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BUILT-IN MATHEMATICA SYMBOL
GradientFilter[image, r]
gives an image corresponding to the magnitude of the gradient of image, computed using discrete derivatives of a Gaussian of pixel radius r.
GradientFilter[image, {r, 
}]
uses a Gaussian with standard deviation .
GradientFilter[image, {{r1, r2}, ...}]
uses a Gaussian with radii 
etc. in the vertical and horizontal directions.
GradientFilter[data, ...]
applies gradient filtering to an array of data.
Details 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.
- GradientFilter[image, r] is equivalent to GradientFilter[image, {r, r/2}].
- 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 Padding->None, 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
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