How can I make a filter with the Lorentzian peak to use in imfilter?

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!

Answer 1

[DGM]

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,:))

[Alicia]

Thank you so much!

Answer 2

[Maik]

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);

    0.0159    0.0120    0.0159    0.0120    0.0120    0.0159    0.0159
    0.0120    0.0159    0.0120    0.0159    0.0159    0.0120    0.0120
    0.0159    0.0159    0.0120    0.0120    0.0159    0.0159    0.0120
    0.0120    0.0159    0.0159    0.0120    0.0159    0.0120    0.0159
    0.0120    0.0159    0.0120    0.0159    0.0159    0.0120    0.0159
    0.0159    0.0159    0.0120    0.0159    0.0120    0.0120    0.0120
    0.0120    0.0120    0.0120    0.0159    0.0159    0.0159    0.0120

%% 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);

    0.0249    0.0249    0.0249    0.0252    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0270    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0314    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0349    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0314    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0270    0.0249    0.0249    0.0249
    0.0249    0.0249    0.0249    0.0252    0.0249    0.0249    0.0249

%% Lorentzian Mask Filter 

%% Image Filtering with Lorentz 
im = imread('coins.png');
imLoren = imfilter(double(im),maskLoren);

figure;imshow(uint8(imLoren));

[Alicia]

Thank you so much!