# 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 local orientation parallel to the gradient of image, computed using discrete derivatives of a Gaussian of pixel radius r, returning values between and .

uses a Gaussian with standard deviation σ.

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 single-channel image for 2D images and a two-channel 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.
• 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 "UndefinedOrientationValue" return value when orientation is undefined
• 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
• With a setting , GradientOrientationFilter[image,] normally gives an image smaller than image.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Gradient orientation of a multichannel image:

 Out[1]=

Gradient orientation of a 3D image:

 Out[1]=