SOLUTIONS

BUILTIN MATHEMATICA SYMBOL
GradientOrientationFilter
GradientOrientationFilter[image, r]
gives an image corresponding to the local orientation parallel to the gradient of image, computed using discrete derivatives of a Gaussian of pixel radius r, returning values between and .
GradientOrientationFilter[image, {r, }]
uses a Gaussian with standard deviation .
GradientOrientationFilter[data, ...]
applies orientation filtering to an array of data.
Details and OptionsDetails and Options
 GradientOrientationFilter works with arbitrary grayscale and color images.
 GradientOrientationFilter works with 3D as well as 2D images, and also with data arrays of any rank.
 GradientOrientationFilter[image, ...] by default gives an image of the same dimensions as image.
 GradientOrientationFilter[image, ...] always returns a singlechannel image for 2D images and a twochannel image for 3D images.
 GradientOrientationFilter[data, ...] returns the orientation as hyperspherical polar coordinate angles. For data arrays of dimensions , for , the resulting array will be of dimensions . The tuples in the resulting array denote the spherical angles.
 By default, defined angles are returned in the interval and the value is used for undefined orientation angles.
 For a single channel image and for data, the gradient at a pixel position is 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 orientation is based on the direction of the eigenvector of that has the largest magnitude eigenvalue. This is the direction that maximizes the variation of pixel values.
 For data arrays with dimensions, a coordinate system that corresponds to Part indices is assumed such that a coordinate corresponds to . For images, the filter is effectively applied to ImageData[image].
 In 1D, the orientation for nonzero gradients is always , and undefined otherwise.
 In 2D, the orientation is the angle such that is a unit vector parallel to .
 In 3D, the orientation is represented by the angles such that is a unit vector parallel to the computed gradient.
 For dimensional data with , the orientation is given by angles such that is a unit vector in the direction of the computed gradient.
 GradientOrientationFilter[image, r] is equivalent to GradientOrientationFilter[image, {r, r/2}].
 The following options can be specified:

Method "Bessel" convolution kernel Padding "Fixed" padding method WorkingPrecision Automatic the precision to use "UndefinedOrientation" value representing undefined angles  With a setting Padding>None, GradientOrientationFilter[image, ...] normally gives an image smaller than image.
 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" firstorder derivatives of exponentials "Sobel" binomial generalizations of the Sobel edgedetection kernels {kernel_{1},kernel_{2},...} explicit kernels specified for each dimension  For GradientOrientationFilter[data, ...], data may be symbolic, and the setting for the option may be symbolic.
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