getEdges {bayesImageS} R Documentation

## Get Edges of a Graph

### Description

Obtain edges of a 1D, 2D, or 3D graph based on the neighbourhood 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 neighbourhood structure. See getNeighbors for details.

### Details

There could be more than one way to define the same 3D neighbourhood 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 neighbours are listed first, and then those corresponding to the second neighbours, and so on and so forth. The order of neighbours is the same as in getNeighbors.

### References

Winkler, G. (2003) "Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction" (2nd ed.) Springer-Verlag

Feng, D. (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.

#Example 2: get all edges of a 2D graph based on neighbourhood structure
#           corresponding to the first-order Markov random field.

#Example 3: get all edges of a 2D graph based on neighbourhood structure
#           corresponding to the second-order Markov random field.

#Example 4: get all edges of a 3D graph based on 6 neighbours structure
#           where the neighbours 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.
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 <- 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 neighbours structure
#           where the neighbours 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)