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 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
    WorkingPrecisionAutomaticthe precision to use
    "UndefinedOrientation"-pi/2value 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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