How can I make a filter with the Lorentzian peak to use in imfilter?
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Hi everyone,
I have been trying to blur images using different functions. Matlab seems to have several options to do this with the gaussian function (I've used Imgaussfilt and fspecial('gaussian'). However, I would now like to do the same for the Lorentzian function.
I know I can do this using Imfilter or simply doing a 2D convolution with conv2, but for both cases I need to make a filter/kernel with the values of my function in a matrix. I am a bit lost at this point, since I'm getting started with matlab, and would appreciate any guidance.
Thank you!
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DGM
2022-11-3
I'm not familiar with the distribution or its application here, but here's a start.
% parameters
gam = 7;
fkradius = 20;
% assuming that filter is centered and rotationally symmetric
x = -fkradius:fkradius;
r = sqrt(x.^2 + (x.').^2);
% generate the distribution
fk = 1/(pi*gam) * (gam^2./(r.^2 + gam^2));
% sum-normalize
fk = fk./sum(fk(:));
% just show it (rescaled for viewing)
subplot(1,2,1); imshow(fk,[])
subplot(1,2,2); plot(fk(fkradius+1,:))
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Maik
2022-11-3
编辑:Maik
2022-11-3
You can try generating Lorentzian mask by fitting on random or Gaussian data and converting it to mask.
For more customization on the Lorentz fitting you can refer to this: https://in.mathworks.com/matlabcentral/fileexchange/13648-lorentzian-fit
%% Generate Lorentzian Fit for Random Data
rangeLoren = [0 1];
row = 49; col =1 ;
x = randi(rangeLoren, row, col);
vCoeff= [0 1 4 7];
y=vCoeff(1)+(2*vCoeff(2)/pi).*(vCoeff(3)./(4*(x-vCoeff(4)).^2+vCoeff(3).^2));
maskLoren = reshape(y,[7 7]);
disp(maskLoren);
%% Lorentzian Mask Filter
%% Image Filtering with Lorentz
im = imread('coins.png');
imLoren = imfilter(double(im),maskLoren);
figure;imshow(uint8(imLoren));
%% Generate Lorentzian fit for Gaussian Data
sigmaLoren = 1.2;
x = fspecial('Gaussian',[row col],sigmaLoren);
figure;plot(x);
vCoeff= [0 2*max(x) 1 2]; % Can be varied or computed
y=vCoeff(1)+(2*vCoeff(2)/pi).*(vCoeff(3)./(4*(x-vCoeff(4)).^2+vCoeff(3).^2));
figure; plot(y);
maskLoren = reshape(y,[7 7]);
disp(maskLoren);
%% Lorentzian Mask Filter
%% Image Filtering with Lorentz
im = imread('coins.png');
imLoren = imfilter(double(im),maskLoren);
figure;imshow(uint8(imLoren));
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