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


convolves image with a kernel formed from the ni^(th) derivatives of the discrete Gaussian.


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


uses radii ri 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^(th) Gaussian derivative of the vertical dimension in an image pointing downward and the n2^(th) 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
    StandardizedTruewhether to rescale and shift the Gaussian matrix to account for truncation
    WorkingPrecisionAutomaticthe 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.  »

Background & Context

  • 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.


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Basic Examples  (3)

Gaussian filter of a list:

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Gaussian filter of a color image:

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Gaussian filter of a 3D image:

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Scope  (4)

Options  (7)

Applications  (1)

Properties & Relations  (2)

Possible Issues  (1)

See Also

Blur  LaplacianFilter  LaplacianGaussianFilter  DerivativeFilter  GradientFilter  GaussianMatrix  ImageConvolve  ListConvolve

Introduced in 2008
| Updated in 2015