CakeWaveletStack[n, size]
constructs a Cake Wavelet stack having n orientations, dimensions size x size with default parameters.

CakeWaveletStack[n,size, options]
constructs a Cake Wavelet stack having n orientations, dimensions size x size with the specified options.


  • CakeWaveletStack creates a set of (complex) orientation sensitive wavelets that can be used to create an Orientation Score from a 2D image (see OrientationScoreTransform).
  • Cake wavelets are constructed in the Fourier domain as , with ω = (ρ cos φ, ρ sin φ). B_k denotes the kth order B-spline given by B_k(x) = (B_(k-1) * B_0)(x), with .
    M_N(rho) specifies the radial function given by
  • Applying Normal to the output of CakeWaveletStack returns an Association.
  • The output of CakeWaveletStack is an ObjCakeWavelet, which is a child of the ObjOrientationWavelet.
  • The following options can be given:
  • "Directional"FalseWhenever the spatial wavelets are single or double headed
    "Design""N"Specifies the design constraints for the wavelets
    "InflectionPoint"0.8Specifies the inflection point in radial direction of the gaussian window
    "SplineOrder"3Specifies the order of the B-Spline that is used to create the wavelets
    "MnOrder"8Specifies the order of the MnWindow
    "DcStandardDeviation"8The standard deviation of the gaussian that is used to remove the center
    "OverlapFactor"1Sets how many B-Splines overlap, thereby not narrowing the angular resolution
  • Symmetry of the orientation axes is used whenever it is possible to limit the use of memory and decrease the computation time from processing steps.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

By using all default settings a cake wavelet stack can be created by only providing the number of orientations

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The shape of the cake wavelets can be modified using options

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To see the individual wavelets

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