getEdges {PottsUtils}

Get Edges of a Graph

Description

Obtain edges of a 1D, 2D, or 3D graph based on the neighborhood structure.

Usage

   getEdges(mask, neiStruc)

Arguments

mask

a vector, matrix, or 3D array specifying vertices of a graph. Vertices of value 1 are within the graph and 0 are not.

neiStruc

a scalar, vector of four components, or 3\times4 matrix corresponding to 1D, 2D, or 3D graphs. It specifies the neighborhood structure. See getNeighbors for details.

Details

There could be more than one way to define the same 3D neighborhood structure for a graph (see Example 4 for illustration).

Value

A matrix of two columns with one edge per row. The edges connecting vertices and their corresponding first neighbors are listed first, and then those corresponding to the second neighbors, and so on and so forth. The order of neighbors is the same as in getNeighbors.

References

Gerhard Winkler (1995) Image Analysis, Random Fields and Dynamic Monte Carlo Methods Springer-Verlag

Dai Feng (2008) Bayesian Hidden Markov Normal Mixture Models with Application to MRI Tissue Classification Ph. D. Dissertation, The University of Iowa

Examples

  #Example 1: get all edges of a 1D graph. 
  mask <- c(0,0,rep(1,4),0,1,1,0,0)
  getEdges(mask, neiStruc=2)

  #Example 2: get all edges of a 2D graph based on neighborhood structure
  #           corresponding to the first-order Markov random field.
  mask <- matrix(1 ,nrow=2, ncol=3)
  getEdges(mask, neiStruc=c(2,2,0,0))

  #Example 3: get all edges of a 2D graph based on neighborhood structure
  #           corresponding to the second-order Markov random field.
  mask <- matrix(1 ,nrow=3, ncol=3)
  getEdges(mask, neiStruc=c(2,2,2,2))

  #Example 4: get all edges of a 3D graph based on 6 neighbors structure
  #           where the neighbors of a vertex comprise its available
  #           N,S,E,W, upper and lower adjacencies. To achieve it, there
  #           are several ways, including the two below.
  mask <- array(1, dim=rep(3,3))
  n61 <- matrix(c(2,2,0,0,
                  0,2,0,0,
                  0,0,0,0), nrow=3, byrow=TRUE)
  n62 <- matrix(c(2,0,0,0,
                  0,2,0,0,
                  2,0,0,0), nrow=3, byrow=TRUE)
  e1 <- getEdges(mask, neiStruc=n61)
  e2 <- getEdges(mask, neiStruc=n62)
  e1 <- e1[order(e1[,1], e1[,2]),]
  e2 <- e2[order(e2[,1], e2[,2]),]
  all(e1==e2)

  #Example 5: get all edges of a 3D graph based on 18 neighbors structure
  #           where the neighbors of a vertex comprise its available
  #           adjacencies sharing the same edges or faces.
  #           To achieve it, there are several ways, including the one below.

  n18 <- matrix(c(2,2,2,2,
                  0,2,2,2,
                  0,0,2,2), nrow=3, byrow=TRUE)  
  mask <- array(1, dim=rep(3,3))
  getEdges(mask, neiStruc=n18)