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, dx = 1,dy = 1 )
plot.vgram.matrix(x,...)

Arguments

Value

A list with the following components: d, a vector of distances for the differences, and vgram, the variogram values. This is the traditional variogram ignoring direction.

d.full, a vector of distances for all possible shifts up distance R, ind, a two column matrix giving the x and y increment used to compute the shifts, and vgram.full, the variogram at each of these separations. Also computed is vgram.robust, Cressie's version of a robust variogram statistic.

Also returned is the component N the number of differences found for each separation csae.

Details

For the "full" case the statistics can summarize departures from isotropy by separating the variogram differences according to orientation. For small R this runs efficiently because the differences are found by sub-setting the image matrix.

For example, suppose that a row of the ind matrix is (2,3). The variogram value associated with this row is the mean of the differences (1/2)*(X(i,j)- X( i+2,j+3))**2 for all i and j. (Here X(.,.) are the values for the spatial field.) In this example d= sqrt(13) and there will be another entry with the same distance but corresponding to the direction (3,2). plot.vgram.matrix attempts to organize all the different directions into a coherent image plot.

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, R=8)  

plot( out$d, out$vgram) 
# add in different orientations 
points( out$d.full, out$vgram.full, col="red")

#image plot of variogram values for different directions. 
set.panel(1,1)
plot.vgram.matrix( out)
# John Lennon appears remarkably isotropic!