How to find the radii of circles, centers of circles,euclidean distance between each circle and angle among (small circle-->large circle -->small circle)?

I have 3 circled masks and i want to find the radii , centers of the circles,euclidean distance between each circle and angle between small circle-->large circle -->small circle?

(PS:i have attached the original image)

Here is the code so far (Thanks to Mathworks and Image Analyst, where i followed their guidelines to get upto this point).

% Read the original image (1st convert  from RGB to grey )

clear all;clc;

originalimage=rgb2gray(imread('new_whole_mask_P3290258.jpg'));

subplot(2,4,1);imshow(originalimage);

set(gcf,'units','normalized','outerposition',[0 0 1 1]);

drawnow;

caption=sprintf('original image showing\n1 large circle and 2 small circles.');

title(caption);

axis image;

% Obtain and display the histogram

[pixelCount,greyLevels]=imhist(originalimage);

subplot(2,4,2);

bar(pixelCount);

title('Histogram of original image');

xlim([0 greyLevels(end)]);

grid on;

% In order to get the binary, set the threshold value as 25
thresholdValue=25;

binaryImage=originalimage>thresholdValue;

% Show the threshold as a vertical red bar on the histogram

hold on;

maxYValue = ylim;

line([thresholdValue, thresholdValue], maxYValue, 'Color', 'r');

% Display the binary image
subplot(2, 4, 3);

imshow(binaryImage); 

title('Binary Image, obtained by thresholding'); 

% Label each circle to make it feasibe for calculations

labeledImage = bwlabel(binaryImage, 8);     % Label each circle 

subplot(2,4,4);

imshow(labeledImage,[]);

title('Labeled Image,from bwlabel()');

% calculate the standard deviation of each region
s = regionprops(binaryImage,originalimage, {'Centroid','PixelValues','BoundingBox'});
subplot(2,4,5); imshow(originalimage);

title('Standard Deviation of Regions');

hold on

% compare the weighted with unweighted centroid locations superimpose the centroids 
numObj = numel(s);

for k = 1 : numObj

      s(k).StandardDeviation = std(double(s(k).PixelValues));

      text(s(k).Centroid(1),s(k).Centroid(2), ...

          sprintf('%2.1f', s(k).StandardDeviation), ...

          'EdgeColor','b','Color','r');

end

hold off

% Assign pseudo random colors to each circle

coloredLabels = label2rgb (labeledImage, 'hsv', 'k', 'shuffle'); 

% pseudo random color labels

subplot(2, 4, 6);

imshow(coloredLabels);

axis image; % Make sure image is not artificially stretched 

caption = sprintf('Pseudo colored labels, from label2rgb().\nCircles are numbered from top to bottom,\n then from left to right.');

title(caption);

% Get all the circle properties

circleMeasurements = regionprops(labeledImage, originalimage, 'all');

numberOfCircles = size(circleMeasurements, 1);

% Plot the borders of all the circles on the original grayscale image 

subplot(2, 4, 7);

imshow(originalimage);

title('Outlines, from bwboundaries()'); 

axis image; % Make sure image is not artificially stretched

hold on;

% bwboundaries() returns a cell array, where each cell contains the row/column coor

boundaries = bwboundaries(binaryImage);

numberOfBoundaries = size(boundaries, 1);

for k = 1 : numberOfBoundaries

  thisBoundary = boundaries{k};

  plot(thisBoundary(:,2), thisBoundary(:,1), 'g', 'LineWidth', 2);

end

hold off;

%Calculate properties of regions in the image and return the data in a table.
cal= regionprops('table',binaryImage,'Centroid','Area','FilledArea','Perimeter')

Below is the answer which i got:

cal = 
    Area                  Centroid                  FilledArea    Perimeter

      2866    679.763782274948    956.926378227495    2866          187.709  

      5122     837.71710269426     1122.0909800859    5122          258.353  

         1                 814                1157       1                0  

         1                 863                1157       1                0  

      2735    1060.16599634369    964.146983546618    2739           190.81

But this is not what i expect (as i have only 3 circles).

Kindly help me to figure this out.

Answer 1

[Walter Roberson]

I do not have the toolbox to test with, so I cannot tell exactly what is happening. I would point out, though, that you are using a JPG file, so you are creating compression artifacts. Depending on the exact level you threshold at, you can end up with isolated around the circles, where due to the compression artifacts a value might happen to be just above the threshold while adjacent values are below the threshold.

With that particular image with a clean black background, you can use

binaryImage = any(originalimage,3);

which is to say that you can threshold against 0.

If you must use JPEG images then your algorithm needs to take into account that the values stored in the array might not be what you think you are seeing.

[Chathu]

Hi walter, Thanks alot for your quick response.

Thanks a bunch for your hint.

After following your hint,i used the following code (thanks to Image Analyst)

% Get rid of border.

binaryImage = imclearborder(binaryImage);

% Get rid of small blobs
binaryImage = bwareaopen(binaryImage, 400);
subplot(2, 4, 4);
imshow(binaryImage);
title('Obtained clean black background')

And i obtained the following:

   Area                  Centroid                  FilledArea    Perimeter
      2866    679.763782274948    956.926378227495    2866          187.709  
      5122     837.71710269426     1122.0909800859    5122          258.353  
      2735    1060.16599634369    964.146983546618    2739           190.81

So now i am getting 3 values(as expected,which is great !).

But (as i mentioned earlier), can you kindly advise me how to calculate the euclidean distance between center of each circle and angle between small circle-->large circle -->small circle? If you can atleast give me a hint, that would be highly appreciated. (i am attaching my result so far)

[Chathu]

Thanks again Walter. Is there anyone who can just can give me a hint to find the following: Distance between centers of each circle (image is attached)

[Walter Roberson]

stats = regionprops(YouImage, 'Centroid');
cents = [stats.Centroid];
centdists = pdist(cents);              %packed triangular matrix
sq_centdists = squareform(centdists);  %if you want a square symmetric matrix

[Chathu]

Thank you so much Wallter. (i wish i can accept your answer twice as it is very helpful). Thank you again.

[Walter Roberson]

You can vote for it ;-)

[Chathu]

:-)

Sorry, i came up with couple of qu:

i just now realized i am getting four answers for distances between centers of each circle as there are only three circles,pls see the below output:

cents centdists sq_centdists

   679.8    956.9    837.7
  1122.1    814.0   1157.0
   863.0   1157.0   1060.2
   964.1

(i)why so?

(ii) why am i getting 2 sets of answers for centroids (see my original qu above, you will see the output)?

(iii) How to find the angle among, small circle-->large circle -->small circle(see my original qu above, kindly see the attachment). In my case, finding the angle is crucial hence can you kindly give me a hint for that? (sorry i am reiterating the last question, as i dont know how to overcome that issue.)

Anyhow, thank you sooo much (Walter) for your kind support so far even.

[Walter Roberson]

You should look at either centdists or sq_centdists but not both.

The output of squareform would be expected in this situation to be a 3 x 3 matrix with 0 along the diagonal.

Unfortunately I do not have the toolboxes to test with so I cannot run the code.

[Chathu]

Thank you so much for the hint,Walter. Really appreciate it. (glad that i had the opportunity to vote, as your responses are quite helpful :) Thanks again.