GaborMatrix

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`GaborMatrix`

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GaborMatrix[r,k]

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

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GaborMatrix[r,k,ϕ]

uses phase shift ϕ.

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GaborMatrix[{r,σ},…]

uses the specified standard deviation σ.

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GaborMatrix[{{r₁,r₂,…}},…]

gives an array corresponding to a Gabor kernel with radius r_i in the i 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 direction is defined by the i column of RotationMatrix[{{1,0,…},k}].
For data arrays with n dimensions and a wave vector {k₁,…,k_n}, k_i is pointing in the same direction as the i dimension of data. For images, the filter is effectively applied to ImageData[image].
The following options can be specified:

	Standardized	True	whether to rescale the matrix to account for truncation
	WorkingPrecision	Automatic	the precision with which to compute matrix elements

Examples

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Basic Examples (3)Summary of the most common use cases

Visualize a Gabor matrix:

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https://wolfram.com/xid/01y98uar4u6-gezb54

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MatrixPlot of a Gabor matrix:

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https://wolfram.com/xid/01y98uar4u6-kilgdo

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1D Gabor vector:

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https://wolfram.com/xid/01y98uar4u6-v4a1ut

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Scope (9)Survey of the scope of standard use cases

Gabor matrix using a 45° wave vector. Notice that the wave vector is perpendicular to the wave front:

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https://wolfram.com/xid/01y98uar4u6-x98y0s

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Specify an isotropic standard deviation :

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-x8r3wq

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Specify an anisotropic standard deviation and :

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-ocb7ia

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Decrease the wave number to get a Gabor matrix with a larger wavelength:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-1jaqkh

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Create a rectangular Gabor matrix:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-7y8t0r

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An anisotropic Gabor matrix with a large wavelength and a node at the center:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-bqqhqm

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Visualize a 1D Gabor vector with different wave number and phase shift:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-b846jd

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Visualize the magnitude spectrum of a 1D Gabor vector for different values of the wavenumber:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-jpzq5

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A 3D Gabor matrix:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-nl9i65

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Options (2)Common values & functionality for each option

Standardized (1)

The default setting is True:

In[7]:=7

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https://wolfram.com/xid/01y98uar4u6-ggy8i

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Use StandardizedFalse:

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https://wolfram.com/xid/01y98uar4u6-f9v0fb

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WorkingPrecision (1)

MachinePrecision is used by default:

In[5]:=5

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https://wolfram.com/xid/01y98uar4u6-b9bieq

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Perform exact computation instead:

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https://wolfram.com/xid/01y98uar4u6-b8ufl0

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Properties & Relations (3)Properties of the function, and connections to other functions

GaborFilter is equivalent to a convolution with a GaborMatrix:

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https://wolfram.com/xid/01y98uar4u6-es6t43

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https://wolfram.com/xid/01y98uar4u6-ri8l57

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In[4]:=4

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https://wolfram.com/xid/01y98uar4u6-bfgtky

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Visualize the 1D Gabor kernel on its equivalent Gabor wavelet function:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-ccnr7p

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With a zero-length wave vector, Gabor matrix is equivalent to GaussianMatrix:

In[1]:=1

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https://wolfram.com/xid/01y98uar4u6-gppcpj

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