Evaluate the centre of gravity in dependence of horizontal position for each interfernece fringe of image

% Calculating the Centre of Gravity
grayImage = img;
binaryImage = true(size(grayImage));
labeledImage = bwlabel(binaryImage);
measurements = regionprops(labeledImage, grayImage, 'WeightedCentroid')
centerOfMass = measurements.WeightedCentroid
hold on;
plot(centerOfMass(1), centerOfMass(2), 'r*', 'LineWidth', 2, 'MarkerSize', 16);

Using this code I am able to find the Centre points but if I need to crop my image and the dimensions are changed there are bugs which I don't understand or able to correct.

What I am trying to do is to select one line / row from y-axis where I think is the most noticeable change is and finding the centre of gravity for that particular line. My image has a 1000*1000 pixel and along x-axis I want to see all the 1000 pixels.

For the solution, I think I need to crop the image after selecting one line and take the centre of gravity any one can explain how to do that?

% Calculate Sum Or Mean
A = sum(img,2);
B = sum(img,1);
% I get a matrix A =1000*1 and B= 1*1000
%% 
(C,D)= size(img);
figure(5)
[X Y] = size(img);
xcentre = img(:,X./2);
figure(5);
plot(xcentre);

[MUHAMMAD ANUS]

@Image Analyst

[Bjorn Gustavsson]

If you were my colleague and tried to argue that you'd get a "centre of gravity" from regionprops I'd go absolutely ballistic.

INTENSITY MATTERS!

[MUHAMMAD ANUS]

Can you explain how can I do that, so I should take the mean Intensity of whole image?

[Image Analyst]

Attach your image. Explain which part of the image you want cropped out. And regionprops() works on a 1-D vector just like it does with a 2-D matrix. And PNG files are better to attach than FIG files because we can view PNG files right here in the web browser than having to save a fig file to disk and open it in MATLAB.

[Bjorn Gustavsson]

@MUHAMMAD ANUS: The definition of "center of gravity" is:

This can be directly adapted to 2-D images to get a corresponding "center of intensity". Sure isolate individual interference fringes and set the remaining image to zero, after proper background reduction. Then the above equation should be simple enough to implement, most likely component-by-component.

[MUHAMMAD ANUS]

@Image Analyst I have attached screen shot as the format of my file is unsupported.

Initially I want to crop image(200:800,700:900) and than isolate the fringes and evaluate the centre of gravity of a straight line along x-axis. I hope, I am able to explain the problem.

Answer 1

[Image Analyst]

Try extracting the one line of the image you want, then doing a weighted ratio

[rows, columns, numColorChannels] = size(croppedImage)
oneLine = croppedImage(73, :); % Get all pixel values of line 73 in the cropped image.
x = 1 : columns;
numerator = sum(oneLine .* x)
denominator = sum(oneLine)
weightedXCentroid = numerator / denominator

[MUHAMMAD ANUS]

Thank you for the answer. For plotting I can do the same method by plotting the image and use hold to impose the coordinates of the centroid right?

What I don't understand is that if this weighted centroid is intensity dependent or not because for the analysis I need to understand if there is a change in my fringe due to gas flow by naked eye I can see that there is something and now I have to analyze whether it is from gas or some other factors.

[Image Analyst]

Correct. You can do

plot(x, oneLine, 'b-', 'LineWidth', 2);
xline(weightedXCentroid, 'Color', 'r');

or if you have an old version of MATLAB that does not have xline() yet, you can put hold on and do

hold on;
plot([weightedXCentroid, weightedXCentroid], ylim, 'r-', 'LineWidth', 2);
hold off;

The weighted centroid is of course intensity weighted. You can see right there in the numerator and denominator that oneLine (the vector of intensities) in in them. I don't know what your fringes look like changed and unchanged so I don't know if weighted centroid of a particular line is the right thing to do or not -- I just trusted you on that. You can also get the 2-D weighted centroid like you have done but you need a gray scale image, not a pseudocolored image or not a pseudocolored image converted to gray scale with rgb2gray(). That would not make sense.

I'm sure there is probably open source fringe analysis software out there somewhere, like maybe from the College of Optical Sciences at the University of Arizona, or from U.Rochester's Institute of Optics, or maybe MATLAB's File Exchange or the similar plug-in web site for ImageJ.