BUILT-IN MATHEMATICA 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, }, ...]
uses a Gaussian kernel with radius r and standard deviation .

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 grayscale or multichannel images, operating separately on each channel.
• GaussianFilter works with 3D as well as 2D images, and also with data arrays of any rank.
• GaussianFilter[image, r] is equivalent to GaussianFilter[image, {r, r/2}].
• GaussianFilter[image, ...] by default gives a real image 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.
• GaussianFilter can take the following options:
•  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.

## ExamplesExamplesopen allclose all

### Basic Examples (5)Basic Examples (5)

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

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Apply an elliptic Gaussian to blur more in the horizontal direction:

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Vertical Gaussian derivative:

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Horizontal Gaussian derivative:

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Horizontal and vertical derivatives combined:

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Apply a Gaussian filter to a list of values:

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