pppmatching.object
Class of Point Matchings
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
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 
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
Examples
# NOT RUN {
# 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$matrix
# }
# NOT RUN {
plot(m)
# }
# NOT RUN {
# an optimal complete unweighted matching
m2 < pppdist(X,Y)
summary(m2)
m2$matrix
# }
# NOT RUN {
plot(m2)
# }