gives a matrix that corresponds to the real part of a Gabor kernel of radius r and wave vector k.


uses phase shift ϕ.


uses the specified standard deviation σ.


gives an array corresponding to a Gabor kernel with radius ri in the i^(th) index direction.

Details and Options

  • GaborMatrix[{r,σ},k,ϕ] gives values proportional to at index position from the center.
  • GaborMatrix[r,k] is equivalent to GaborMatrix[{r,r/2},k,0].
  • By default, the matrix is rescaled so that the elements of Abs[GaborMatrix[r,k,0]+I GaborMatrix[r,k,π/2]] sum to 1.
  • For integer r, GaborMatrix[r,] yields a × matrix.
  • For noninteger r, the value of r is effectively rounded to an integer.
  • Either of the r or σ can be lists, specifying different values for different directions.
  • With GaborMatrix[{r,{σ1,σ2,}},k], σ1 is the standard deviation along k, and σ2, are standard deviations perpendicular to k. The i^(th) direction is defined by the i^(th) column of RotationMatrix[{{1,0,},k}].
  • For data arrays with n dimensions and a wave vector {k1,,kn}, ki is pointing in the same direction as the i^(th) dimension of data. For images, the filter is effectively applied to ImageData[image].
  • The following options can be specified:
  • StandardizedTruewhether to rescale the matrix to account for truncation
    WorkingPrecisionAutomaticthe precision with which to compute matrix elements


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Basic Examples  (3)

Visualize a Gabor matrix:

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MatrixPlot of a Gabor matrix:

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1D Gabor vector:

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Scope  (8)

Properties & Relations  (3)

See Also

GaborFilter  GaborWavelet  GaussianMatrix  ShenCastanMatrix  Fourier

Introduced in 2012
| Updated in 2015