http://dbpedia.org/ontology/abstract
|
The grid cell topology is studied in digit … 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. 2004. It is related to digital manifolds.
|
http://dbpedia.org/ontology/wikiPageID
|
5909220
|
http://dbpedia.org/ontology/wikiPageLength
|
1616
|
http://dbpedia.org/ontology/wikiPageRevisionID
|
785276645
|
http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Digital_manifold +
, http://dbpedia.org/resource/Heinz_Hopf +
, http://dbpedia.org/resource/Topology +
, http://dbpedia.org/resource/Pavel_Sergeevich_Alexandrov +
, http://dbpedia.org/resource/Computer_image_analysis +
, http://dbpedia.org/resource/Category:Digital_topology +
, http://dbpedia.org/resource/Alexandrov_topology +
, http://dbpedia.org/resource/Pixel_connectivity +
, http://dbpedia.org/resource/Digital_topology +
, http://dbpedia.org/resource/Computer_graphics +
, http://dbpedia.org/resource/Partial_order +
, http://dbpedia.org/resource/Two-dimensional +
, http://dbpedia.org/resource/Poset_topology +
|
http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:ISBN +
, http://dbpedia.org/resource/Template:Topology-stub +
, http://dbpedia.org/resource/Template:Cite_book +
|
http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Digital_topology +
|
http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Grid_cell_topology?oldid=785276645&ns=0 +
|
http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Grid_cell_topology +
|
owl:sameAs |
http://rdf.freebase.com/ns/m.0fd196 +
, http://www.wikidata.org/entity/Q5608608 +
, https://global.dbpedia.org/id/4kWrT +
, http://dbpedia.org/resource/Grid_cell_topology +
|
rdfs:comment |
The grid cell topology is studied in digit … 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.) partial order. (See also poset topology.)
|
rdfs:label |
Grid cell topology
|