How can I find the centre of gravity of an image?

I tried regionprops but it is giving out more than one centroid and I need the centre of gravity of the entire image. Thank you.

[Walter Roberson]

Do the different colors correspond to different densities? If so then you need to know how color maps to density in order to find the center of gravity.

Answer 1

[Image Analyst]

You need to have the binary image be the entire image. Just do something like this (untested):

binaryImage = true(size(grayImage));
measurements = regionprops(binaryImage, grayImage, 'WeightedCentroid');
cog = measurements(1).WeightedCentroid;

[Tola]

Thank you. Only one set of coordinates came out. If I want to divide the image into blocks through the center of gravity coordinates gotten, how do I go about it.

[Image Analyst]

Of course, because there was one image. If you want to divide the image into blocks, you can change your binary image to reflect where the block is:

% Initialize to false.
binaryImage = false(size(grayImage));
% Set the upper left 128x128 block true.
binaryImage(1:128, 1:128) = true;
% Remainder of code is the same.

[Lieu-Kim Dang]

Hi Image Analyst,

I have have the same task to find center gravity of an image.

Using your code:

clc 
Path = 'C:\Users\danglie\OneDrive - Hilti\Desktop';
FileName = ['bild.bmp'];
IM = imread(fullfile(Path,FileName));

grayImage = rgb2gray(IM);
binaryImage = true(size(grayImage));
labeledImage = double(binaryImage);
measurements = regionprops(labeledImage, grayImage, 'WeightedCentroid')
centerOfMass = measurements.WeightedCentroid
hold on;
plot(centerOfMass(1), centerOfMass(2), 'r*', 'LineWidth', 2, 'MarkerSize', 16);

I get following error:

??? Error using ==> regionprops>ParseInputs at 867

What is wrong? Could you please help?

Thanks.

[Image Analyst]

@Lieu-Kim Dang it works fine with a standard demo image:

% clc 
% Path = 'C:\Users\danglie\OneDrive - Hilti\Desktop';
% FileName = ['bild.bmp'];
% IM = imread(fullfile(Path,FileName));
IM = imread('peppers.png'); % Read in standard demo image.
imshow(IM);
grayImage = rgb2gray(IM);
binaryImage = true(size(grayImage));
labeledImage = double(binaryImage);
measurements = regionprops(labeledImage, grayImage, 'WeightedCentroid')

measurements = struct with fields:
    WeightedCentroid: [256.8955 201.4011]

centerOfMass = measurements.WeightedCentroid

centerOfMass = 1×2

256.8955 201.4011

hold on;
plot(centerOfMass(1), centerOfMass(2), 'r*', 'LineWidth', 2, 'MarkerSize', 16);

so it must have something to do with your image, which you forgot to attach.

[Lieu-Kim Dang]

Here is the attached image

[Walter Roberson]

@Lieu-Kim Dang

The output looks plausible to me.

Could you remind us which MATLAB version you are using? If I recall correctly, especially old versions of MATLAB did not support WeightedCentroid.

FileName = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/932699/bild.bmp';
IM = imread(FileName);
grayImage = rgb2gray(IM);
binaryImage = true(size(grayImage));
labeledImage = double(binaryImage);
whos

  Name                Size                Bytes  Class      Attributes

  FileName            1x78                  156  char                 
  IM                281x281x3            236883  uint8                
  binaryImage       281x281               78961  logical              
  grayImage         281x281               78961  uint8                
  labeledImage      281x281              631688  double               

measurements = regionprops(labeledImage, grayImage, 'WeightedCentroid')

measurements = struct with fields:
    WeightedCentroid: [140.1917 141.3839]

centerOfMass = measurements.WeightedCentroid

centerOfMass = 1×2

140.1917 141.3839

imshow(IM)
hold on;
plot(centerOfMass(1), centerOfMass(2), 'r*', 'LineWidth', 2, 'MarkerSize', 16);

[Lieu-Kim Dang]

my Matlab version is 7.5.0.342 (R2007b)

[Image Analyst]

You need to upgrade. regionprops() does not accept the gray scale image before R2008b.

Or (less preferably) you will need to compute the weighted centroid through the traditional for loop method.

You can try adapting the attached program.

[Lieu-Kim Dang]

Applying your program moments_spatial_central.m runs without error message.

The results show totally 21blobs. Each blob has following format:

For blob #1, here are the spatial central moments:

mu =

Columns 1 through 4

-9358.66590413221 8362.17574289679 -1957125.27291212 -4443145.48561106

-24412.8211260538 21106267.3532366 -8277723.03853213 2048579989.92776

-184819.491434359 3339718.84020671 -47744743.2258976 408202945.246678

1283801.02068901 972454798.952707 -232100536.57775 80571043871.7573

-1183590.02816366 167804910.70315 -1900013052.35973 18402381239.5187

Column 5

-390319528.954651

-1519823990.34286

-8292589433.66191

-53537445790.6316

-291797732991.784

Which blob is the correct one and which numbers are wanted center gravity?

[Image Analyst]

For the demo, I just took the largest blob only. The rows and columns are the p and q'th moments. You probably want the ones along the diagonal. So the upper left is the first central moment. This is basically

moment1 = sum(x*g(x))

but if you want the LOCATION of it then you'll need to compute

xCOG = sum(x*g(x)) / sum(g(x))

That's just for the x. Do the same for y

Then since it's a central moment (i.e. it's relative to the centorid), you'll need to add back in the x centroid value to get the absolute x value so you can use plot() to put a red crosshairs over the location.

[Lieu-Kim Dang]

These dsteps are too complicated to me. To be honset I don't know how to proceed.

I will try to upgrade my MathLab.

Thank you very much for your great supports and helps.

[Image Analyst]

OK, here's a nested for loop way of doing it that doesn't use regionprops():

grayImage = imread('moon.tif');
[rows, columns, numberOfColorChannels] = size(grayImage);
imshow(grayImage);
axis('on', 'image');
sumgx = 0;
sumgy = 0;
sumg = 0;
for col = 1 : columns
    for row = 1 : rows
        gl = double(grayImage(row, col));
        sumg = sumg + gl;
        sumgx = sumgx + col * gl;
        sumgy = sumgy + row * gl;
    end
end
xCOG = sumgx / sumg

xCOG = 148.8500

yCOG = sumgy / sumg

yCOG = 263.7007

hold on
xline(xCOG, 'LineWidth', 2, 'Color','r');
yline(yCOG, 'LineWidth', 2, 'Color','r');
caption = sprintf('Center of Gravity: (%.2f, %.2f)', xCOG, yCOG);
title(caption, 'FontSize', 18)

[Lieu-Kim Dang]

@ImageAnalyst

This code works perfect for me! Thank you so much for your incessantly efforts!

I appreciate a lot your help.