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BUILT-IN 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 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. - 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" first-order derivatives of exponentials "Sobel" binomial generalizations of the Sobel edge-detection kernels {kernel1,kernel2,...} 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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