Gaussian blur of an array

This function takes a numeric array of any dimension as input and returns a blurred array of the same dimensions as output.

blur(
  x,
  xmin = 0,
  xmax = 2^ceiling(log(max(x + 1), 2)) - 1,
  sigma = max(dim(x))/2^(length(dim(x)) + 1)
)

Arguments

x

a numerical 'array' (including 'matrix')

xmin

the smallest possible value in x; defaults to 0

xmax

the largest possible value in x; defaults to the smallest integer \(2^k - 1 \leq \code{max(x)}\)

sigma

the standard deviation of the gaussian distribution with which to convolve x; defaults to \(\code{max(dim(x))} / 2^{D+1}\), where \(D\) is the dimensionality of x

Value

An array of the same dimensions as x.

Details

This function is adapted from spatstat.explore::blur(), part of the spatstat package collection.

The procedure takes the following steps:

1. Rescale the value range from \([\code{xmin},\code{xmax}]\) to \([0,1]\).

2. Convolve x with \(N(0,\code{sigma}^2)\).

3. Rescale the result back to the original value range.

Examples

square <- matrix(byrow = TRUE, nrow = 6L, c(
  0, 0, 0, 0, 0, 0, 0, 0,
  0, 1, 1, 1, 1, 0, 0, 0,
  0, 1, 0, 0, 1, 1, 1, 0,
  0, 1, 0, 0, 1, 0, 1, 0,
  0, 1, 1, 1, 1, 1, 1, 0,
  0, 0, 0, 0, 0, 0, 0, 0
))
square_blur <- blur(square)
image(t(square))

image(t(square_blur))