How can I find exactly the coordinates of the center of the yellow circle?

Hi everybody,

maybe my problem is stupid, but I need your help. I need to find exactly the center of the yellow circle in my image. It's an electromagnetic field distribution and I need to know whwre is centered, because it's not in the center of the image. Is there a way to find it out? I'm working with a 601x601x13 double matrix, I plotted the distribution at a certain height along the Z axis. Thanks to anyone who will give me a hand.

[Walter Roberson]

No, you have quantized inputs, you cannot hope to get exactly the center, as the exact center would require continuous coordinates.

Do you have access to the raw data? Is it rgb or is it grayscale that has been colormapped (which is what it appears to be)

[Martina Falchi]

I got the matrix myself, so I have access to all the data. To view the field distribution I use the imagesc function, so I assume it is a grayscale image that is colormapped

[Matt J]

If you have a mathematical model for the field distribution, it would be most accurate to fit the model parameters to your data and determine the center from the continuous model.

[Martina Falchi]

I calculated my field distribution with the Biot-Savart low. I have to work on the image now.

Answer 1

[Walter Roberson]

You can calculate the center of mass of the image.

https://www.mathworks.com/matlabcentral/answers/363181-center-of-mass-and-total-mass-of-a-matrix#answer_287665

[Martina Falchi]

I'll try, thank you.

[Image Analyst]

I'd try Matt's answer below instead.

[Martina Falchi]

Yes, but it's almost the same, because I plot my distribution at a certain height, so it's like I'm working with a 2D matrix. But sure, I can try both.

[Image Analyst]

If you've extracted one particular slice out of your 3-D image, then use the 2-D version, called regionprops():

props = regionprops(true(size(oneSliceImage)), oneSliceImage, 'WeightedCentroid')
xyCentroid = props.WeightedCentroid

[Martina Falchi]

OK thank you very much. Can I ask you how accurate I can be to obtain the coordinates of the center in this way? Because I know that the centroid is not exactly the center, so I was wondering if it was a very rough method or a fairly accurate one.

[Walter Roberson]

Experimenting:

format long g
rvec = linspace(-5,5,100);
cvec = linspace(-5,5,100);
[r, c] = ndgrid(rvec, cvec);
actual_center = randn(1,2)

actual_center = 1×2

1.11743259398499 -2.42572497175217

A = 10 .* exp(-(r-actual_center(1)).^2/2) .* exp(-(c-actual_center(2)).^2/2);
pcolor(r, c, A)

ideal_array_r = interp1(rvec, 1:length(rvec), actual_center(1))

ideal_array_r = 
          61.5625826804514

ideal_array_c = interp1(cvec, 1:length(cvec), actual_center(2))

ideal_array_c = 
          26.4853227796535

tot_mass = sum(A(:));
[ii,jj] = ndgrid(1:size(A,1),1:size(A,2));
R = sum(ii(:).*A(:))/tot_mass;
C = sum(jj(:).*A(:))/tot_mass;
out = [tot_mass,R,C]

out = 1×3

6131.2848647514 61.5608654718254 26.6115951119575

calculated_array_r = R

calculated_array_r = 
          61.5608654718254

calcualted_array_c = C

calcualted_array_c = 
          26.6115951119575

So that is actual 61.5628526804514 versus calculated 61.5608654718254 and actual 26.4853227796535 versus calculated 26.6115951119575

Accuracy in the first case was about 1/100 which is less than 1 / number of bins in that direction.

Accuracy in the second case was about 13/100 which is notably less precise.

This hints that the accuracy can depend upon how close to the edge of the image that you are, in cases where data is being effectively truncated. This makes sense from a mathematical perspective.

[Martina Falchi]

Thank you a lot for this explanation, it was exhaustive.

Answer 2

[Matt J]

regionprops3(  true(size(yourImage))   ,yourImage, 'WeightedCentroid')

[Martina Falchi]

Thank you Matt! I think it's what I needed.

Answer 3

[Rakesh Das]

circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point. this is the concept of obtating the coordinates of yellow circle.