How to find Center of Mass for my entire binary image?

Question

I'm interested in finding the coordinates (X,Y) for my whole, entire binary image, and not the CoM for each component seperatly. How can I make it efficiently? I guess using regionprops, but couldn't find the correct way to do so.

Answer 1

You can define all regions as a single region for regionprops

props = regionprops( double( BW ), 'Centroid' ); 

According to the data type of BW regionprops decides whether it should label each connected component as a different region or treat all non-zeros as a single region with several components.

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Alternatively, you can compute the centroid by yourself

[y x] = find( BW );
cent = [mean(x) mean(y)];

Answer 2

Just iterate over all the pixels calculate the average of their X and Y coordinate

void centerOfMass (int[][] image, int imageWidth, int imageHeight)
{
    int SumX = 0;
    int SumY = 0;
    int num  = 0; 
    for (int i=0; i<imageWidth; i++)
    {
        for (int j=0; j<imageHeight; j++)
        {
            if (image[i][j] == WHITE)
            {
               SumX = SumX + i;
               SumY = SumY + j; 
               num = num+1;
            }
        }
    }

    SumX = SumX / num;
    SumY = SumY / num;
    // The coordinate (SumX,SumY) is the center of the image mass
}

Extending this method to gray scale images in range of [0..255]: Instead of

if (image[i][j] == WHITE)
                {
                   SumX = SumX + i;
                   SumY = SumY + j; 
                   num = num+1;
                }

Use the following calculation

SumX = SumX + i*image[i][j];
SumY = SumY + j*image[i][j]; 
num = num+image[i][j];

In this case a pixel of value 100 has 100 times higher weight than dark pixel with value 1, so dark pixels contribute a rather small fraction to the center of mass calculation. Please note that in this case, if your image is large you might hit a 32 bits integer overflow so in that case use long int sumX, sumY variables instead of int.