How to control the order of detected objects by regionprops in matlab?

Question

I am working on a MATLAB project where the user will upload a scanned image of ellipse-like objects, and the program have to calculate measurements (height, width, area,..etc) of every object in the image.

I started with thresholding that produces a binary image (a black background and white independent objects). This is the BW image after thresholding:

After that, I used regionprops since it returns most of the measurements that I need, and it worked perfectly.

The problem is that the order in which the function "recognizes/detects" objects is not consistent. I added a code to show the number of each object so I could know which object has regionprops considered as the first and which one is the second..etc.

The code:

% read image
rgb=imread('bw');

s = regionprops(bw,'Area', 'BoundingBox', 'Eccentricity', 'MajorAxisLength', 'MinorAxisLength', 'Orientation', 'Perimeter','Centroid');


% show the number of each object

imshow(bw)
hold on;

for k = 1:numel(s)
    c = s(k).Centroid;
    text(c(1), c(2), sprintf('%d', k), ...
        'HorizontalAlignment', 'center', ...
        'VerticalAlignment', 'middle', 'color', 'r');
end

hold off;

This is the image after showing the order of objects:

I need the order to be from top-left to bottom-right. ( first row of objects is numbered from 1 to 6, second row from 7 to 12..etc). Is that possible?

Many thanks.

Answer 1

Working off of Suever's suggestion to use the Centroid data, and assuming that s contains only the 18 regions of interest in the examples, here's one way to sort s from left-to-right, top-to-bottom using histcounts and sortrows:

coords = vertcat(s.Centroid);  % 2-by-18 matrix of centroid data
[~, ~, coords(:, 2)] = histcounts(coords(:, 2), 3);  % Bin the "y" data
[~, sortIndex] = sortrows(coords, [2 1]);  % Sort by "y" ascending, then "x" ascending
s = s(sortIndex);  % Apply sort index to s

And here's a picture showing the labeling of each area (as you did in your code sample):

The binning of the "y" data first allows us to group objects into 3 rows of 6. The sortrows function, after sorting by this bin value, is then able to do sub-sorting of all the "x" values for each unique binned group.