Hi Afra,
To set the amplitude of low-frequency components to 0, you can apply a mask to the Fourier transformed image. Here's how you can modify your code:
f = fft2(im);
fshifted = fftshift(f);
fabs = abs(fshifted);
% define a mask
[x,y] = meshgrid(1:size(im,2),1:size(im,1));
center_x = size(im,2)/2;
center_y = size(im,1)/2;
r = 3;
mask = sqrt((x - center_x).^2 + (y - center_y).^2) > r;
% apply the mask to the Fourier transformed image
fmasked = fshifted .* mask;
Here, we first define a mask using meshgrid, where the values within a certain radius of the center are set to 0, and the values outside are set to 1. We then apply this mask to the Fourier transformed image by element-wise multiplication.
To find the six points with the maximum amplitude in the frequency domain, you can use the maxk function in MATLAB. Here's an example:
% find the six points with the maximum amplitude
[maxvals, maxidx] = maxk(fabs(:), 6);
% convert linear indices to subscripts
[maxy, maxx] = ind2sub(size(im), maxidx);
% extract corresponding parameters for each point
a = maxvals;
f = sqrt((maxx - center_x).^2 + (maxy - center_y).^2);
theta = atan2(maxy - center_y, maxx - center_x);
phi = angle(fshifted(maxidx));
w = @(x,y) a .* sin(2*pi*f.*(x*cos(theta) + y*sin(theta) + phi));
Here, we first use the maxk function to find the indices of the six points with the largest amplitude in fabs. We then convert these linear indices to subscripts using the ind2sub function. Finally, we extract the corresponding amplitude, frequency, phase, and direction parameters for each point and define the corresponding sine wave function w(x, y) using an anonymous function.
Note that in the above code, we assume that the image is square, and the size of the image is even. If your image is rectangular or the size is odd, you may need to adjust the code accordingly.
