# Wolfram Language & System 10.3 (2015)|Legacy Documentation

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

gives an image corresponding to the magnitude of the gradient of image, computed using discrete derivatives of a Gaussian of pixel radius r.

uses a Gaussian with standard deviation σ.

uses a Gaussian with radii etc. in the vertical and horizontal directions.

applies gradient filtering to an array of data.

## Details and OptionsDetails and Options

• GradientFilter works with arbitrary 2D and 3D images, as well as data arrays of any rank.
• For a single-channel image and for data, the gradient magnitude is the Euclidean norm of the gradient at a pixel position, approximated using discrete derivatives of Gaussians in each dimension.
• For multichannel images, define the Jacobian matrix to be , where is the gradient for channel . The gradient magnitude is the square root of the largest eigenvalue of .
• GradientFilter[image,] always returns a single-channel image.
• The following options can be specified:
•  Method Automatic convolution kernel Padding "Fixed" padding method WorkingPrecision Automatic the precision to use
• The following suboptions can be given to Method:
•  "DerivativeKernel" "Bessel" convolution kernel "NonMaxSuppression" False whether to use non-maximum suppression
• Possible settings for include:
•  "Bessel" standardized Bessel derivative kernel, used for Canny edge detection "Gaussian" standardized Gaussian derivative kernel, used for Canny edge detection "ShenCastan" first-order derivatives of exponentials "Sobel" binomial generalizations of the Sobel edge-detection kernels {kernel1,kernel2,…} explicit kernels specified for each dimension
• GradientFilter[image,] by default gives an image of the same dimensions as image.
• With a setting , GradientFilter[image,] normally gives an image smaller than image.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Apply gradient filtering to a vector of numbers:

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Gradient filtering of a 3D image:

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