vgram.matrix: Computes a variogram from an image

Description

Computes a variogram for an image taking into account different directions and returning summary information about the differences in each of these directions.

Usage

vgram.matrix(dat, R=5, nsum=1:8, collapse=TRUE)

Arguments

dat

A matrix spacing of rows and columns are assumed to have the same distance.

Maximum radius for finding variogram differences assuming that the grid points are spaced one unit a part. Default is go out to a radius of 5.

nsum

The components returned from applying the FIELDS/FUNFITS stats function. Default is to return all 8 statistics, n, mean, s.d. quantiles etc.

collapse

If true the default just gives variogram as a function of distance between points.

Value

If collapse=T A list with components: d, a vector of distances for the differences, and vgram, the variogram values. This is the tradiational variogram ignoring direction. If collapse=F A list with components: d, a vector of distances for the differences, ind, a two column matrix giving the x and y increment used to compute the differences, stats, the result of applying the stats function to each set of differences, and vgram, the mean of the differences

Details

When collapse=F this function is designed to look for departures from isotropy but separating the variogram differences according to orientation. For small R this runs efficiently because the differences are found by subsetting the image matrix. For example the mean associated with the row of ind = ( 2,3) will be found from all the differences (X(i,j)- X( i+2,j+3)) Here X(.,.) are the values for the spatial field. In this example d= sqr(13) and there will be another entry with the same distance but corresponding to the direction (3,2).

Examples

Run this code

# variogram for Lennon image.
data(lennon)
out<-vgram.matrix( lennon) 

plot( out$d, out$vgram, xlab="separation distance", ylab="variogram") 
# image plot of vgram values by direction.  

# look at different directions 
out<-vgram.matrix( lennon, collapse=FALSE) #this takes a bit of time 

set.panel(2,1)
plot( out$d, out$vgram) 
plot(out$d, out$vgram.robust) 

# different directions do not appear to have different variances

# matrix plot of orientations.

M<- max( out$ind[,1]) +1 
N<- max( out$ind[,2]) +1
# make up matrix of right size 
temp<- matrix( NA, M,N) 
# fill the matrix 
temp[ out$ind+1]<- out$vgram 
# note values for diagonal elements 
image.plot( (1:M)-1, (1:N)-1, temp, xlab="x difference", 
ylab="y difference") 
set.panel(1,1)