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• A graph, non-tree representation of the topology of a gray scale image by Saveliev
  ...f these sets, and the [[topology]] of the image, by means of a graph. This graph contains the well-known [[inclusion tree]]s, but it is not a tree in genera ...e also a clear hierarchy based on [[inclusion]]. This hierarchy provides a graph representation of the topology of the image. It is called the [[inclusion t
  41 KB (6,854 words) - 15:05, 28 October 2011
• Topology of graphs
  ...structure that needs to be analyzed topologically is ''graphs''<!--\index{graph}-->: [[Image:graph examples.png|center]]
  25 KB (4,214 words) - 16:08, 28 November 2015
• Algebra on graphs
  ...structure that needs to be analyzed topologically is ''graphs''<!--\index{graph}-->: [[Image:graph examples.png| center]]
  36 KB (6,177 words) - 02:47, 21 February 2016
• Maps of graphs
  ...mations with their discrete counterparts, as functions of graphs<!--\index{graph}-->: So, we have learned that a function<!--\index{graph function}--> $f:G\to J$ between graphs should be a combination of two, the
  29 KB (5,042 words) - 17:57, 28 November 2015
• The topology of a binary image
  ...d holes is constructed. The algorithm for the construction of the topology graph is incremental – every time a pixel is added, the topology of the resulti ==A graph representation of the topology of a binary image==
  16 KB (2,639 words) - 15:00, 27 October 2012
• Binary images - implementation
  ...of the objects. Geometrically, these boundaries are circular sequences of directed edges of pixels in the image. In other words, these are 0- and 1-cycles. Th .... In particular, the 0- and 1-Betti numbers are updated at every step. The graph is implemented as a linked list. Each element of the list has pointers to t
  26 KB (4,036 words) - 21:05, 28 December 2009
• A graph representation of the topology of color images by Saveliev
  ''A graph representation of the topology of color images'' by [[Peter Saveliev]] ...nsion of this lower/upper level set approach by introducing the [[topology graph]].
  6 KB (1,011 words) - 15:33, 28 October 2011
• Higher order votes
  but now ''all'' of the edges are also present -- in the complete graph over $A$. The set of possible ratings is still the integers. The ratings ar ...There are $n$ alternatives/candidates and they are the nodes of a directed graph $K$:
  41 KB (6,942 words) - 05:04, 22 June 2016
• Elections
  ...al, a ''valid ballot'' (an element of $Z$) is a complete, acyclic directed graph on the set of $n$ vertices/candidates. Let's drop both of these restriction *a ''ballot'' is a directed graph on the set of $n$ vertices.
  33 KB (5,872 words) - 13:13, 17 August 2015
• Functions in higher dimensions
  ...ough in the early calculus (Chapters 7 -13) we deal with only numbers, the graph of a function of one variable lies in the $xy$-plane, a space of dimension ...ordinates of $P$. If we ignore the third variable ($z=0$), we can plot the graph of the resulting function of two variables:
  113 KB (19,680 words) - 00:08, 23 February 2019
• Pseudocode for binary images
  .... Then this correspondence takes the form of a table, T, so that for every directed edge E, T(E) is the cycle that passes through E. This table is updated at e ...he face of the pixel. Adding an edge means assigning cycles to both of the directed edges: forward E and backward -E. After all the edges have been added, ther
  5 KB (905 words) - 05:31, 6 February 2011
• The algebra of cubical cells
  <!--150-->[[image:Graph example 4 boundaries.png| center]] ...added complexity. We will rebuild the algebra of chains and boundaries for directed edges and, furthermore, “oriented” cells. It appears that all we need t
  46 KB (7,844 words) - 12:50, 30 March 2016
• The algebra of oriented cells
  ...added complexity. We will rebuild the algebra of chains and boundaries for directed edges and, furthermore, “oriented” cells. ...as if cell $x$ is visited twice. These are the interpretations of the new, directed chains:
  36 KB (6,395 words) - 14:09, 1 December 2015
• Vector fields
  [[image:gravity graph.png| center]] This force is directed down, just as the movement of the ball. The work done on the ball by this f
  91 KB (16,253 words) - 04:52, 9 January 2019
• Data made Euclidean
  A graph<!--\index{graphs}--> is pure data. It consists of two sets: <!--s-->[[Image:realizations of a graph.png|center]]
  31 KB (5,219 words) - 15:07, 2 April 2016
• Topology Illustrated -- Index
  *[[directed edge|directed edge]] *[[graph|graph]]
  16 KB (1,773 words) - 00:41, 17 February 2016
• PageRank: testing
  ...of edges of a [[directed graph]] and $N$ the total number of nodes in the graph then the [[PageRank]] of the $i$-th node is: [[image:graph PR.png|right|200px]]
  3 KB (546 words) - 16:08, 23 October 2011
• Graph
  ...ected graph'' is a collection of points, ''nodes'', connected by arrows, ''directed edges''. An ''undirected graph'' can be thought of as a one-dimensional [[simplicial complex]].
  359 bytes (47 words) - 21:38, 19 February 2010
• PageRank as a flow
  ...be the set of edges of the graph and $N$ the total number of nodes in the graph. This is the formula for the PageRank: This formula can be interpreted as a [[PDE]] on a graph:
  4 KB (580 words) - 14:58, 5 January 2013
• Grayscale images - implementation
  ...of the objects. Geometrically, these boundaries are circular sequences of directed edges of pixels in the image. In other words, these are 0- and 1-cycles. Th ...ding Pixels]]. There are no circular sequences of arrows. Each node of the graph contains a pair of links (pointers) to next nodes. If the cycle is merged w
  13 KB (2,095 words) - 16:48, 4 December 2009

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