Hurst exponent in matlab

Hello,

i need to calculate the slope of the relationship between the log of the semivariance and the log of the distance determined by regression for a distance (x), varying from 0

to 1.5 cm. Any help?

Thank you

Answer 1

[Meg Noah]

Here's one way, but you'll have to change it to have pixels as length dimensions:

%% *fractalDimension*
%% *definition*
function [fractalDim,Hurst,outImage] = fractalDimension(inImage,epsilon,window)
%% *purpose*
% to compute the fractal dimension of an image
%% *example*
%{
    MaxLevel = 12; % size of image is 2^MaxLevel+1
    seed = 8675309; % seed enables repeatability
    H = 0.5; % Hurst parameters a values between 0 and 1
    myImage = midpoint(MaxLevel,H,seed);
    N = 2.0^MaxLevel;
    figure('Color','white');
    imagesc(-N/2:N/2,-N/2:N/2,h01,[-3 3]);
    title({'Fractional Brownian Motion';['Hurst =' num2str(H) ...
            ' Fractal Dimension =' num2str(3-H)]},'fontsize',14);
    axis equal
    axis tight
    colormap(bone);
    colorbar
    set(gca,'fontweight','bold');

    epsilon = 11;
    window = 21;
    [fractalDim,Hurst,outImage] = fractalDimension(myImage,epsilon,window);
%}
%% *inputs*
% inImage  - input image
% epsilon  - scaling parameter for search (typically between 3 and 11)
% window   - dimension of fractal homogeneity (local fractal dimension)
%% *outputs*
% outImage - local fractal dimension
%% *history*
%  when     who   why
%  20200115 mnoah original code 
%%
% compute window region and log epsilon
halfmask = floor(window/2);
window = 2*halfmask + 1;
nmask = double(window)^2;
mask = ones(window,window)./nmask;
log_epsilon = log(double(epsilon));

%% allocate space for temporary arrays
[nrow,ncol] = size(inImage);
idata2e = zeros(nrow,ncol);
idata2r = zeros(nrow,ncol);
outImage  = zeros(nrow,ncol);

%% create difference arrays
idata2r = ...
    abs(inImage - circshift(inImage, 1,1)) + ...
    abs(inImage - circshift(inImage,-1,1)) + ...
    abs(inImage - circshift(inImage, 1,2)) + ...
    abs(inImage - circshift(inImage,-1,2));
idata2e = ...
    abs(inImage - circshift(inImage, epsilon,1)) + ...
    abs(inImage - circshift(inImage,-epsilon,1)) + ...
    abs(inImage - circshift(inImage, epsilon,2)) + ...
    abs(inImage - circshift(inImage,-epsilon,2));
    
datavalr = conv2(idata2r,mask,'same');
datavale = conv2(idata2e,mask,'same');
idx = (datavalr > 0.0 & datavale > 0.0);
outImage(idx) = log(datavalr(idx)) - log(datavale(idx));
outImage(idx) = 3.0 + outImage(idx)/log_epsilon;

fractalDim = mean(mean(outImage(halfmask:end-halfmask,halfmask:end-halfmask)));
Hurst = 3 - fractalDim;

disp(['Image average fractal dimension = '  num2str(fractalDim)]);
disp(['Image average Hurst Parameter = '  num2str(Hurst)]);

end

The example uses a function I shared on matlab central

https://www.mathworks.com/matlabcentral/fileexchange/71774-midpoint-displacement-images-fractional-brownian-motion