GaussianFilter

filters data by convolving with a Gaussian kernel of radius r.

GaussianFilter[data,r,{n₁,n₂,…}]

convolves data with a kernel formed from the n_i derivatives of the discrete Gaussian.

GaussianFilter[data,{r,σ},…]

uses a Gaussian kernel with radius r and standard deviation σ.

GaussianFilter[data,{{r₁,r₂,…},…}]

uses radius r_i at level i in data.

Details and Options

GaussianFilter is a filter commonly used in image processing for smoothing, reducing noise, and computing derivatives of an image. It is a convolution-based filter that uses a Gaussian matrix as its underlying kernel.
The data can be any of the following:

	list	arbitrary-rank numerical array
	tseries	temporal data such as TimeSeries, TemporalData, …
	image	arbitrary Image or Image3D object
	audio	an Audio object

GaussianFilter[data,r] uses standard deviation .
GaussianFilter[data,…] by default gives an array, audio or image of the same dimensions as data.
The following options can be specified:

Method	"Bessel"	how to determine elements of the Gaussian matrix
Padding	"Fixed"	padding method
Standardized	True	whether to rescale and shift the Gaussian matrix to account for truncation
WorkingPrecision	Automatic	the precision to use

Possible settings for the Method option are "Bessel" and "Gaussian".
With a setting Padding->None, GaussianFilter[data,…] normally returns an array, audio or image smaller than data. »

GaussianFilter is a filter commonly used in image processing for smoothing, reducing noise, and computing derivatives of an image. It is a convolution-based filter that uses a Gaussian matrix as its underlying kernel.
Gaussian filtering is linear, meaning it replaces each pixel by a linear combination of its neighbors (in this case with weights specified by a Gaussian matrix). It is also local, meaning it produces output pixel values based only upon the pixel values in its neighborhood as determined by the convolution kernel.
Gaussian filtering is not edge preserving, so other filters such as BilateralFilter and MeanShiftFilter may be more appropriate in applications where edges must be preserved.
Applying GaussianFilter is equivalent to using ImageConvolve with a GaussianMatrix kernel. MeanFilter is a similar smoothing filter.