cell topology, for the two-dimensional case, within an exercise in their text ''Topologie'' I (1935). A recursive method to obtain ''n''-dimensional grid cells and an intuitive definition for grid cell manifolds can be found in Chen, 2004. It is related to digital manifolds. == See also == * Pixel connectivity 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「grid cell topology」の詳細全文を読む スポンサード リンク
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