2D wavelet transform and multifractals

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Whatzat 2015-5-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/215374-2d-wavelet-transform-and-multifractals

回答： Nadya 2017-4-8

Hi everybody,

I'm working on a Matlab project which uses 2D wavelet transform. I am working on a Wavelet Transformation Modulus Maxima method (WTMM). I work with the Matlab wavelet toolbox. I have some questions about wavelets and WTMM method : - I use the 2D discrete wavelet transformation (dwt2 and wavedec2 too) but I don't really understand the role of the dwt2 outputs Approximation/Vertical/Horizontal/Diagonal. I saw they were the result of low pass and high pass filters ( https://www.clear.rice.edu/elec301/Projects02/artSpy/dwt.html ), but which output should I use to find local maximas on the image ?

[A,H,V,D] = dwt2(X,'wname')

I also use multifractal formalism in my project. In order to plot the scale function, I have to plot firstly the partition function (according to this article http://www.scholarpedia.org/article/Wavelet-based_multifractal_analysis , in the "WTMM method" part). However I don't know how to plot correctly this; here my code :

     [A,H,D,V] = dwt2(im,'haar');         
     im_max = imregionalmax(abs(A)); % Modulus Maxima of the wavelet 
                                     Transform, using the Approximation 
                                     wavelet
     figure, imshow(im_max);
     %%Partition Function Z
     Z = 0; % Initialization of the partition function
     for q = -5:5
     Z = Z + abs(im_max).^q ;% Definition of the partition function.
     %Certainly wrong, I think q can't be the variable for the loop and 
     % im_max is not the correct input in abs.
     end
    a = 2; % scale factor. It is supposed to vary, I put it to 2 just for
           %  tests
    tau =  log(Z)/log(a); % scaling function, in function of q according to
                          % the article
    plot(tau,q);

Thanks in advance for your help, I am available for any questions or clarification

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Answer 1

Nadya 2017-4-8

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/215374-2d-wavelet-transform-and-multifractals#answer_262322

Hello, Please, have you solved your problem ? I'm also working on this method, I did not implement it in this way, I used the continuous wavelet transform, but I had difficulties in calculating the multifractal spectrum starting from the partition function. Thanks