spatstat (version 1.31-3)

pppmatching.object: Class of Point Matchings

Description

A class "pppmatching" to represent a matching of two planar point patterns. Optionally includes information about the construction of the matching and its associated distance between the point patterns.

Details

This class represents a (possibly weighted and incomplete) matching between two planar point patterns (objects of class "ppp").

A matching can be thought of as a bipartite weighted graph where the vertices are given by the two point patterns and edges of positive weights are drawn each time a point of the first point pattern is "matched" with a point of the second point pattern.

If m is an object of type pppmatching, it contains the following elements ll{ pp1, pp2 the two point patterns to be matched (vertices) matrix a matrix specifying which points are matched and with what weights (edges) type (optional) a character string for the type of the matching (one of "spa", "ace" or "mat") cutoff (optional) cutoff value for interpoint distances q (optional) the order for taking averages of interpoint distances distance (optional) the distance associated with the matching }

The element matrix is a "generalized adjacency matrix". The numbers of rows and columns match the cardinalities of the first and second point patterns, respectively. The [i,j]-th entry is positive if the i-th point of X and the j-th point of Y are matched (zero otherwise) and its value then gives the corresponding weight of the match. For an unweighted matching all the weights are set to $1$.

The optional elements are for saving details about matchings in the context of optimal point matching techniques. type can be one of "spa" (for "subpattern assignment"), "ace" (for "assignment only if cardinalities differ") or "mat" (for "mass transfer"). cutoff is a positive numerical value that specifies the maximal interpoint distance and q is a value in $[1,\infty]$ that gives the order of the average applied to the interpoint distances. See the help files for pppdist and matchingdist for detailed information about these elements. Objects of class "pppmatching" may be created by the function pppmatching, and are most commonly obtained as output of the function pppdist. There are methods plot, print and summary for this class.

See Also

matchingdist pppmatching

Examples

# a random complete unweighted matching
  X <- runifpoint(10)
  Y <- runifpoint(10)
  am <- r2dtable(1, rep(1,10), rep(1,10))[[1]]
        # generates a random permutation matrix
  m <- pppmatching(X, Y, am)
  summary(m)
  m$matrix
  plot(m)

  # an optimal complete unweighted matching
  m2 <- pppdist(X,Y)
  summary(m2)
  m2$matrix
  plot(m2)