LIE ANALYSIS SYMBOL

MultiScaleCakeWaveletStack

MultiScaleCakeWaveletStack[orientations, size, {, , n}]
Constructs a multi-scale cake wavelet stack having orientations orientations with dimensions size x size, and the scales going from to using n scales.

DetailsDetails

  • MultiScaleCakeWaveletStack extends CakeWaveletStack by dividing the wavelets (in the Fourier domain) in log-radial direction.
  • The radial envelope is defined by: B()=() := Bk() with al=a0 l sρ, where Bk(x) is the kth order B-spline function, ρ is the radial parameter in the polar coordinates, Nρ is the total number of scales to sample ans sρ > 0 is the step size in log-scale.
  • 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
    "SplineOrder"3Specifies the order of the B-Spline that is used to create the wavelets
    "OverlapFactor"1Sets how many B-Splines overlap, thereby not narrowing the angular resolution
  • Symmetry in the orientation axes is used whenever possible to limit the use of resources.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Compute a multi scale cake wavelet stack having 12 orientations and 4 scales between = .1 and 0.9

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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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Scope  (1)Scope  (1)

Generalizations & Extensions  (2)Generalizations & Extensions  (2)

Options  (4)Options  (4)

Applications  (1)Applications  (1)

Properties & Relations  (4)Properties & Relations  (4)

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