MATLAB: Wavelet translation and dilation

continuous wavelet transformcwtscaleswavelet

Continous wavelet transform is done by convoluting a signal with various translated and dilated daughter wavelets, right? In order to do so the Matlab Wavelet Toolbox´s User Guide mentions two parameters a and b. When actually usiung the cwt function , you actually only assign valuse for the scale a which is responsible for the wavelet´s dilation.

 What about the translation?

Does a tighter wavelet so to say fit more often onto the signal, hence providing for the different time resoultion compared to broader scaled wavelets?

Best Answer

The translation parameter ranges over the length of the input signal. However, this means that you have to think about edge effects. If you look at the function conofinf.m, you can see how the values of the input series that affect the wavelet coefficients at increasing scales increases.

Look at the section -- Interpreting the CWT Coefficients

http://www.mathworks.com/help/toolbox/wavelet/gs/f3-1000759.html#bsor2go

Related Solutions

MATLAB: What is the difference between wavelets and framelets?

Yes and no.

The discrete wavelet transform is often used as synonymous with the discrete nonredundant (critically-sampled) wavelet transform.

Framelets are redundant wavelet transforms. The Wavelet Toolbox currently features the stationary wavelet transform and the nondecimated wavelet transform which are highly-redundant framelet transforms. There are framelet decompositions with less redundancy than those two.

The CWT as implemented in a computer is also a wavelet frame decomposition.

MATLAB: Dilation of specific objects

First, I would label regions in your image:

   bwl = bwlabel(img,8);

Area of regions:

   a = regionprops(img,'area');
   a = {a.Area}; %turn into cell array

Create a mask for what you want to be dilated:

   xarea = 10;
   idx = find(cellfun(@(x)x<xarea,a));
   bwl2 = sum(reshape(cell2mat(arrayfun(@(x)x==bwl,idx,'un',0)),size(img,1),size(img,2),[]),3);

Dilate the mask:

   bwl2 = bwmorph(bwl2,'dilate',1);

And finally, apply this dilated mask back to the original bw image:

   img = img | bwl2;

Best Answer

Related Solutions

MATLAB: What is the difference between wavelets and framelets?

MATLAB: Dilation of specific objects

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