# blur

0th

Percentile

##### Apply Gaussian Blur to a Pixel Image

Applies a Gaussian blur to a pixel image.

Keywords
spatial, nonparametric
##### Usage
blur(x, sigma = NULL, ..., normalise=FALSE, bleed = TRUE, varcov=NULL)
##### Arguments
x
The pixel image. An object of class "im".
sigma
Standard deviation of isotropic Gaussian smoothing kernel.
...
Ignored.
normalise
Logical flag indicating whether the output values should be divided by the corresponding blurred image of the window itself. See Details.
bleed
Logical flag indicating whether to allow blur to extend outside the original domain of the image. See Details.
varcov
Variance-covariance matrix of anisotropic Gaussian kernel. Incompatible with sigma.
##### Details

This command applies a Gaussian blur to the pixel image x.

The blurring kernel is the isotropic Gaussian kernel with standard deviation sigma, or the anisotropic Gaussian kernel with variance-covariance matrix varcov. The arguments sigma and varcov are incompatible. Also sigma may be a vector of length 2 giving the standard deviations of two independent Gaussian coordinates, thus equivalent to varcov = diag(sigma^2).

If the pixel values of x include some NA values (meaning that the image domain does not completely fill the rectangular frame) then these NA values are first reset to zero.

The algorithm then computes the convolution $x \ast G$ of the (zero-padded) pixel image $x$ with the specified Gaussian kernel $G$. If normalise=FALSE, then this convolution $x\ast G$ is returned. If normalise=TRUE, then the convolution $x \ast G$ is normalised by dividing it by the convolution $w \ast G$ of the image domain w with the same Gaussian kernel. Normalisation ensures that the result can be interpreted as a weighted average of input pixel values, without edge effects due to the shape of the domain.

If bleed=FALSE, then pixel values outside the original image domain are set to NA. Thus the output is a pixel image with the same domain as the input. If bleed=TRUE, then no such alteration is performed, and the result is a pixel image defined everywhere in the rectangular frame containing the input image. Computation is performed using the Fast Fourier Transform.

##### Value

• A pixel image with the same pixel array as the input image x.

interp.im for interpolating a pixel image to a finer resolution, density.ppp for blurring a point pattern, Smooth.ppp for interpolating marks attached to points.

• blur
##### Examples
data(letterR)
Z <- as.im(function(x,y) { 4 * x^2 + 3 * y }, letterR)
par(mfrow=c(1,3))
plot(Z)