# blur

##### 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)`## S3 method for class 'im':
Smooth(X, sigma = NULL, ...,
normalise=FALSE, bleed = TRUE, varcov=NULL)

##### Arguments

- x,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`

.

`Smooth.im`

is a method for the generic `Smooth`

for pixel images. It is currently identical to `blur`

,
apart from the name of the first argument.
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`

.

##### See Also

`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.

##### Examples

```
data(letterR)
Z <- as.im(function(x,y) { 4 * x^2 + 3 * y }, letterR)
par(mfrow=c(1,3))
plot(Z)
plot(letterR, add=TRUE)
plot(blur(Z, 0.3, bleed=TRUE))
plot(letterR, add=TRUE)
plot(blur(Z, 0.3, bleed=FALSE))
plot(letterR, add=TRUE)
par(mfrow=c(1,1))
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*