image.smooth: Kernel smoother for irregular 2-d data

Description

Takes an image matrix and applies a kernel smoother to it. Missing values are handled using the Nadaraya/Watson normalization of the kernel.

Usage

image.smooth
 (Y, wght = NULL, dx = 1, dy = 1, Nwidth = nrow(Y), Mwidth = ncol(Y),
    kernel.function = function(x) {
        exp(-abs(x))
    }, theta = 1, grid = NULL, tol = 1e-08, xwidth = NULL, ywidth = NULL,
    weights = NULL)

Arguments

A matrix image with missing values are indicated by NA.

wght

FFT of smoothing kernel. If this is NULL the default is to compute this object.

Grid spacing in x direction

Nwidth

Half the width of the kernel in the y direction. Default is the maximum needed the number of columns of Y

Mwidth

Half the width of the kernel in the x direction Default is the maximum needed the number of rows of Y

kernel.function

An S function that takes as its argument the squared distance between two points divided by the bandwidth. The default is exp( -x) yielding a normal kernel

theta

The bandwidth

...

Other arguments to be passed to the kernel function

Value

The smoothed matrix.

Details

The function works by taking convolutions using an FFT. The missing pixels are taken into account and the kernel smoothing is correctly normalized following the classical Nadaraya-Watson estimator.

Examples

Run this code

# first convert precip data to the 128X128 discretized image format ( with 
# missing  values to indicate where data is not observed) 
# 
out<- as.image( precip$y, x= precip$x, nrow=128, ncol=128) 
# out$z is the image matrix 

dx<- out$x[2]- out$x[1] 
dy<-  out$y[2] - out$y[1] 
#  
look<- image.smooth( out$z, dx=dx, dy=dy, theta= .25) 

# grid scale in degree and so kernel bandwidth is .25 degrees. 
image.plot( x= out$x, y=out$y, z= look) 
points( precip$x)

# to save on computation, decrease the padding with zeroes 

look<- image.smooth( out$z, dx=dx, dy=dy, theta= .25, Mwidth=32,Nwidth=32) 

# the range of these data is ~ 10 and so  32*( 10/128) =  2.5 
# about 10 standard deviations of the normal kernel so there is still 
# lots of room for padding  
# a minimal choice might be  Mwidth = 4* (.25/dx)  4 SD for the normal  
# 
# creating weighting object outside the call  
# this is useful when one wants to smooth different data sets but on the 
# same grid with the same kernel function 
# 

wght<- image.smooth.setup( nrow=128, ncol=128,  dx=dx, dy=dy, theta= .25,
Mwidth=32, Nwidth=32)

#
# 6 random fields from smoothing white noise with this filter.
#
set.panel( 3,2)
par( pty="s")
look<- image.smooth( out$z, wght) 
for( k in 1:6) {
look<- image.smooth( matrix( rnorm(128**2), 128,128), wght)
image( look)
}