BUILT-IN MATHEMATICA 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 .

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 grayscale and multichannel images.
• GradientFilter works with 3D as well as 2D images, and also with 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 "Bessel" convolution kernel Padding "Fixed" padding method WorkingPrecision Automatic the precision to use "NonMaxSuppression" False whether to use non-maximum suppression
• 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.
• In GradientFilter[data, ...], data can be an array of any rank and can contain symbolic as well as numerical entries.
• Possible settings for Method 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

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Gradient filtering of a multichannel image:

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Apply gradient filtering to a vector of numbers:

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