# [R] correlation between two 2D point patterns?

William Simpson william.a.simpson at gmail.com
Sun Aug 30 08:51:16 CEST 2009

```Suppose I have two sets of (x,y) points like this:

x1<-runif(n=10)
y1<-runif(n=10)
A<-cbind(x1,y1)

x2<-runif(n=10)
y2<-runif(n=10)
B<-cbind(x2,y2)

I would like to measure how similar the two sets of points are.
Something like a correlation coefficient, where 0 means the two
patterns are unrelated, and 1 means they are identical. And in
addition I'd like to be able to assign a p-value to the calculated
statistic.

cor(x1,x2)
cor(y1,y2)
gives two numbers instead of one.

cor(A,B)
gives a correlation matrix

I have looked a little at spatial statistics. I have seen methods
that, for each point, search in some neighbourhood around it and then
compute the correlation as a function of search radius. That is not
what I am looking for. I would like a single number that summarises
the strength of the relationship between the two patterns.

I will do procrustes on the two point sets first, so that if A is just
a rotated, translated, scaled, reflected version of B the two patterns
will superimpose and the statistic I'm looking for will say there is
perfect correspondence.

Thanks very much for any help in finding such a statistic and
calculating it using R.

Bill

```