Trying to figure out the roughness of a circle imfindcircles pol2cart, but not getting the results I expect

Hi everyone

So this is maybe a simple question, but for some reason I'm not getting the answer I expect. I start of with an image that has circles in it. In my case, the circles are not perfect circles, and I want to get an idea of how rough te circles are. To do this, I have a 2 step process. Find the center of the circles by using imfindcircles. After I've figured out my centers, I then use pol2cart to figure out where the drop-off point in my circle for that particular theta is. Now, I say the circles are rough, but they are still supposed to be very circular, so when I run the following code, I expected to see a regular p[attern that only changes very mildy. However, this is not the case.

 d = dir(directory(i) + "\\*.png");
d = arrayfun(@(x) x.folder + "\\" + x.name, d);
I = (imread(d(1)));
[centers,radii,metric] = imfindcircles(I,[400 700],'Sensitivity',0.99);
%%figure out bottom to top 
y = centers (:,2);
[B,k] = sort(y);

centers =  centers(k,:);
radii = radii(k);

subplot(1,3,i)
imshow(I);
viscircles(centers,radii);

I = double(I);

figure
%%for all centers, go through 360 degrees 
for j = 1:size(centers,1)
    xo = centers(j,1);
    yo = centers(j,2);
    xo = round(xo);
    yo = round(yo);
    for theta = 1:360
        rho = 0:round(1.2*radii(j));
        for r = 1:length(rho)
            try
                [x,y] = pol2cart(theta,rho(r));
                x = round(x);
                y = round(y);
                line(r) = I(xo + x, yo + y);
            catch
                line(r) = 0;
            end
        end
        line = medfilt1(line);
        hold on
        plot(line)
    end
end

I've plotted the first few thetas to show what I mean about the results not being what I expected.

Answer 1

[Image Analyst]

What I'd do is to use bwboundaries to get the coordinates of the boundaries and then computer the MAD or RMS of the actual boundary from the fitted circle. Let me know if you can't figure it out and need code.

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[Alexander Dumont]

Hi Image Analyst

I'm looking at the bwboundary fx in the MATLAB documentation. I am not sure how I would go about using this to get the circle imperfections though. How would I "unwrap" whatever bwboundary throws at me? I can use a slightly bigger circular mask to reject all data outside of the circle + 20% more, use bwboundaries with the noholes setting to get the boundary of the circle, but I am not sure what to do after that. If you could provide code, that would be very helpful.

[Image Analyst]

It doesn't matter where the boundary starts. For a single boundary, try something like

boundaries = bwboundaries(mask);
b = boundaries{1}; % Get the first boundary out of the cell into a matrix.
x = b(:, 1);
y = b(:, 2);
meanAbsDev = mean(sqrt((x - xCenter).^2 + (y - yCenter).^2));

[Alexander Dumont]

This helps a lot thank you!