Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

GaussianFilter

GaussianFilter[image,r]
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 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 etc. in vertical and horizontal directions.

GaussianFilter[data,]
applies Gaussian filtering to an array of data.

Details and OptionsDetails 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 Gaussian derivative of the vertical dimension in an image pointing downward and the 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 WorkingPrecision Automatic the precision to use "Standardization" True whether to rescale and shift the Gaussian matrix to account for truncation
• Possible settings for the Method option are and .
• With a setting , GaussianFilter[image,] normally gives an image smaller than image.

BackgroundBackground

• 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.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Gaussian filter of a three-channel image, using a four-pixel radius:

 Out[1]=

Gaussian filter of a 3D image:

 Out[1]=