How to count pixels/measure area in binary image?

I have an image (attached) where I want to count the number of pixels/measure the area of pixels that are in the space between the circles. I also want to individually count each sapce between the circles as its own element (as opposed to counting all the total spaces as one element). I have looked thorough the documentation on regionprops and am thinking perhaps I could attempt to get this using maybe ConvexHull in regionprops, but I am not really sure. I was thinking also maybe I could use bwconvhull, but when I tried to apply it I just got a blank image. I apologize as I am new to iamge processing in MATLAB, but could anyone provide guidance on how I could best achieve my goal? My current code is attached below, which is really just converting the image to binary and trying to use bwconvhull.

% Clear variables, figures, screen
clear all
close all
clc

% Read in image, display image
image = imread('image.png');
imshow(image)

% Convert image to grayscale
image_gray = rgb2gray(image);
figure
imshow(image_gray)

% Convert image to binary
threshold = 0.65;
image_binary = imbinarize(image_gray,threshold);
figure
imshow(image_binary)

% Calculate specific properties of image
stats = regionprops('table',image_binary,'Centroid','MajorAxisLength','MinorAxisLength','ConvexArea','ConvexHull','ConvexImage');

% Create subplot of original & binary image
figure
subplot(1,2,1);
imshow(image)
subplot(1,2,2);
imshow(image_binary)

% Create convex hull around objects
CH_objects = bwconvhull(image_binary,'objects');
figure
imshow(CH_objects);
title('Objects Convex Hull');

[Matt J]

Please make life easy and attach image_binary in a .mat file.

[Andrew Ferguson]

I have attached a .fig and .m file for "image_binary" above. Will that work? I appreciate the help on the question.

Answer 1

[Kevin Holly]

img = imread("sample.png");
img = im2bw(img);
imshow(img)

se = strel('sphere',15);;
circles=imopen(~img,se);
imshow(circles)

se = strel('sphere',2);
spacebetween = imopen(~img-circles,se);
figure
imshow(spacebetween)

rp = regionprops('table',spacebetween>0,"Centroid", "Area")

rp = 20×2 table
    Area        Centroid    
    ____    ________________

     117    4.4359    66.795
      18    1.9444    412.67
     276    10.964    420.72
    1749    143.78    67.376
    1049    133.53    243.34
    1071    149.16    418.44
      26    286.88    294.77
    1882    323.67    74.011
     445    303.78    238.35
    1535    325.22    416.11
      51    357.47    233.24
    1758    493.47     233.9
    1590    496.42    74.286
    1442    499.51    411.27
      65    593.95    109.18
      26    611.23    98.769

rp.Area

ans = 20×1

117 18 276 1749 1049 1071 26 1882 445 1535

Answer 2

[Matt J]

Let's consider 3 regions B (the background, which you have as a binary image), C (the circles), and D (the connective arms between the circles that you are trying to obtain). You can use bwlalphaclose in this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/90762-further-tools-for-analyzing-objects-in-n-dimensional-images

to seal the gaps between the circles, giving you B|D. The complement of B|D gives you the circles C. Once you have C, you obtain the region of interst D according to ~(B|C).

I could demonstrate this for you if you would attach image_binary as suggested above.