Find Periodicity of a plot to do Fourier Transformation

Hello Guys, i have following code, and which produces some plots, i would like to find the periodicity of the plot to do a Fourier. But it does not work, maybe one of you can tell me why?

pic01=imread("1.tiff");
pic050=im2gray( imread("50.tiff") );
newpicture=imsubtract(pic01,pic050);
%imshow(newpicture)
% level = graythresh(newpicture);
level = 0.1405;
newbinpic = imbinarize(newpicture,level);
%imshowpair(newpicture,newbinpic,'montage')
newbinpic2=bwpropfilt(newbinpic,'perimeter',1);
% imshowpair(newbinpic2,newpicture,'montage');
boundaries = bwboundaries(newbinpic2,'noholes');
% Plot raw (x,y) values
x = boundaries{1}(:,2);
y = boundaries{1}(:,1);
figure()
subplot(2,2,1)
plot(x,y, 'r-')
title('raw values')
axis equal tight
hold on
% Assuming (x,y) is a noisy circle, find center 
cnt = [min(x)+range(x)/2, min(y)+range(y)/2];
xline(cnt(1))
yline(cnt(2))
% Shift to (0,0) and compute polar coordinates
[theta, rho] = cart2pol(x-cnt(1), y-cnt(2));
% Plot in polar coord
subplot(2,2,2)
polarplot(theta, rho)
title('Polar coord.')
% Define a reasonable threshold to isolate the spike in RHO values
% 90% of the median looks OK
subplot(2,2,3)
plot(rho)
threshold = median(rho)*.9; 
yline(threshold, '-k', 'Threshold')
ylabel('rho'); xlabel('index')
title('rho values')

% Find start and end of peak
peakIdx = find(rho < threshold); 
peakIdx(2:end-1) = []; 
xline(peakIdx(1))  % plot start of peak
xline(peakIdx(2))  % plot end of peak
% Remove the peak
theta(peakIdx(1):peakIdx(2)) = [];  % you can do the same with x 
rho(peakIdx(1):peakIdx(2)) = [];    % you can do the same with y 
% Plot the circle without the interior object
subplot(2,2,4)
plot(theta,rho)
t=[1:1:1730]';
title('Inner removed')
[pks,locs] = findpeaks(rho(:,1));                                     % Peaks & Locations
mean_period = mean(diff(t(locs)));                                  % Period

text(min(thetalim)+0.1*diff(thetalim), min(thetalim)+0.95*diff(thetalim), sprintf('Mean Period = %.2f time units', mean_period))

I attached the Pictures, but because it does not accept .tiff , i uploaded in png, just change it in the code.

[Star Strider]

The .png files have errors and will not diplay at all here.

[Alex Perrakis]

Maybe now?

[Star Strider]

Those images work!

However, I don’t see any fft or fft2 calls (or anything similar) anywhere. How are the Fourier transforms being calculated?

.

[Alex Perrakis]

well first i wanted to calculate the period, because as i read in the matlab website i.e here , one needs the period to do that and my algorithm for the period does not work yet.

[Alex Perrakis]

Do you have any idea why?

[Star Strider]

Well, no, knowing the period in the data is not necessary to do any sort of Fourier analysis (the Fourier analysis can reveal that), however knowing as much as possible about the data are.

The necessary parameter is the sampling rate and the maximum number of samples (in each specific dimension). The data have to be sampled regularly for best results, or interpolated to a regular sampling interval. The fundamental frequency is then the inverse of the (regular) sampling interval, so if ‘Ts’ is the samping interval, ‘1/Ts’ is the sampling frequency and half that, ‘Fs/2’ is the Nyquist frequency, the highest uniquely-resolvable frequency in the data.

With that information, the subsequent Fourier analysis has meaning.

.

[Alex Perrakis]

And how am i able to compute this frequency? As you can the only data i have is those two images.

[Star Strider]

For spatial data, the sampling interval would be the pixel interval in each dimension. Add spatial calibration (e.g. parsecs/pixel) if available and necessary. The rest follows directly.

.