This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# GaussianFilter

 GaussianFilter filters image by convolving with a Gaussian kernel of pixel radius r. GaussianFilterconvolves image with a kernel formed from the derivatives of the discrete Gaussian. GaussianFilter[image, {r, }, ...] uses a Gaussian kernel with radius and standard deviation . GaussianFilteruses radii etc. in vertical and horizontal directions. GaussianFilterapplies Gaussian filtering to an array of data.
• GaussianFilter is a linear smoothing filter commonly used in image processing applications.
• GaussianFilter works with arbitrary grayscale or multichannel images, operating separately on each channel.
• GaussianFilter by default gives a real image of the same dimensions as image.
• GaussianFilter computes the Gaussian derivative of the vertical dimension in image and the horizontal derivative.
 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 .
• In GaussianFilter, data can be an array of any rank, and can contain symbolic as well as numerical entries.
Gaussian filter of a 3-channel image, using a 4-pixel radius:
Apply an elliptic Gaussian to blur more in the horizontal direction:
Vertical Gaussian derivative:
Horizontal Gaussian derivative:
Horizontal and vertical derivatives combined:
Apply a Gaussian filter to a list of values:
Gaussian filter of a 3-channel image, using a 4-pixel radius:
 Out[1]=

Apply an elliptic Gaussian to blur more in the horizontal direction:
 Out[1]=

Vertical Gaussian derivative:
 Out[1]=
Horizontal Gaussian derivative:

Horizontal and vertical derivatives combined:
 Out[1]=

Apply a Gaussian filter to a list of values:
 Out[1]=
 Applications   (1)