blur: Gaussian blur of an array

In tdarec: A 'recipes' Extension for Persistent Homology and Its Vectorizations

Gaussian blur of an array

Description

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

Usage

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

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.

Value

An array of the same dimensions as x.

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))

tdarec documentation built on June 8, 2025, 10:41 a.m.