cwt2d

Compute several 2D continuous wavelet transforms

Syntax

out = cwt2d(fimg, wavname, scales, angles [,WaveletParameter] [,'Norm',NormValue] [,'Contrast'])

out = cwt2d(fimg, wavname, scales, angles [,'WaveletOptionName', WaveletOptionValue] [,'Norm',NormValue] [,'Contrast'])

Description

This function computes the 2d continuous wavelet transform of an image. Wavelets are taken inside the sub directory 'wave_defs' (see the README to know how to write your own wavelet)

Input Data

fimg

[CPLX MATRIX]: the fourier transform of the image;

wavname

[STRING]: the name of the wavelet to use;

scales, angles

[REALS]: contains the scales and the angles of the transform. The 'angles' parameter is needed but not use in the case of istropic wavelet.

WaveletParameter

[MISC]: a wavelet parameter. His type depend of the wavelet used. See the corresponding wavelet mfile (inside wave_defs) for the correct parameters.

WaveletOptionName, WaveletOptionValue

[STRING, MISC]: Another way of writting wavelet parameters. The wavelet parameter name (a string) is followed by its value. See the corresponding wavelet mfile (inside wave_defs) for the parameter to enter.

NormValue

['l1'|'l2']: is a string which describes the normalization of the wavelet transform, namely the 'L1' or 'L2' normalization. The 'L2' is taken by default.

'Contrast'

[BOOLEAN]: if implemented, normalized the CWT by the convolution of the image with a kernel of the same geometry than the wavelet. The mfile implementing this kernel has a name of the form <wavname>_ctr.m. See [1] for explanations.

Output Data

out

[STRUCT]: the output of the transform. A structured data with the following fields:

• "out.data" (the resulting matrix)
• "out.type" (the type of the transform)

Example(s)

>> [x,y] = meshgrid(-64:64);
>> img   = max( abs(x), abs(y) ) < 30;
>> fimg  = fft2(img);
>> wimg  = cwt2d(fimg, 'morlet', 2, 0);
>> yashow(wimg);

Give the 2D Morlet wavelet transform of a 64 pixel width square for a scale equal to 2 and angle equal to 0. The implicit values are the Morlet wavelet parameters: w0=6; sigma=1. For other values, you can type something like

>> wimg  = cwt2d(fimg, 'morlet', 2, 0, 7, 2);

or,

>> wimg  = cwt2d(fimg, 'morlet', 2, 0, 'w0', 7 , 'sigma', 2);

This change values of w0 and sigma respectively to 7 and 2. Note that the first example is order dependant and not the second.

Finally, you can change the normalization of the cwt with the following command:

>> wimg  = cwt2d(fimg, 'morlet', 2, 0, 'w0', 7 , 'sigma', 2, ...
                 'norm','l1');

for the L1 normalization (and 'l2' for L2).

References

[1]: M. Duval-Destin, M.A. Muschietti and B. Torresani, Continous wavelet decompositions, multiresolution and contrast analysis" SIAM J. Math Anal. 24 (1993).

See Also

cauchy2d cwt2d dergauss2d dog2d esmex2d gauss2d gaussx2d gaussz2d mexican2d morlet2d samcwt2d sarcwt2d sdog2d sqdog2d yashow

Location

continuous/2d/cwt2d.m