GaussianFilter

filters image by convolving with a Gaussian kernel of pixel radius r.

GaussianFilter[image,r,{n₁,n₂}]

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

GaussianFilter[image,{r,σ},…]

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

GaussianFilter[image,{{r₁,r₂},…}]

uses radii r_i etc. in vertical and horizontal directions.

applies Gaussian filtering to an array of data.

Details and Options

GaussianFilter is a linear smoothing filter commonly used in image processing applications.
GaussianFilter works with arbitrary 2D and 3D images, operating separately on each channel, as well as data arrays of any rank.
GaussianFilter[image,r] uses .
GaussianFilter[image,…] by default gives an image of a real type of the same dimensions as image.
GaussianFilter[image,r,{n₁,n₂}] computes the n₁ Gaussian derivative of the vertical dimension in an image pointing downward and the n₂ horizontal derivative pointing toward the right.
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[image,…] normally gives an image smaller than image. »

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.